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Heat transfer to objects immersed in fluidized beds
Powder Technology. 0 Elsevier Sequoia
8 (1973)
S-A.,
273-282
Lausanne -
Printed in The Netherlands
Heat transfer to objects immersed in fluidized beds A.P. BASKAKOV, B.V. BERG, O.K. VITT, N.F. FILIPPOVSKY, V.A. KIRAKOSYAN, J.M. GOLDOBIN and V.K. MASKAEV Kirov
Jrals Polytechnical
(Received
June 8,1973;
Institute,
accepted
Sverdlovsk
(U.S.S.R.)
June 27,1973)
Summary The modified packet model for heat transfer between a gas-fluidized bed and an imm.ersed surface is presented_ In contrast to the model of Mickley and Fairbanhs, allowance was made for the effective gap heat resistance between the packet of particles and surface (the contact therma resistance Rlz) and for the heat transferred directly by convection through the gas filtering through the particles and between the particles and the immersed object. The convective contribution towards the maximum heat transfer coefficient is found to increase with increasing particle size. This model readily explains the effect of particle moisture content, shape of the immersed body and other factors on bed to immersed body heat transfer_ Radiant heat transfer effects are discussed_
INTRODUCTION
Mickley and Fairbanks’ consider the process of heat transfer between a gas-fluidized bed and an immersed surface by which unsteady-state heat transfer occurs to packets of particles as they are brought into contact with the heat transfer surface. The residence time of packets at the surface is terminated when they are replaced by other packets of particles under the action of bubble-generated circulation patterns within the bed. They showed that the heat transfer coefficient is given by
(1) if the bed may be considered
to be a medium
of uniform thermal properties with an effective conductivity h and heat capacity pPc, (l-c), where E is the bed voidage. This suggests that the instantaneous rate of heat transfer will be very large when a packet first comes into contact with the surface_ However, many experiments show that the heat transfer coefficient is apparently limited by some
thermal
resistance
between
the
packet
and the surface2-” _ Gabor’ showed that the best correspondence between experimental results and more detailed models describing the transfer of heat between a surface and a chain of particles is obtained when allowance is included for a small gap between the surface and adjacent particles and between the particles. He suggested that the gaps may only be a mathematical expedient in the calculation and lack physical reality, and cited an experiment which would seem to show that no such gap really existed. However, the weight of evidence would confirm that there is the thermal resistance of an effective gap between the surface and bedz--5.10.11 or
particles
Although for relatively long contact times, 7, it is permissible to consider the packet of particles and gas as a medium of uniform thermal properties, this is obviously not so for short contact times. For short and intermediate contact times a good approximation to the behaviour is obtained by the assumption that there is an additional contact; thermal resistance, Rk , between the packet of uniform thermal properties and the transfer surface. The legitimacy of this is shown by the good correspondence obtained between the estimated instantaneous coefficients given by (2)
371
du
I
;!I
i IIt
I
I
/III
I
iii
Fig. 1. Comparison of the instantaneous heat transfer coefficient value from an isothermal wail to the particle semi-limited layer, estimated by formula (2) with experimental data8 _ Dimensionless heat transfer coefficient Nu = h,d/h is plotted on ordinate, dimensionless time
F,
=
A4 (1 -
on
the
=
and direct measurements, when an instantaneous heat flux and the contact time of heat transfer surface with the packet bed were strictly controlled (Fig. 1). The resistance R, arises primarily from the increase in bed voidsge in the region directly adjacent to an immersed surface. Gelperin and Ainstein” list. theoretical expressions for the instantaneous and mean transfer coefficients derived for models involving a resistance adjacent to an immersed surface and for different boundary conditions. The situation obtaining in a fluidized bed corresponds most closely to the case of a constant heat transfer surface temperature and for constant bulk bed temperature_ The complicated expressions for the mean coefficients reduce to simple approximations. Thus, for the case where the transfer surface temperature remains constant during the period of contact with the packet3 S5vg3
h, -
1
Rk + 0.5RX
(3)
If the transfer surface is shrouded by gas bubbles for a fraction of the total time fa , the mean coefficient will be correspondingly reduced: h cond
=
(1 --fo)h,
d
&=2X
(5)
abscissa with
C,p, e)dld/2h. Particle diameter, d, for glass bead-air system (X = 0.14 W/m°C): l0.39, 20.93, 32.05, 4- 3.05, 5- 5.05 mm; for glass bead--CO* system (A = 0.1 W/m°C): 6- 0.39, i- 0.9, S- 5.05 mm. Dotted curve by formula (1). Rk
The value of Rx can be estimated from eqn. (l), where the thermal conductivity, h, corresponds to a first approximation to that of the bed at incipient ffuidization or to that of a packed bed and for which the volumetric heat capacity is given by pP c, (1 - E). The effective contact resistance between the packet and the surface (Rk) is inversely proportional to the maximum instantaneous heat transfer coefficient, which is obtained at the first instant of contact. For stationary particles on a cubical lattice, the thermal resistance between the first row and the surface will be half that between adjacent layers of particles in the lattice if there is no supplementary gap between them; thus
Corrections effect surface
of
must any
aud
be
particle
any
included
to allow
movement
gap between
close
particles
for
the
to
the
aud
the
It will be different if the particle packing corresponds more closely to a hexagonal rather than a cubical pattern_ Values of Rk, f0 and shave been estimated experimentally by following the temperature fluctuations of low heat capacity probes mounted in experimental surfaces. Using a probe’s response, it was possible to determine the maximum value of the instantaneous heat transfer coefficient, h,, (the inverse of the contact heat resistance, Rk ) directly between the packet of particles in the gas-fluidized bed and the immersed object in which the probe was mounted. Experiments have been extended to include conditions under which convective heat transfer through the gas and radiative transfer are important, and these are outlined below. Additionally, behaviour when the fluidized bed is moistened by water sprays is discussed. surface.
HEAT TRANSFER CAL OBJECT
TO AN IMMERSED
CYLINDRI-
The probe used in typical experiments consisted of a 5 I.rm thick, 5 X 10 mm strip of platinum glued to the side of 15 and 30 mm diameter vertical rubber cylindrical test objects, or to the side of a 30 mm diameter, vertical, water-cooled, stainless steel tube. The element response was affected by heat trans-
275
fer into the substrate and this effect was determined beforehand by following the response of the element when it was subjected to intermittent blasts of air. By this means, the response of the element was determined over a range of frequencies_ Tests were carried out by immersing the cylinders in beds of corundum (0.12, 0.32 and 0.50 mm mean particle diameter) and in a bed of 0.65 mm diameter slag beads fluidized over a porous tile distributor 10 mm thick. The beds used were of 98 and 92 mm diameter and the fluidizing gases were carbon dioxide, helium (both at temperature 20°C) and air at temperatures from 20°C up to 550°C. Prom the response oscillograms of the foil temperature fluctuations, the mean probe and bubble contact time, rO,, and the probe and packet contact time, 7, bubble frequency and packet interchange frequency LJ+, and pt respectively and the fraction of the time that bubbles shrouded the transfer surface, fo, were all determined directly. Figure 2 shows that the dependence of r and f. on the main fluidizing parameters were given quite well by the empirical correlations
Fig. 2. Probe mean contact time with particle packet 7 (a) and tie fraction of probe contact with gas phase f,-, (b) us. fluidizing velocity. 1,2CO2 and He at 20°C; 3- 7-sir at f = 20, 250. 350, 450, 550°C, respectively. Diameter of vertical cylindrical probe 30 mm.
set
f. = 0.33
w;~(W--A)~ dg
(6)
O-l4
(‘7)
I
The fact that r f - and f. f 0 at the point of minimum fluidization can be readily explained by the effect of the immersed object on the behaviour of the bed. Thus, even when w =GW there was still a tendency for a void to formmf beneath the cylindrical obstruction. Bubbles periodically formed from this and rose along the probe surface causing some particle movement even before the bed generally became fluidized. The empirical factor -cl made allowance for the effects of probe diameter and particle shape. It tended to diminish as the probe diameter increased and as the particles more closely approximate to the spherical shape. Thus for tests with corundum, for example, A equalled 0.8 when the vertical tube diameter was 30 mm in diameter and 0.9 when it was rllduced to 15 mm_ For the slag particles the degree of variation was from 0.7 to 0.75 when the tube diameter was halved from 30 mm to 15 mm. Particle density and gas dynamic viscosity had little apparent effect, esept for their effect on wmf_ The variation in r. with gas ?low rate was independent of particle diameter and shape. The frequency of packet and bubble exchange rates increased with increase in the fiuidizing gas flow rate up to gas flow rates of 2-3 wmf_ Above this, the frequencies were almost independent of the ratio IV. Figure 3 shows that
I
42
44
46
C
Fig. 3. Rk us. particle diameter. lCO2 ; 2- He ar. 20°C; 3, 4, 5, 6, 7- air at temperatures 20, 250, 350, 450, 550°C, respectively.
2’i6 TABLE Air
1 Corundum 0.12mm
0.04
480
Corur.dum 0.32mm
CO,
He
0.045 550
497
0.135 460
0.18 421
0.15 397
0.3 335
0.45 277
0.6 247
0.99
h
m,
W/m20C
530 370
Corundum 0.5 mm
0.25 246
0.3 332
0.45 285
0.6 255
0.75 235
Slag 0.65 mm
0.25 215
0.28 286
0.42 223
0.56 215
0.72 208
270
0.15 326
0.2 302
370
0.5 211
0.61 200
260
0.61 212
0.85 215
220
0.56 20-I
0.7 202
190
Corundum 0.12 mm
0.046 353
0.05 425
z-x c 0.1 s1 T 368 -4
Corundum 0.32 mm
0.14 256
0.16 314
Corundum 0.5 mm
0.2s 199
0.34 266
Slag 0.65 mm
0.25 185
0.28 217
Corundum 0.12 mm
0.035 1080
0.04 1400
Corundum 0.32mm
0.1 s90
0.11 1000
0.22 781
Corundum 0.5 mm
0.27 725
0.32 835 0.3 655
Slag 0.65 mm
W
h
0.27 620
the contact resistance, Rk, reduced almost linearly with reduction in particle diameter; the contact thermal resistance was determined using the foil probe rnd was the inverse of the maximum value of the instantaneous heat transfer coefficient. In this case the part of the heat removed from the surface by convection was taken into account. The fact that it did not tend to zero in the limit of very small particles is further evidence for the existence of a gap between the bed and surface. Rk was approximately dependent on the thermal conductivity of the fluidizing gas to the 0.63 power. That this dependence is not a simple proportionality is evidence for the part played by the particle thermal conductivity on the effective thermal conductivity of the gap. There was negligible apparent dependence of the gap resistance on the fluidizing velocity. The effective resistance was independent of the height at which the probe was located within the bed. Heat transfer coefficients estimated from the estimated contact times and exchange frequencies are summarized in Table 1. The convective heat transfer component
.z 0.32 .-1 253 9 = 0.5 ; 230 b ._ .+ 0.42 2 212 .0.07
310
0.145 1033
1500
0.34 '719
0.42 665
1070
0.35 807
0.42 710
0.48 695
900
0.45 538
0.6 545
0.75 515
775
1273
0.11 1132
was taken into account in calculating the value of h. There is good agreement between these coefficients and values of the maximum time-averaged heat transfer coefficient, h, , given by the empirical correlation of ZabrodsBy7. THE INTERPARTICLE GAS TRANSFER COMPONENT
CONVECTIVE
HEAT
The heat transferred directly by the gas filtering through and bet.ween the particles and the immersed object will increase with increase in the w,*, and the w,~ will increase as the mean particle size in the bed increases. The convective and conductive components can be envisaged to a first approximation as being separate and additive if heat transfer to the bubble phase is included in the convective component too. Similarly, the radiative component, which is increasingly important at higher operating temperatures, may also be regarded as being an additive component so that the overall heat transfer coefficient may be envisaged as:
h = hcond + km,
+ had
(8)
A number of workers’ ‘- ’ 4 have estimated the convective component, hconv_ The following heat transfer correlation has been derived using a mass transfer analogy for gas velocities in excess of w, from measurements of the rate of vaporization of naphthalene from cylindrical objects’ ’ *16 _
N&xl" = 0.0175Ar0-46 Pro-33
(9)
For fluidizing gas flow rates less than w, , the correlation should include the additional group (w/w, )Oq3 _ The relationship given by eqn. (9) suggests that the gas convective component of heat transfer, h,,,, , is proportional to do.38 whereas the conductive component reduces with increasing particle diameter because of increases in R, and 7. Thus the convective contribution toward the maximum heat transfer coefficient, 12, , is found to increase with increasing particle size, being approximately 10, 15, 30, 60 and 90% respectively for corundum and chamotte particles having average diameters of 0.16, 0.32, 0.5, 2.5 and 4 mm respectively1 5. With a bed of 5-mm and more -coarse particles, the bed to surface coefficient is nearly entirely made up from the convective component which is, in turn, equal to the wall transfer coefficient with a packed bed system’ ‘-” _ This does not mean that the overall heat transfer coefficients in fluidized and packed beds +f coarse particles are equal;
Fig. 4. Dependence of maximum heat transfer coefficient upon particle size. lbed of corundum particles; thermozond 6 mm in diam. 3: 2- data obtained in the same bed with a vertical 220 X 160 mm calorimeter3 l; 3data obtained with 40 mm diam. and 100 mm high cylinder vertical thermozond, the same bed.
in the latter, heat transfer into the bulk of the bed is limited by the-relatively low heat conductivity of the static particle phase close to the surface, but this is not the case in the fluidized bed, because the particles are then free to circulate close to the surface. The form of dependence is illustrated in Fig. 4 for heat transfer between an immersed cylindrical object in beds of particles up to 13 mm diameter. Figure 5 gives dimensionless experimental values for 12, and hconv (esperimental results for the convective component being determined from the mass transfer analogy) and comparison is made with values of using eqn. (9) with the &cl n\* estimated Frandtl number raised to the 0.33 power and also to the power 1 as derived for the correlation in an earlier study3 _ The best fit to the values of h,,,,. is given by Nu,,,,
= 0.009
AT-‘-” Pro-33
(10)
However, deviations between all the formulae are no more than 20%, and these for h,,,, may well be a consequence of details of the
1
Fig. 5. Dependence of Nusselt number for maximum heat transfer (Nrc, = 11~dlhf) and convective transfer Nusselt number (Nuc,nv = h,,,,d/Xf) on Archimedes number Ar=gd3 (pP/pf-1)~;'. l-4. Values for Nu,,,,. from ref. 12. 5. Values for Nu,,,, from ref. 15. 6,‘i. Values for Nu, from ref. 21. 8. Values for Nu, measured using a 160 X 220 vertical flat plate calorimeter in a bed of corundum particles. 9-11. Values for Nu, measured using a 40 mm diam. by 100 mm high cylindrical calorimeter in beds of lead, steel and alundum spheres. I and II. Predictions given by eon. 9 with the Prandtl number raised to the powers 1 and 0.33-respectively. III. Predictions given by Nurn = 0.86 _-%S-o*2 (ref. 21). IV. Predictions given by Nn, = 0.21 Arb'-32. V. Predictions given by eqn. 10 shown by dashed line.
apparatus_ It can also be seen from Fig. 5 that the overall heat transfer coefficient is accounted for by the convective transfer component at high values of the Archimedes number (Ar > lo7 ), Le. in beds of coarse particles. Figure 4 illustrates the changing roles of L,,~ and hcond - The decrease of h, in beds of fine particles (< 10 pm) is on account of their poor fluidization characteristics; agglomeration and channelling occurring in the beds.
THE EFFECT
OF SI-IAPE OF THE IMMERSED
BODY
Because of its influence on the local circulation of particles close to it, the shape of the immersed body affects the surface to bed heat transfer behaviour. In this, the behaviour with vert.ical and inclined plates is quite typical. High speed photography shows that unstable, periodically vanishing, gas voids form under an inclined plate and their contact time increases with the angle of deflection of the plate. Thus, when the plate is horizontal, the lower side is in contact with gas voids for up 4m
Fig. 6. Heat transfer coefficient from a flat, calorimeter vs. its orientation in a fluidized bed of corundum particles having a mean diameter of 320 pm. l- w = 0.7 mlsec; 2-7w = 0.5 m/set. No.
CUNC
1,23
4
5
6
7
Bed height, mm
1600
1600
1000
450
300
1500
Calorimeter location height, mm
1300
750
750
220
150
750
Apparatus cross-section, mm
1200 600
1200 600
1200 600
1200 600
420 170
1200 600
Calorimeter size, mm
220X 160
82Cx480
70% of the time. This considerably reduces the average rate of heat transfer from the underside of the plate (Fig. 6). At low fluidizing velocities and at small angles of deflection there can be an advantage because the rising bubbles then keep replacing the particles close to the plate with fresh material_ Transfer coefficients from the top surface of an inclined plate are also reduced from those obtained with a vertical plate because a defluidized layer is formed on it which slowly slips down the plate. However, in some cases with smaller plates mounted in vigorously bubbling beds, it is possible to achieve higher rates of heat transfer from the top surface (Fig. 6) because the material defluidizing on top of the plate is constantly being thrown off and disturbed by the rising bubbles. The unstable gas void forming underneath a thick vertical plate acts as a source of bubbles. These will rise along the surface and in a bed operating at low gas flow rate greatly intensify the rate of particle replacement from the lower section of the vertical plate, thus increasing the attainable heat transfer coefficient in that region. However, a consequence will be that bubble-induced particle replacements and the heat t.ransfer rate will be reduced from the upper part of the plate. If the lower end of a vertical plate is tapered on one side, the gas pocket will drain to one side causing more frequent particle renewal and enhanced heat transfer there. Heat transfer between the two sides of the plate will then be unequal’ * -* 3. In such circumstances, the biggest heat transfer coefficient is realized at the side to which bubble-generated particle circulation is increased, its value being constant over the whole of its area (especially at higher ffuidizing velocities). No temperature gradient into the packet of particles and gas close to the surface becomes established because of the rapid replacement of the material by fresh bed material. The other side, howeyer, will be co&acted by a slowly downward n:oving layer of particles, and local heat transf.;r coefficients will be greatly reduced from 6,le lower part of the surface which will be contacted by particles that have already exchanged heat as they flowed down the plate. Variations in the hydrodynamic conditions also affect local heat transfer coefficients be_ to
279
Fig. 7. Heat transfer coefficient distribution along the perimeter of horizontal cylinders of diameters D = 125 and 220 mm positioned at a height of 750 mm from the gas distributor in an apparatus of 0.6 X 1.2 m with a bed height of 1.5 m. Bed material corundum of mean diameter 0.25 mm.
tween a sphere, a vertical cylinder”’ and particularly between a horizontal cylinder (Fig. 7) and a fluidized bed. From this and the additional work of Noackz5 and Gelperin et al. 2 6, it would seem that at high gas velocities the heat transfer coefficient has a maximum value at the top point of a horizontal cylinder, where fe is small but packets of particles are often changed by gas bubbles passing near the cylinder.
THE
EFFECT
OF PARTICLE
MOISTURE
CONTENT
The modified packet theory readily esplains the effect of water sprayed onto the bed surface on bed to immersed body heat transfer. The effective increase in gas thermal conductivity with increase in humidity is only up to 3%, but water sprayed into the bed affects the bed behaviour directly through aiding the discharge of electrostatic charge. It can also lead to an increase in particle heat capacity if the bed is operating at low temperature and the bed material is porous so that it can absorb much water. Variation in the local coefficient with height was found to be the same for all the bed materials examined (corundum, chamotte and activated charcoal) and was related to the local particle packing density. The heat transfer coefficient to a bed of non-absorbent corundum particles first increased as the quantity of water injected into the bed was increased, reached a maximum which was sustained for some further increase and then decreased. The initial increase can be explained in terms of the decrease in interpar-
Fig. 8. Heat transfer coefficient variation according to height of calorimeter location in fluidized bed for activated carbon. w = 0.26 mlsec, He = 360 mm, Q = the quantity of water sprayed on to the bed surface.
title electrostatic effects within the bed. The maximum in the coefficient corresponds to the condition under which charge effects are a minimum. With further increase in the quantity of water injected, the fluidizing air becomes saturated (the experiments were carried out at 70°C) and the flow properties of the bed change sharply and the heat transfer coefficient reduces. With this material, the effective thermal properties of a packet of particles is affected by water by less than 1%. When the experiments were repeated with porous charcoal particles, the particle heat capacity increased as moisture was absorbed into the particle. For particles that had absorbed 13% by weight. moisture, the heat transfer coefficient rose from 190 to 240 W/m2 a C (Fig. 8). With beds of charcoal particles, electrostatic effects were negligible and consequently the effect of sprayed water on heat transfer was brought about through the increase in the particle heat capacity alone. This effect was observed earlier by Mickley and Fairbanks’ _
RADIANT
HEAT
TRANSFER
EFFECTS
Many applications, especially for the rapid operate at high temperaheating of metals3, tures, a?d estimation of the radiant heat transfer coefficient, brad (eqn. ES), is of paramount importance. Published work is not clear on this effect. In some instances radiant heat transfer is ignored and in others it is suggested that the heat transfer problem between the bed and sensing element should be treated as a problem involving transfer be-
Fig. 9. Comparison of experimental data and theoretical values of Hrad as a function of t,%. at t,, = S50°C. Points represent mean values. The limits of the theoretical RMS experimental error are indicated by dashed !ines. From experiments”: a- tb = 880°C, d = 1.8 mm;b--fb = 800°C, d = 1.8 mm; c- tb = ‘isO%, d = 3 mm. Our data: chamotte particle, e- d = 0.35 mm; f- d = 0.63 mm; k-d = 1.25 mm. Curves calculated. lby ref.‘i; 2, 3, 4- ref.29; 5- ref.30; 6- by ref.3 for 0.35-mm particles.
tween two grey bodies or, alternatively, between a grey body (the calorimeter) and a black body (the bed)_ The radiative heat transfer coefficient has been measured by following the changing temperatures of two spheres of low Biot number immersed in the bed. The one sphere had an oxidized surface (emissivity 0.8) and the other had a silver-plated surface (emissivity 0.1). The radiative coefficient, brad , increased by a factor of 7-8 as the surface temperature of the sphere was increased from 160°C up to 730°C whilst the bed was maintained at a temperature of 850°C (Fig. 9). The StephanBoltzman equation would only predict a fourfold increase in the transfer coefficient for a surface varying in temperature from 0°K to the bed temperature at constant bed and body emissivities. This can be explained in that the fluidized particles close to the transfer surface have been cooled by heat exchange with the surface so that the radiant heat flux from these particles to the surface is less than if particles were at the bed temperature. This was tested by making measurements to a flat quaiiz glass surface immersed within the bed whose inside temperature was controlled by circulating air through it. The radiant energy passing through the quartz was measured by an actinometer and, in contrast to other ex-
3M
k4
WI
Fig. 1G. Emissivity temperature.
&!I
100
an
900
of non-isothermal
fLm
fc
bed us. surface
was made for the abperiments’ 7, allowance sorption characteristics of the quartz glass. The effective emissivity e,. = qradiuO T;‘, of the fluidized bed in contact with the glass surface was found to depend both on the surface temperature and bed temperature (Fig. 10). Here qrad is the radiative heat flux from the bed to actinometer. The emissivity of a free surface of a fluidized bed coincides = tb and decreases with with that for t, increase in bed temperature (Fig. 10). The radiative component in the total heat transfer coefficient increases with increase in the temperature of the radiative surface and reaches 2O-30% for a receiver surface temperature of 725°C and bed temperature of 850°C (Fig. 11). The larger the particle diameter, the
1011200
500
600
700
800 t
J
aC
Fig. 11. Radiation component fraction of overall heat transfer coefficient at different surface temperatures. Fluidized bed of chaxnotte particles: ld = 0.35 mm; 2- d = 0.63 mm; 3- d = 1.25 mm; tb = 850°C.
281
larger is the fractional quantity of heat transferred by radiation, although the absolute quantity of heat transferred by radiation is independent of the particle diameter (within the tested range) and of the fluidizing velocity (during intensive fluidization). The effective temperature of the radiating particles near the receiving surface reduces both with reduction in the surface temperature and with that of the bulk of the bed.
ACKNOWLEDGEMENTS
The authors thank Dr. J.S.M. Botterill of the Department of Chemical Engineering, University of Birmingham for his help in the preparation of the final version of the English manuscript.
fer coefficient
(at opt.imum
gas veloc-
ity) time-averaged heat transfer coefficient h for period of surface and packet contact water flow rate sprayed on bed level, Q ml/min radiative heat flux from the bed to qrad the actinometer R?.,Rk packet and contact thermal resistances, m* “C/W temperature, oC t temperature of wall, “C L temperature of bed, “C *b absolute temperature of bed, K Tb W fluidizing gas flow rate, m/set minimum fluidizing velocity, m/set W,i fluidizing gas flow rate optimum (corW, responding to maximum time-averaged heat transfer coefficient), m/set fiuidization number w = W/W,f
LIST OF SYMBOLS E
Gf
A, Xf Ppt Pi 7 TO
vf 00 90
Pt
A a
d, D Fo
fo
Ho h h, h max hm
porosity (void fraction) fluidized bed-surface effective emissivity, dimensionless thermal conductivity of particle packet and gas, W/m “C particle and gas density, kg/m3 time, set mean probe with bubble contact time gas kinematic viscosity, m’/sec 5.7 - lo-’ W/m* (“K)4 bubble frequency packet interchange frequency empirical coefficient, dimensionless coefficient of gas thermal diffusivity, m* /set mass heat capacity of particles, joule/ kg°C particle and probe diameter, m dimensionless time coefficient fraction of the total time when probe shrouded by gas bubbles acceleration of gravity, m/se2 probe point height above distributor, Inn-l packed bed height, mm heat transfer coefficient, W/m* o C instantaneous heat transfer coefficient at the moment 7 instantaneous heat transfer coefficient atr=O time-averaged maximum of heat trans-
Subscripts conduction cond convection conv radiation rad REFERENCES 1 H.S.
Mickley
and
D.F.
Fairbanks,
rlnz.
Inst.
J., 1 (1955) 374. 20. 2 A.P. Baskakov, Inzh. Fiz. Zh., 6 (11) (1963) Rapid Non-Oxidizing Heat and 3 A.P. Baskakov, Thermal Treatment in a Fluidized Bed, MetalChem.
Engrs.
lurgiya, Moscow, J.S.M. Botterill,
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Technol.,
4
(1970/71)
19-26.
A.P.
Baskakov,
Transport,
(3)
Izuest.
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Nauk
SSSR,
Energ.
i
(1966j122.
T.D.
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iVeft_
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24 25 26 27
28 29 30 31
B.V. Berg, AI’. Baskakov and B. Sereeterijn, Inzh. Fiz. Zh.. 21 (6) (1971) 985-991. R. Noack, Chem. Ingx-Tech., 42 (1970) 371. N-1. Gelperin, V-G. Ainstein and A-V. Znikovsky. Inzh. Fiz. Zh., 10 (6) (1966) 799-802. VS. Pikashov. S.S. Zabrodskv. - . K.E. Makhorin and A-1. Ilchenko, in Heat and Moss Transfer in Disperse Systems, Vol. 5, Izd. Nauka i tekhnika, hIinsk, 1968, pp. 309-313. A.G. Tischenko and J-1. Khvastukhin, Khim. Prom., (6) (1967). S-S. Zabrodsky and S.A. Malyukovich, Inzh. Fir. Zh.. 4 (2) (1968) 224-234. AI. Iichenko, V.S. Pikashov and K.E. Makhorin, Znzh. Fizz. Zh.. 14 (4) (1968) 602-609. N.F. Filippovsky and A-P. Baskakov, Inzh. Fiz. Zh.. 12 (2) (1972) 234-241.
8 (1973)
S-A.,
273-282
Lausanne -
Printed in The Netherlands
Heat transfer to objects immersed in fluidized beds A.P. BASKAKOV, B.V. BERG, O.K. VITT, N.F. FILIPPOVSKY, V.A. KIRAKOSYAN, J.M. GOLDOBIN and V.K. MASKAEV Kirov
Jrals Polytechnical
(Received
June 8,1973;
Institute,
accepted
Sverdlovsk
(U.S.S.R.)
June 27,1973)
Summary The modified packet model for heat transfer between a gas-fluidized bed and an imm.ersed surface is presented_ In contrast to the model of Mickley and Fairbanhs, allowance was made for the effective gap heat resistance between the packet of particles and surface (the contact therma resistance Rlz) and for the heat transferred directly by convection through the gas filtering through the particles and between the particles and the immersed object. The convective contribution towards the maximum heat transfer coefficient is found to increase with increasing particle size. This model readily explains the effect of particle moisture content, shape of the immersed body and other factors on bed to immersed body heat transfer_ Radiant heat transfer effects are discussed_
INTRODUCTION
Mickley and Fairbanks’ consider the process of heat transfer between a gas-fluidized bed and an immersed surface by which unsteady-state heat transfer occurs to packets of particles as they are brought into contact with the heat transfer surface. The residence time of packets at the surface is terminated when they are replaced by other packets of particles under the action of bubble-generated circulation patterns within the bed. They showed that the heat transfer coefficient is given by
(1) if the bed may be considered
to be a medium
of uniform thermal properties with an effective conductivity h and heat capacity pPc, (l-c), where E is the bed voidage. This suggests that the instantaneous rate of heat transfer will be very large when a packet first comes into contact with the surface_ However, many experiments show that the heat transfer coefficient is apparently limited by some
thermal
resistance
between
the
packet
and the surface2-” _ Gabor’ showed that the best correspondence between experimental results and more detailed models describing the transfer of heat between a surface and a chain of particles is obtained when allowance is included for a small gap between the surface and adjacent particles and between the particles. He suggested that the gaps may only be a mathematical expedient in the calculation and lack physical reality, and cited an experiment which would seem to show that no such gap really existed. However, the weight of evidence would confirm that there is the thermal resistance of an effective gap between the surface and bedz--5.10.11 or
particles
Although for relatively long contact times, 7, it is permissible to consider the packet of particles and gas as a medium of uniform thermal properties, this is obviously not so for short contact times. For short and intermediate contact times a good approximation to the behaviour is obtained by the assumption that there is an additional contact; thermal resistance, Rk , between the packet of uniform thermal properties and the transfer surface. The legitimacy of this is shown by the good correspondence obtained between the estimated instantaneous coefficients given by (2)
371
du
I
;!I
i IIt
I
I
/III
I
iii
Fig. 1. Comparison of the instantaneous heat transfer coefficient value from an isothermal wail to the particle semi-limited layer, estimated by formula (2) with experimental data8 _ Dimensionless heat transfer coefficient Nu = h,d/h is plotted on ordinate, dimensionless time
F,
=
A4 (1 -
on
the
=
and direct measurements, when an instantaneous heat flux and the contact time of heat transfer surface with the packet bed were strictly controlled (Fig. 1). The resistance R, arises primarily from the increase in bed voidsge in the region directly adjacent to an immersed surface. Gelperin and Ainstein” list. theoretical expressions for the instantaneous and mean transfer coefficients derived for models involving a resistance adjacent to an immersed surface and for different boundary conditions. The situation obtaining in a fluidized bed corresponds most closely to the case of a constant heat transfer surface temperature and for constant bulk bed temperature_ The complicated expressions for the mean coefficients reduce to simple approximations. Thus, for the case where the transfer surface temperature remains constant during the period of contact with the packet3 S5vg3
h, -
1
Rk + 0.5RX
(3)
If the transfer surface is shrouded by gas bubbles for a fraction of the total time fa , the mean coefficient will be correspondingly reduced: h cond
=
(1 --fo)h,
d
&=2X
(5)
abscissa with
C,p, e)dld/2h. Particle diameter, d, for glass bead-air system (X = 0.14 W/m°C): l0.39, 20.93, 32.05, 4- 3.05, 5- 5.05 mm; for glass bead--CO* system (A = 0.1 W/m°C): 6- 0.39, i- 0.9, S- 5.05 mm. Dotted curve by formula (1). Rk
The value of Rx can be estimated from eqn. (l), where the thermal conductivity, h, corresponds to a first approximation to that of the bed at incipient ffuidization or to that of a packed bed and for which the volumetric heat capacity is given by pP c, (1 - E). The effective contact resistance between the packet and the surface (Rk) is inversely proportional to the maximum instantaneous heat transfer coefficient, which is obtained at the first instant of contact. For stationary particles on a cubical lattice, the thermal resistance between the first row and the surface will be half that between adjacent layers of particles in the lattice if there is no supplementary gap between them; thus
Corrections effect surface
of
must any
aud
be
particle
any
included
to allow
movement
gap between
close
particles
for
the
to
the
aud
the
It will be different if the particle packing corresponds more closely to a hexagonal rather than a cubical pattern_ Values of Rk, f0 and shave been estimated experimentally by following the temperature fluctuations of low heat capacity probes mounted in experimental surfaces. Using a probe’s response, it was possible to determine the maximum value of the instantaneous heat transfer coefficient, h,, (the inverse of the contact heat resistance, Rk ) directly between the packet of particles in the gas-fluidized bed and the immersed object in which the probe was mounted. Experiments have been extended to include conditions under which convective heat transfer through the gas and radiative transfer are important, and these are outlined below. Additionally, behaviour when the fluidized bed is moistened by water sprays is discussed. surface.
HEAT TRANSFER CAL OBJECT
TO AN IMMERSED
CYLINDRI-
The probe used in typical experiments consisted of a 5 I.rm thick, 5 X 10 mm strip of platinum glued to the side of 15 and 30 mm diameter vertical rubber cylindrical test objects, or to the side of a 30 mm diameter, vertical, water-cooled, stainless steel tube. The element response was affected by heat trans-
275
fer into the substrate and this effect was determined beforehand by following the response of the element when it was subjected to intermittent blasts of air. By this means, the response of the element was determined over a range of frequencies_ Tests were carried out by immersing the cylinders in beds of corundum (0.12, 0.32 and 0.50 mm mean particle diameter) and in a bed of 0.65 mm diameter slag beads fluidized over a porous tile distributor 10 mm thick. The beds used were of 98 and 92 mm diameter and the fluidizing gases were carbon dioxide, helium (both at temperature 20°C) and air at temperatures from 20°C up to 550°C. Prom the response oscillograms of the foil temperature fluctuations, the mean probe and bubble contact time, rO,, and the probe and packet contact time, 7, bubble frequency and packet interchange frequency LJ+, and pt respectively and the fraction of the time that bubbles shrouded the transfer surface, fo, were all determined directly. Figure 2 shows that the dependence of r and f. on the main fluidizing parameters were given quite well by the empirical correlations
Fig. 2. Probe mean contact time with particle packet 7 (a) and tie fraction of probe contact with gas phase f,-, (b) us. fluidizing velocity. 1,2CO2 and He at 20°C; 3- 7-sir at f = 20, 250. 350, 450, 550°C, respectively. Diameter of vertical cylindrical probe 30 mm.
set
f. = 0.33
w;~(W--A)~ dg
(6)
O-l4
(‘7)
I
The fact that r f - and f. f 0 at the point of minimum fluidization can be readily explained by the effect of the immersed object on the behaviour of the bed. Thus, even when w =GW there was still a tendency for a void to formmf beneath the cylindrical obstruction. Bubbles periodically formed from this and rose along the probe surface causing some particle movement even before the bed generally became fluidized. The empirical factor -cl made allowance for the effects of probe diameter and particle shape. It tended to diminish as the probe diameter increased and as the particles more closely approximate to the spherical shape. Thus for tests with corundum, for example, A equalled 0.8 when the vertical tube diameter was 30 mm in diameter and 0.9 when it was rllduced to 15 mm_ For the slag particles the degree of variation was from 0.7 to 0.75 when the tube diameter was halved from 30 mm to 15 mm. Particle density and gas dynamic viscosity had little apparent effect, esept for their effect on wmf_ The variation in r. with gas ?low rate was independent of particle diameter and shape. The frequency of packet and bubble exchange rates increased with increase in the fiuidizing gas flow rate up to gas flow rates of 2-3 wmf_ Above this, the frequencies were almost independent of the ratio IV. Figure 3 shows that
I
42
44
46
C
Fig. 3. Rk us. particle diameter. lCO2 ; 2- He ar. 20°C; 3, 4, 5, 6, 7- air at temperatures 20, 250, 350, 450, 550°C, respectively.
2’i6 TABLE Air
1 Corundum 0.12mm
0.04
480
Corur.dum 0.32mm
CO,
He
0.045 550
497
0.135 460
0.18 421
0.15 397
0.3 335
0.45 277
0.6 247
0.99
h
m,
W/m20C
530 370
Corundum 0.5 mm
0.25 246
0.3 332
0.45 285
0.6 255
0.75 235
Slag 0.65 mm
0.25 215
0.28 286
0.42 223
0.56 215
0.72 208
270
0.15 326
0.2 302
370
0.5 211
0.61 200
260
0.61 212
0.85 215
220
0.56 20-I
0.7 202
190
Corundum 0.12 mm
0.046 353
0.05 425
z-x c 0.1 s1 T 368 -4
Corundum 0.32 mm
0.14 256
0.16 314
Corundum 0.5 mm
0.2s 199
0.34 266
Slag 0.65 mm
0.25 185
0.28 217
Corundum 0.12 mm
0.035 1080
0.04 1400
Corundum 0.32mm
0.1 s90
0.11 1000
0.22 781
Corundum 0.5 mm
0.27 725
0.32 835 0.3 655
Slag 0.65 mm
W
h
0.27 620
the contact resistance, Rk, reduced almost linearly with reduction in particle diameter; the contact thermal resistance was determined using the foil probe rnd was the inverse of the maximum value of the instantaneous heat transfer coefficient. In this case the part of the heat removed from the surface by convection was taken into account. The fact that it did not tend to zero in the limit of very small particles is further evidence for the existence of a gap between the bed and surface. Rk was approximately dependent on the thermal conductivity of the fluidizing gas to the 0.63 power. That this dependence is not a simple proportionality is evidence for the part played by the particle thermal conductivity on the effective thermal conductivity of the gap. There was negligible apparent dependence of the gap resistance on the fluidizing velocity. The effective resistance was independent of the height at which the probe was located within the bed. Heat transfer coefficients estimated from the estimated contact times and exchange frequencies are summarized in Table 1. The convective heat transfer component
.z 0.32 .-1 253 9 = 0.5 ; 230 b ._ .+ 0.42 2 212 .0.07
310
0.145 1033
1500
0.34 '719
0.42 665
1070
0.35 807
0.42 710
0.48 695
900
0.45 538
0.6 545
0.75 515
775
1273
0.11 1132
was taken into account in calculating the value of h. There is good agreement between these coefficients and values of the maximum time-averaged heat transfer coefficient, h, , given by the empirical correlation of ZabrodsBy7. THE INTERPARTICLE GAS TRANSFER COMPONENT
CONVECTIVE
HEAT
The heat transferred directly by the gas filtering through and bet.ween the particles and the immersed object will increase with increase in the w,*, and the w,~ will increase as the mean particle size in the bed increases. The convective and conductive components can be envisaged to a first approximation as being separate and additive if heat transfer to the bubble phase is included in the convective component too. Similarly, the radiative component, which is increasingly important at higher operating temperatures, may also be regarded as being an additive component so that the overall heat transfer coefficient may be envisaged as:
h = hcond + km,
+ had
(8)
A number of workers’ ‘- ’ 4 have estimated the convective component, hconv_ The following heat transfer correlation has been derived using a mass transfer analogy for gas velocities in excess of w, from measurements of the rate of vaporization of naphthalene from cylindrical objects’ ’ *16 _
N&xl" = 0.0175Ar0-46 Pro-33
(9)
For fluidizing gas flow rates less than w, , the correlation should include the additional group (w/w, )Oq3 _ The relationship given by eqn. (9) suggests that the gas convective component of heat transfer, h,,,, , is proportional to do.38 whereas the conductive component reduces with increasing particle diameter because of increases in R, and 7. Thus the convective contribution toward the maximum heat transfer coefficient, 12, , is found to increase with increasing particle size, being approximately 10, 15, 30, 60 and 90% respectively for corundum and chamotte particles having average diameters of 0.16, 0.32, 0.5, 2.5 and 4 mm respectively1 5. With a bed of 5-mm and more -coarse particles, the bed to surface coefficient is nearly entirely made up from the convective component which is, in turn, equal to the wall transfer coefficient with a packed bed system’ ‘-” _ This does not mean that the overall heat transfer coefficients in fluidized and packed beds +f coarse particles are equal;
Fig. 4. Dependence of maximum heat transfer coefficient upon particle size. lbed of corundum particles; thermozond 6 mm in diam. 3: 2- data obtained in the same bed with a vertical 220 X 160 mm calorimeter3 l; 3data obtained with 40 mm diam. and 100 mm high cylinder vertical thermozond, the same bed.
in the latter, heat transfer into the bulk of the bed is limited by the-relatively low heat conductivity of the static particle phase close to the surface, but this is not the case in the fluidized bed, because the particles are then free to circulate close to the surface. The form of dependence is illustrated in Fig. 4 for heat transfer between an immersed cylindrical object in beds of particles up to 13 mm diameter. Figure 5 gives dimensionless experimental values for 12, and hconv (esperimental results for the convective component being determined from the mass transfer analogy) and comparison is made with values of using eqn. (9) with the &cl n\* estimated Frandtl number raised to the 0.33 power and also to the power 1 as derived for the correlation in an earlier study3 _ The best fit to the values of h,,,,. is given by Nu,,,,
= 0.009
AT-‘-” Pro-33
(10)
However, deviations between all the formulae are no more than 20%, and these for h,,,, may well be a consequence of details of the
1
Fig. 5. Dependence of Nusselt number for maximum heat transfer (Nrc, = 11~dlhf) and convective transfer Nusselt number (Nuc,nv = h,,,,d/Xf) on Archimedes number Ar=gd3 (pP/pf-1)~;'. l-4. Values for Nu,,,,. from ref. 12. 5. Values for Nu,,,, from ref. 15. 6,‘i. Values for Nu, from ref. 21. 8. Values for Nu, measured using a 160 X 220 vertical flat plate calorimeter in a bed of corundum particles. 9-11. Values for Nu, measured using a 40 mm diam. by 100 mm high cylindrical calorimeter in beds of lead, steel and alundum spheres. I and II. Predictions given by eon. 9 with the Prandtl number raised to the powers 1 and 0.33-respectively. III. Predictions given by Nurn = 0.86 _-%S-o*2 (ref. 21). IV. Predictions given by Nn, = 0.21 Arb'-32. V. Predictions given by eqn. 10 shown by dashed line.
apparatus_ It can also be seen from Fig. 5 that the overall heat transfer coefficient is accounted for by the convective transfer component at high values of the Archimedes number (Ar > lo7 ), Le. in beds of coarse particles. Figure 4 illustrates the changing roles of L,,~ and hcond - The decrease of h, in beds of fine particles (< 10 pm) is on account of their poor fluidization characteristics; agglomeration and channelling occurring in the beds.
THE EFFECT
OF SI-IAPE OF THE IMMERSED
BODY
Because of its influence on the local circulation of particles close to it, the shape of the immersed body affects the surface to bed heat transfer behaviour. In this, the behaviour with vert.ical and inclined plates is quite typical. High speed photography shows that unstable, periodically vanishing, gas voids form under an inclined plate and their contact time increases with the angle of deflection of the plate. Thus, when the plate is horizontal, the lower side is in contact with gas voids for up 4m
Fig. 6. Heat transfer coefficient from a flat, calorimeter vs. its orientation in a fluidized bed of corundum particles having a mean diameter of 320 pm. l- w = 0.7 mlsec; 2-7w = 0.5 m/set. No.
CUNC
1,23
4
5
6
7
Bed height, mm
1600
1600
1000
450
300
1500
Calorimeter location height, mm
1300
750
750
220
150
750
Apparatus cross-section, mm
1200 600
1200 600
1200 600
1200 600
420 170
1200 600
Calorimeter size, mm
220X 160
82Cx480
70% of the time. This considerably reduces the average rate of heat transfer from the underside of the plate (Fig. 6). At low fluidizing velocities and at small angles of deflection there can be an advantage because the rising bubbles then keep replacing the particles close to the plate with fresh material_ Transfer coefficients from the top surface of an inclined plate are also reduced from those obtained with a vertical plate because a defluidized layer is formed on it which slowly slips down the plate. However, in some cases with smaller plates mounted in vigorously bubbling beds, it is possible to achieve higher rates of heat transfer from the top surface (Fig. 6) because the material defluidizing on top of the plate is constantly being thrown off and disturbed by the rising bubbles. The unstable gas void forming underneath a thick vertical plate acts as a source of bubbles. These will rise along the surface and in a bed operating at low gas flow rate greatly intensify the rate of particle replacement from the lower section of the vertical plate, thus increasing the attainable heat transfer coefficient in that region. However, a consequence will be that bubble-induced particle replacements and the heat t.ransfer rate will be reduced from the upper part of the plate. If the lower end of a vertical plate is tapered on one side, the gas pocket will drain to one side causing more frequent particle renewal and enhanced heat transfer there. Heat transfer between the two sides of the plate will then be unequal’ * -* 3. In such circumstances, the biggest heat transfer coefficient is realized at the side to which bubble-generated particle circulation is increased, its value being constant over the whole of its area (especially at higher ffuidizing velocities). No temperature gradient into the packet of particles and gas close to the surface becomes established because of the rapid replacement of the material by fresh bed material. The other side, howeyer, will be co&acted by a slowly downward n:oving layer of particles, and local heat transf.;r coefficients will be greatly reduced from 6,le lower part of the surface which will be contacted by particles that have already exchanged heat as they flowed down the plate. Variations in the hydrodynamic conditions also affect local heat transfer coefficients be_ to
279
Fig. 7. Heat transfer coefficient distribution along the perimeter of horizontal cylinders of diameters D = 125 and 220 mm positioned at a height of 750 mm from the gas distributor in an apparatus of 0.6 X 1.2 m with a bed height of 1.5 m. Bed material corundum of mean diameter 0.25 mm.
tween a sphere, a vertical cylinder”’ and particularly between a horizontal cylinder (Fig. 7) and a fluidized bed. From this and the additional work of Noackz5 and Gelperin et al. 2 6, it would seem that at high gas velocities the heat transfer coefficient has a maximum value at the top point of a horizontal cylinder, where fe is small but packets of particles are often changed by gas bubbles passing near the cylinder.
THE
EFFECT
OF PARTICLE
MOISTURE
CONTENT
The modified packet theory readily esplains the effect of water sprayed onto the bed surface on bed to immersed body heat transfer. The effective increase in gas thermal conductivity with increase in humidity is only up to 3%, but water sprayed into the bed affects the bed behaviour directly through aiding the discharge of electrostatic charge. It can also lead to an increase in particle heat capacity if the bed is operating at low temperature and the bed material is porous so that it can absorb much water. Variation in the local coefficient with height was found to be the same for all the bed materials examined (corundum, chamotte and activated charcoal) and was related to the local particle packing density. The heat transfer coefficient to a bed of non-absorbent corundum particles first increased as the quantity of water injected into the bed was increased, reached a maximum which was sustained for some further increase and then decreased. The initial increase can be explained in terms of the decrease in interpar-
Fig. 8. Heat transfer coefficient variation according to height of calorimeter location in fluidized bed for activated carbon. w = 0.26 mlsec, He = 360 mm, Q = the quantity of water sprayed on to the bed surface.
title electrostatic effects within the bed. The maximum in the coefficient corresponds to the condition under which charge effects are a minimum. With further increase in the quantity of water injected, the fluidizing air becomes saturated (the experiments were carried out at 70°C) and the flow properties of the bed change sharply and the heat transfer coefficient reduces. With this material, the effective thermal properties of a packet of particles is affected by water by less than 1%. When the experiments were repeated with porous charcoal particles, the particle heat capacity increased as moisture was absorbed into the particle. For particles that had absorbed 13% by weight. moisture, the heat transfer coefficient rose from 190 to 240 W/m2 a C (Fig. 8). With beds of charcoal particles, electrostatic effects were negligible and consequently the effect of sprayed water on heat transfer was brought about through the increase in the particle heat capacity alone. This effect was observed earlier by Mickley and Fairbanks’ _
RADIANT
HEAT
TRANSFER
EFFECTS
Many applications, especially for the rapid operate at high temperaheating of metals3, tures, a?d estimation of the radiant heat transfer coefficient, brad (eqn. ES), is of paramount importance. Published work is not clear on this effect. In some instances radiant heat transfer is ignored and in others it is suggested that the heat transfer problem between the bed and sensing element should be treated as a problem involving transfer be-
Fig. 9. Comparison of experimental data and theoretical values of Hrad as a function of t,%. at t,, = S50°C. Points represent mean values. The limits of the theoretical RMS experimental error are indicated by dashed !ines. From experiments”: a- tb = 880°C, d = 1.8 mm;b--fb = 800°C, d = 1.8 mm; c- tb = ‘isO%, d = 3 mm. Our data: chamotte particle, e- d = 0.35 mm; f- d = 0.63 mm; k-d = 1.25 mm. Curves calculated. lby ref.‘i; 2, 3, 4- ref.29; 5- ref.30; 6- by ref.3 for 0.35-mm particles.
tween two grey bodies or, alternatively, between a grey body (the calorimeter) and a black body (the bed)_ The radiative heat transfer coefficient has been measured by following the changing temperatures of two spheres of low Biot number immersed in the bed. The one sphere had an oxidized surface (emissivity 0.8) and the other had a silver-plated surface (emissivity 0.1). The radiative coefficient, brad , increased by a factor of 7-8 as the surface temperature of the sphere was increased from 160°C up to 730°C whilst the bed was maintained at a temperature of 850°C (Fig. 9). The StephanBoltzman equation would only predict a fourfold increase in the transfer coefficient for a surface varying in temperature from 0°K to the bed temperature at constant bed and body emissivities. This can be explained in that the fluidized particles close to the transfer surface have been cooled by heat exchange with the surface so that the radiant heat flux from these particles to the surface is less than if particles were at the bed temperature. This was tested by making measurements to a flat quaiiz glass surface immersed within the bed whose inside temperature was controlled by circulating air through it. The radiant energy passing through the quartz was measured by an actinometer and, in contrast to other ex-
3M
k4
WI
Fig. 1G. Emissivity temperature.
&!I
100
an
900
of non-isothermal
fLm
fc
bed us. surface
was made for the abperiments’ 7, allowance sorption characteristics of the quartz glass. The effective emissivity e,. = qradiuO T;‘, of the fluidized bed in contact with the glass surface was found to depend both on the surface temperature and bed temperature (Fig. 10). Here qrad is the radiative heat flux from the bed to actinometer. The emissivity of a free surface of a fluidized bed coincides = tb and decreases with with that for t, increase in bed temperature (Fig. 10). The radiative component in the total heat transfer coefficient increases with increase in the temperature of the radiative surface and reaches 2O-30% for a receiver surface temperature of 725°C and bed temperature of 850°C (Fig. 11). The larger the particle diameter, the
1011200
500
600
700
800 t
J
aC
Fig. 11. Radiation component fraction of overall heat transfer coefficient at different surface temperatures. Fluidized bed of chaxnotte particles: ld = 0.35 mm; 2- d = 0.63 mm; 3- d = 1.25 mm; tb = 850°C.
281
larger is the fractional quantity of heat transferred by radiation, although the absolute quantity of heat transferred by radiation is independent of the particle diameter (within the tested range) and of the fluidizing velocity (during intensive fluidization). The effective temperature of the radiating particles near the receiving surface reduces both with reduction in the surface temperature and with that of the bulk of the bed.
ACKNOWLEDGEMENTS
The authors thank Dr. J.S.M. Botterill of the Department of Chemical Engineering, University of Birmingham for his help in the preparation of the final version of the English manuscript.
fer coefficient
(at opt.imum
gas veloc-
ity) time-averaged heat transfer coefficient h for period of surface and packet contact water flow rate sprayed on bed level, Q ml/min radiative heat flux from the bed to qrad the actinometer R?.,Rk packet and contact thermal resistances, m* “C/W temperature, oC t temperature of wall, “C L temperature of bed, “C *b absolute temperature of bed, K Tb W fluidizing gas flow rate, m/set minimum fluidizing velocity, m/set W,i fluidizing gas flow rate optimum (corW, responding to maximum time-averaged heat transfer coefficient), m/set fiuidization number w = W/W,f
LIST OF SYMBOLS E
Gf
A, Xf Ppt Pi 7 TO
vf 00 90
Pt
A a
d, D Fo
fo
Ho h h, h max hm
porosity (void fraction) fluidized bed-surface effective emissivity, dimensionless thermal conductivity of particle packet and gas, W/m “C particle and gas density, kg/m3 time, set mean probe with bubble contact time gas kinematic viscosity, m’/sec 5.7 - lo-’ W/m* (“K)4 bubble frequency packet interchange frequency empirical coefficient, dimensionless coefficient of gas thermal diffusivity, m* /set mass heat capacity of particles, joule/ kg°C particle and probe diameter, m dimensionless time coefficient fraction of the total time when probe shrouded by gas bubbles acceleration of gravity, m/se2 probe point height above distributor, Inn-l packed bed height, mm heat transfer coefficient, W/m* o C instantaneous heat transfer coefficient at the moment 7 instantaneous heat transfer coefficient atr=O time-averaged maximum of heat trans-
Subscripts conduction cond convection conv radiation rad REFERENCES 1 H.S.
Mickley
and
D.F.
Fairbanks,
rlnz.
Inst.
J., 1 (1955) 374. 20. 2 A.P. Baskakov, Inzh. Fiz. Zh., 6 (11) (1963) Rapid Non-Oxidizing Heat and 3 A.P. Baskakov, Thermal Treatment in a Fluidized Bed, MetalChem.
Engrs.
lurgiya, Moscow, J.S.M. Botterill,
1968. Powder
Technol.,
4
(1970/71)
19-26.
A.P.
Baskakov,
Transport,
(3)
Izuest.
Akad.
Nauk
SSSR,
Energ.
i
(1966j122.
T.D.
Gabor, Chem. Eng. Progr. Symp. Ser., 66 (1971) 76-86. S.S. Zabrodsky, Hydrodynamics and Heat Transfer in a Fluidized Bed, Gosenergoizdat, MoscowLeningrad, 1963. Antonishin and L.V. Sinchenko, Heat and 8 N.V. mass transfer in disperse systems, Naukn i Tekhn., Minsk, 5 (1969) (trans. j. 9 J.F. Davidson and D. Harrison, Fluidization, Academic Press, 1971. Chapter 10 by N-1. Gelperin and V.G. Ainstein. P.D. Pate1 and J.T. Holmes, ,%.m. 10 L.B. Koppel, (105)
Inst. 11 12 13 14
Chem.
Engrs.
J., 16 (1970)
456-471.
R. Ernst, Chem. Ingr.-Tech., 32 (1960) 17-22. E.N. Ziegler and W.T. Brazelton; Ind. Eng. Chem. Fundamentals, 3 (1964) 94-98. E.N. Ziegler and -F-T. Holmes, Chem. Eng. Sci., 21 (1966) 117-122. Shirai Takashi, Rept. Ann. Congr. Japan Chem. Eng. Sot..
April.
1967.
282 15 16 17 18 19 20
21 22 23
A.P.
Baskakov
and
V.M.
Suprun,
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