PARTICLE-TO-GAS HEAT T R A N S F E R IN FLUIDIZED BEDS A . C. J U V E L A N D , H . P. D E I N K E N , A N D J .
E. D O U G H E R T Y
Los Alamos Scient& Laboratory, Unioersity of California, Los Alamos, JY. 1 4 4 .
Particle-to-gas heat transfer measurements were made in shallow beds of ZrC particles fluidized b y helium or argon. The particles were heated b y induction to temperatures as high as 1150" C. Transfer coefficients were obtained using a steady-state system from measurements of the temperature of the solids and the gas temperature downstream from the bed. Four average particle sizes were used, ranging from 385 to 1 4 2 0 microns. The static bed depth was varied from 0.1 8 to 1.31 cm. Reynolds numbers of from 0.23 to 84 were investigated. A qualitative explanation of the low heat transfer coefficients in fluidized beds i s presented.
YE
of the inherent properties of fluidized beds is the high
O'rate of heat transfer bet\veen the beds a n d the fluidizing
medium. .A number of investigations on particle-to-gas heat transfer have been published ( 7 . 2. 4- 6. 8-70) and have been revieiced by Frantz ( 3 ) . T h e results vary a great deal. partly because of difficulties in measuring the gas and solids temperatures. I n some experiments. thermocouples ivere placed in the bed itself. where it is difficult to decide Lvhether the measurement being made is the gas temperature, the solids temperature. or some intermediate temperature. T h e solids temperature was usually assumed to be equal to the exit gas temperature. O u r investigation \vas similar to that attempted by Eichorn a n d LYhite (2). \vho heated the solids by dielectric heating. I n our experiment, the solids were heated by induction to temperatures which could be measured by a n optical pyrometer. a n d the gas temperature donmstream from the bed was measured by a high-speed thermocouple probe. T h e temperature difference betwcen the bed and the exit gas temperature \vas as high as 150' C. in some cases.
OPTICAL PYROMETER
MIRROR
d-----< d J ~
THERMOCOUPLE LEADS TO RECORDER ~ +
TO VACUUM PUMP
GAS TEMPERATURE PROBE ( H I G H SPEED THERMOCOUPLE)
GAS EXHAUST
FLUIDIZED BED (21RCON IU M CARBIDE PARTICLES 1
INDUCTION HEATER COIL
GAS DISTRIBUTING I N L E T (DISC D R I L L E D WITH SMALL HOLES)
Figure 1. ment
Schematic drawing of experimental arrange-
Apparatus
A schematic drawing of the experimental arrangement is sho\vn in Figure 1. T h e gas used was of commercial grade. supplied through a pressure regulator valve and a calibrated Brooks rotameter flowmeter. After passing through the heated particles, mos of the gas \vas released directly into the room. Part of it was draLvn through the high-velocity thermocouple. bvhich measured the gas temperature doumstream from the bed. T h e voltage signal from the thermocouple was fed to a Brown recorder calibrated to read temperature in ' C . T h e bed \vas vie\ved by means of a Pyro Micro-Optical pyrometer and mirror arranged as shown in Figure 1 . A correction \vas applied a t each temperature to account for the reflectivity a n d absorption of the mirror. 'Ihe bed container \vas made of quartz because of its desirable electrical a n d mechanical properties a t elevated temperatures (Figure 2). T h e gas inlet and fluidized bed support was a 0.020-inch thick quartz disk perforated with 0.013-inch diameter drilled holes _ . uniformly spaced about 0.025 inch between centers. I he top and bottom parts were cemented together kvith Sauereisen Insa-lute cement. T h e fluidized beds were heated by a n induction heater which utilized a push-pull circuit and operated a t 110 megacycles. T h e bvork coil \vas one turn of .,-inch copper tubing which carried cooling water. I t \vas coaxial with the cylindrical bed container and was positioned near the midpoint of the bed as shoxvn in Figure 1 . RF discharges in the helium gas
4k-l/16"
Figure 2.
Fluidized bed container VOL. 3
NO. 4
NOVEMBER
1964
329
~
~
T h e value of h can be determined by measuring t, a t some value of L such as the total bed depth, Lo; then
SAUEREISEN INSA-LUTE CEMENT
CpG h=-ln--
aLo
CHROMEL- ALUMEL THERMOCOUPLE LEADS
Figure 3.
High-speed thermocouple probe
during operation were a source of some difficulty. They were minimized by carefully shielding the oscillator and allowing only the work coil to protrude outside the shielding cage. T h e cage, in turn, was grounded at several points, using the optimum length of grounding \vire to minimize RF radiation from the cage. The'one-turn Lvork coil, rather than a multiturn coil, placed a t a voltage node in the tank circuit also tended to reduce discharge. However, \vhen a bare thermocouple \vas positioned above the bed, R F discharges \vere sometimes initiated at the thermocouple. Placing the thermocouple in the probe about 3 V 8 inch do\vnstream from the probe tip (see Figure 3 ) and placing RF chokes in the thermocouple leads eliminated this type of discharge and completely eliminated the electrical discharge in the hot helium gas a t the power levels used in our experiment. About 500 ivatts of heating po\ver per cubic centimeter could be transmitted to the bed by properly matching the oscillator to the rvork coil. T h e thermocouple probe used for sampling the gas from the upper surface of the bed is shown in Figure 3. T h e thermocouple \vas made with 28-gage Chrome1 and Alumel wire hvith the junction located inside the probe tip about 3 / 8 inch from the gas inlet. T h e probe body was made of quartz with joints sealed by Sauereisen Insa-lute cement. T h e tip was a ',',e-inch o.d., "C4-inch Lvall quartz tube, the closed end of which was perforated Lvith six 0.010-inch diameter holes to allow sampling the gas. The hot gas \vas drawn through the holes in the end of the probe and past the thermocouple junction a t high velocity by a mechanical vacuum pump. T o observe the direct effect of the induction heater on the thermocouple, the particles were removed from the bed container and the thermocouple probe was placed in the position used for taking temperature readings as close as possible to the bed. TVith no gas flowing in the bed container or the probe, the thermocouple reading rose to 35' C. above room temperature with the induction heater a t full power. TVhen the gas was drawn through the probe, the reading dropped to 10' C. above room temperature. Since in actual measurements at high temperatures the thermocouple reading ahvays increased when gas was draivn through the probe, the induction heating of the thermocouple was actually aiding the action of the high-speed thermocouple probe in compensating for heat losses from the thermocouple junction, and we estimated that no correction was necessary for this effect. T h e nearly spherical ZrC particles used for the heat transfer measurements were made by sintering spherical agglomerates of ZrC powder. T h e density of these particles was about 5 grams per cc. Particles were graded, using standard sieves, into groups in the size ranges 1190 to 1650, 710 to 840, 500 to 590, and 350 to 420 microns.
to
- tt
tb
- to
(3)
where tu is the exit temperature of the gas. The product aL, is independent of the state of fluidization and was evaluated under static conditions. The value of a \\.as calculated, assuming a void fraction of 0.42, to be equal to 3.48,'Dp sq. cm. per cc., where D, is the average particle diameter in centimeters. For particles in the size range from 1190 to 1650, 710 to 840, 500 to 590, and 350 to 420 microns, the values of a used in evaluating h were 24.5, 45.0, 64.0, and 90.4 sq. cm. per cc., respectively. The value of Lo used \vas the static bed depth, D. T h e temperature of the inlet gas, t t , proved to be difficult to measure, so it was calculated with what is believed to be acceptable accuracy. T o find t l , it was necesyary to calculate the heat transfer to the gas as it flowed through the cylindrical bottom part of the quartz bed container and through the perforated gas inlet. It \vas assumed that the flow was established pipe florv and that the side of the perforated inlet disk nearest the bed !\.as at the bed temperature. Since the value of h was more sensitive to ( t o - t o ) than to ( t b - t t ) in our experiments, these approximate values for t f \Yere considered adequate. I t proved to be essentially impossible to measure gas temperature a t the upper surface of the bed with any reproducibility, since particles clustered about the holes in the thermocouple probe tip and reduced the gas flow in the probe. Mechanical vibration of the probe would keep the holes free of particles when the probe was as close as '/4 inch above the bed surface. T h e temperature of the gas as it left the bed was then determined by plotting the measured gas temperature as a function of distance down to '/4 inch above the bed and then
1000 350-4202
A 710-04Op 0 1100 - 1 6 6 0 ) ~
900
D s0357CM.
P
z z-a
800
m
Qw mo W -I
n
a
ou
Procedure
0
A steady-state method was used to obtain a heat transfer coefficient, the gas flow and the bed temperature being held constant during a n experimental r u n . T h e heat balance equation under these conditions is
.W$
eo0
II -
0.0 357 CM. 600
C,G dt, f ha ( t e -
tb)
dL = 0
(1)
By assuming all quantities in Equation 1 to be constant except t u and L , and allowing t o to be equal to t t when L equals zero at the bed gas inlet, one can integrate to obtain
400
'
0 * 0.367 CM.
ais 0.80 0.46 I!O P.O DISTANCE OF THERMOCOUPLE PROBE TIP ABOVE BED IN INCHES
Figure 4. Representative plots of gas temperature as a function of height above bed 330
I&EC FUNDAMENTALS
extrapolating to the gas temperature a t zero height above the bed. Figure 4 shows several representative plots of gas temperature as a function of Gistance above the bed. I n actual operation of the thermocouple, the gas velocity in the thermocouple probe was increased until a plateau in the temperature reacling was reached. T h e reading a t this plateau was 25’ to 200’ C . higher than that without suction, depending upon the gas flow rate, gas temperature, and height of the probe above the bed. This is close to the value which was calculateu from the measured temperature gradient, the distance of the thermocouple junction to the probe gas inlet holes, and estimates of the radiation and conduction losses from the junction. a further check on the validity of the exit gas temperature measurement, thick beds were used under conditions calculated to give values of (ta - t o ) less than 1’ C. These runs gave values equal to zero Lvithin the experimental error.
Table 1. Superjcial Mass Velocit);, G, G . : Sq. Cm.See. ( x lo3)
Summary of Heat Transfer Data and Results Supei Jicial Mass I’elocit.y,
Partide Temp.,
Inlet Gas
Particle-to-Gas Run0 Tep., Heat Transfer .Yo. tb, c. ti, c. t b - t o b COefiCient, h, Watts/(Sq. Cm.) ( ” c.1 D = 0,357 Cm. D, = 0 . 1 4 2 C m . 312 137 i 1 3 234 X 24.7 987 1 247 100 i 11 24.7 780 246 2 Dp = 0 , 1 4 2 C m . D = 0.595 Cm. 45 f 1 0 217 765 242 24 7 3 70 i 1 3 138 765 256 19 45 4 50 i 8 240 760 233 28 4 3 972 308 75 f 12 192 24 7 6 7 1109 371 69 i 15 165 19 45 1113 412 113 i 20 83.7 12 8 8 172 i 15 56.5 987 365 12 8 9 72 i 1 3 153 967 324 19 45 10 0 . 1 4 2 Cm. D = 0.952 Cm. DP 35 i 35 116 765 256 19 45 11 25 i 10 167 765 242 24 7 12 194 25 i 8 765 234 28 4 13 950 354 84 i 1 5 57.3 12 8 14 69 i 20 66.7 1109 410 12 9 15 44 i 1 5 123 1114 374 19 45 16 977 327 17 i 12 158 19 45 1’ D = 1 . 3 1 Crn. D, 0 142 C m . 10 i 10 159 775 246 24 ’ 18 15 f 11 112 780 262 19 45 19 49 i 15 52.6 12 8 979 362 20 1124 417 24 i 20 70.5 12 8 21 95 i 11 34.4 78.5 290 12 8 22 D = 0.35’ C m . 0 . 0 7 5 Cm. DP 750 27’ 55 f 11 89.7 12 8 23 770 235 40 i 8 238 28 4 24 75 i 21 40.5 775 360 ’ 3’ 25 ’ 37 977 453 67 i 23 48.0 26 1120 521 60 41 255.0 3’ 2’ 1124 6’5 109 i 40 20.7 4 52 28 157 f 31 13.5 98’ 591 4 52 29 990 366 50 f 15 105 12 8 30 D = 0 595 C m . 0.0775 Cm. DP 793 293 28 i 11 71.9 12 8 31 109 f 40 12.5 1124 674 4 52 32 4 52 122 i 31 10.2 9’2 583 33 ’ 37 97’ 454 52 i 23 33.1 34 76.5 356 37 55 f 21 28.8 35 49 i 27 36.0 1129 524 36 355 21 28.9 ”0 358 3’ 3982 589 122 i 31 10.3 38 4 52 Argon gas zn runs 75 and 76. a Helium Ras uspd in runs 7 through 74.
-
Measurements were made only with beds which were well fluidized and which gave no indication of bubbling. Under these conditions the solids temperature, as observed by an optical pyrometer, was very uniform and dropped only about 10’ C. in the l,’I6 inch of the bed nearest the walls. The general pattern of solids motion was an upward movement in the center of the bed and a downward drift near the walls. A few particles. which probably had lingered too long near the bed inlet, occasionally came to the surface as much as 50’ C. cooler than the rest of the bed. These were not considered in reading the bed temperature. The variation in temperature with radius a t several heights above the bed measured \vith the high-velocity thermocouple probe is shown in Figure 5. As can be seen, the wall influence on the gas temperature increases with height above the bed. Fluctuations of the temperature of as much as 5’ C. could be observed with both the optical pyrometer and the high-
Run5 .Vo.
5 to =
Partzcls Temp.,
( X TO3)
Dp 4.52 4.52 D, 7.37 12 8 4.52 24.7 28.4 19.45 12.8 7 17
tb,
C.
Inlet Gas Temp., t,, C .
0,0775 Cm. 967 534 1109 665 = 0.0545 Cm. 760 41 353 42 770 285 43 765 459 44 758 243 45 747 228 46 980 328 47 975 360 985 457 48 49 7.1’ 1166 514 50 1109 664 4 52 51 4 52 980 588 D, = 0 . 0 5 4 5 C m . 7.37 745 346 52 7.37 976 453 53 7.37 54 1140 530 55 2.86 1134 822 56 4.52 977 586 4.52 765 459 57 58 12.8 775 287 D, = 0.0385 C m . 59 4 52 778 466 60 7 3772 359 61 12 8 -52 2’8 62 19 47 755 253 63 110’ 515 3” 64 3’ 982 45’ 65 4 52 1109 665 66 4 52 97’ 585 67 2 86 1119 810 D , = 0 0385 C m 68 22 8 710 228 69 19 4 783 267 70 12 8 95’ 354 71 7 37 1134 52’ 72 3’ 785 365 12 8 ’65 283 73 4 52 1099 659 74 D, = 0 1 4 2 C m 75 720 145 194 76 236 726 140 outlet temperature. 39 40
+
G: G./ Sq. Cm.Sec.
=
VOL. 3
Particle-to-Gas Heat Transfer tb - to5 Coe@cient: h. Watts/(Sq. C m . ) ( C.) D = 0.952 Cm. 77 i 31 9.5 59 i 40 11.1 D = 0.357 Cm. 45 i 21 37.1 30 i 11 81.4 75 i 28 14.5 15 i 10 200 32 i 8 181 15 i 1 3 168 30 i 15 88.1 60 i 23 36 56 f 27 39 6 79 i 40 1’ 8 100 f 31 14.1 D = 0.595 Cm. 20 f 21 30 1 26 f 23 30 2 20 f 234 4 109 i 59 4 45 47 i 31 13.1 45 i 28 11.8 15 i 11 61.2 D = 0.1785 Cm. 98 i 28 16.8 52 i 21 49.5 42 i 11 100 30 i 11 1757 i 27 57 ’ 62 i 23 51 89 i 40 27 4 117 i 31 6 119 i 59 8 83 D = 0 357 Cm 20 i 11 117 18 i 11 105 42 i 15 55 2 84 i 2’ 23 8 75 f 21 20 6 55 i 6 45 0 104 i 40 10 7 D = 0 595 C m . 170 f 7 86 186 f 7 97
NO. 4
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NOVEMBER 1 9 6 4
331
800
I
10
I I
9 5
I 1/16. ABOVE BED
700.
-
' '
1F
-
.' D.
a
0.l42CMl ARGON OAS USED
0
X
1.0
-
c
0.0383C M A 0 I785 C b. 0 357 cc. 0 5 9 1 CM. 0 952 CM. 7 3 r CM'.
400
speed thermocouple. The magnitude and frequency of these oscillations depended on the temperature, flow rate, and particle size. Both the pyrometer and the thermocouple readings Lvere taken near the axis of the cylindrical bed container, and the peak readings were used for each in determining (tb - tu).
REYNOLDS NUMBER
Figure 6.
Nusselt number vs. Reynolds number
Data and Results
The experimental data and values of the heat transfer coefficients as defined by Equation 3 are given for each run in Table I . For comparison with other data, the Nusselt number, hD,,'k, and the Reynolds number, GD,/p, were calculated for each r u n . The thermal conductivity of the gas, k, was evaluated a t the bed temperature, and the gas viscosity, p , was evaluated at the average gas temperature, tav, where
(4) For each depth, particle size, and flow rate where runs a t different bed temperatures were made, the Nusselt numbers and Reynolds numbers were averaged for the various temperatures. The Nusselt numbers and Reynolds numbers found in this way are plotted in Figure 6 , and points for various depths and particle sizes are connected by straight lines which are so labeled. The heavy solid line from Zenz and Othmer ( 7 7 ) is representative of many of the published data. T h e other heavy line \vas obtained from an equation proposed by Frantz ( 3 ) to predict true gas-to-particle coefficients and is based on the data of Heertjes and McKibbins ( 4 ) and Walton, Olson, and Levenspiel ( 9 ) . (By true coefficients are meant those obtained by using high velocity thermocouple probes rather than bare thermocouples.) The only appreciable source of statistical error in the experimental values is from the error in the value of ( t o t o ) resulting from errors in the measurement of l b and tu. The error in ( t o - t u ) . given in column 5 of Table I, is obtained in part hy assuming an error of =k5' C . in ( t b - t u ) due to reading the optical pyrometer and the high velocity thermocouple. An additional error in some of the measurements is due to the accuracy in determining the height of the gas temperature probe above the upper surface of the bed. This error is estimated to be +0.10 inch and the corresponding error in temperature varies with operating conditions. For lobver gas f l o ~ v sand higher temperature, the slope of the plot of gas temperature above the bed becomes steeper (see Figure 5), and hence a larger probable error in t u is expected.
-
332
l&EC
FUNDAMENTALS
There are several possible systematic errors in our data. The wall of our container could transfer heat to or from the gas. The surface area of the particles per unit depth of bed was always a t least a factor of 10 higher than the wall area per unit depth, however, and since temperature readings were taken near the'axis of the bed, the wall effect should be small. A small systematic error is also introduced in the calculation of t i because of the many assumptions and approximations made in the calculation. Some error might also be introduced from the assumption in Equation 3 that the heat transfer coefficient is a constant throughout the bed even though the gas temperature and, hence, the state of fluidization vary in the bed. Another cause of differences between our data and those of other experimenters might be our rather arbitrary choice of the temperatures a t which to evaluate the gas properties in the determination of the Nusselt and Reynolds numbers. Discussion and Conclusions
At the lowest Reynolds numbers used in this experiment, the Nusselt numbers were more than two orders of magnitude lower than for single spheres (7). The explanation for these low values which is consistent with this experiment is poor gas-solids contact. Since the thermal diffusivity is so large for helium in this experiment (about 5 sq. cm. per second), it is unlikely that low Nusselt numbers could be caused by any nonsteady-state heat conduction effects (3. 8). It was also visually apparent that there were no variations in the temperature of the particles which could cause such a large effect. One form of gas bypassing might be that the gas passes around aggregates of particles. For shallow beds the diameter of these aggregates might be approximately the same as the bed depth, and one might expect overlapping of aggregates. T h e gas would then flow in channels in the regions of incomplete overlap of the aggregates. Hence. one would expect that as bed depth increases there lvould be longer but feewer channels and that the amount of heat transferred Lvould be independent of bed depth. This would imply. also. that the Nusselt number would be proportional to D , ' D . and one sees
from Figure 6 that this is approximatel>- true for the smallest particles a t the shallo\\-er depths. From Table I. one can see that the heat transfer coefficient is usually greater a t higher temperatures when all other. parameters are the same. \.ariatiom \\-ith temperature are zignificant compared to the experimental error only \\-hen large parrs of the data are considered. 'They may be due in part to the increased thermal conductivity of the gas. and in part to the greater degree of fluidization a t higher temperature which causes a breakup of aggregates and. therefore. less gas bypassing. Acknowledgment
'The authors are indebted to P. M. Giles and N. hl. Schnurr for their contributions. They also thank G. M. Grover. E. \Y. Snlmi, and Joseph I>.Smith, J r . , for their advice a n d encouragement. Nomenclature
surface area of solid per unit volume of bed, sq. c m . cc. heat capacity of gas. joules g. C. D = static bed depth. cm. D , = average particle diameter, cm. G = superficial gas flow rate: g.,'sq. cm.-sec. h = particle to gas heat transfer coefficient, wattsjsq. cm.u
=
C',
=
t o
Nu = Nusselt number = hD, k R e = R e p o l d s number = GD, p to = temperature of solids. ' C. t , = temperature of gas. O C . to = temperature of gas a t bed exit, O C. t i = remperature of gas a t bed inlet, O C p = gas viscosity, poises Literature Cited (1) .4nton. .J. K . . thesis. University of Iowa. 1953. (2) Lichorn. J.. \Vhite. K. R.; Chem. En?. Proqr. Symp. Ser.. 48, No. 4. 11 (1952). (3) Frantz. J . F., Chem. En,?. P r o ~ r .5 7 , N o . 7,35 (1961). (4) Heertjes. P. M,, McKibbins, S. I V , : Chrm. En:. Scz. 5 , 161 (1 956). (5)' .Johkstone. H. F., Pigford. K.L.. Chapin, J. H.!Trans. .4m. Inst. Cheni. Engrs. 37, 95 (1941). (6) Ketternrinp. K. N.. Mand?rfield. E. L.:Smith. J. M . , Cheni. Etlg. P70g7. 46, 139 (1950). ( 7 ) Kramers. H.. Phvszca 12. 61 11946). ( 8 ) Richardson. .J. P.. Aver's. P . . ~Tran's. Inst. Chem. Eners. (London) 37. 314 11959) (9)
