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Particle temperature measurement in a gas—solid fluidized bed
The Chemical Engineering Journal, 15 (1978) 169 - 178 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
Particle Temperature Measurement in a Gas-Solid Fluidized Bed A. N. SINGH* and JOHN R. FERRON Chemical Engineering
Department,
University
of Rochester,
Rochester
(U.S.A.)
lations which shows a wide variation in the values of heat transfer coefficients. He attributes this variation mainly to the choice of surface area and temperature difference. Whatever may be the flow pattern, the problem of the correct temperature difference has been a matter of great concern in studies of gas-solid heat transfer. This may be because it has not been possible to measure the particle temperature. As pointed out by Leva [3] measurement of particle temperature is difficult because it is not possible to attach a thermocouple without impairing the mobility of the particle. An attempt to measure temperature gradients with a thermocouple has been made by Walton et al. [ 41 but it was not clear whether the thermocouple indicated the true temperature of the solid or that of the gas or some average between them. Eichhom and White [5] were unable to measure the temperature difference between the solid and the gas, although the particle temperature was kept constant by dielectric heating. Wamsley and Johanson [6] and Ferron and Watson [ 21 avoided estimating the temperature of the solids by using unsteady state experimental conditions. All the investigations carried out in the past have involved some compromise in interpreting the measured temperatures. With the advances in IR technology it has become possible to measure small amounts of radiation with great accuracy. Astheimer and Wormser [‘7] have developed a high speed IR radiation pyrometer using a thermistor as a temperature sensing element, and they claim to be able to detect a black-body temperature difference of 0.01 “C!. Sapphire (Also,) has long been used as a window glass to transmit IR radiation in the region 1 -6 pm and also as a light pipe. Window transmission has been reported by Astheimer and Wormser [7]. The
Abstract In this work, particle temperature w.as measured in a gas-solid fluidized bed. We used a pyrometer consisting of a 6 in sapphire rod, $44in in diameter, and two 2000 a thermistors. The sapphire rod transmits radiation from the heated particles and a thermistor is used to detect this radiation. The second thermistor measures the temperature of the enclosure. The pyrometer was calibrated using a packed bed heated to different temperatures. Experiments were carried out in a fluidized bed under heating, cooling and steady state conditions to illustmte the use of this pyrometer. We observed that the tempem ture of the particles in a fluidized bed is substantially different from the tempemture of the bed as measured by an immersed thermometer.
1. INTRODUCTION
Studies of gas-solid heat transfer are necessary to understand the mechanism of addition, dissipation and recovery of heat in a fluidization or packed-bed process with or without chemical reaction. The flow behaviour of a fluidized bed is complex and this is probably the reason for the lack of agreement in the various definitions of gas-solid heat transfer coefficients found in the literature [ 1,2] . The choice of heat transfer coefficient depends on the definitions of the “effective surface area” and the “mean temperature difference” between the particles and the gas. Barker [l] has provided a graphical summary of existing corre*Present address: Chemical Engineering Department, Bihar Institute of Technology, Sindri, Dhanbad, Bihar, India. 169
170
optical characteristics of sapphire rods of various lengths have been investigated by Vollmer et al. [ 81 . By using a sapphire rod as a light pipe and a thermistor as a sensing element we can predict the temperature of solid particles in a fluidized bed. The temperature distribution so obtained can be compared with the temperature distribution obtained by a bare thermocouple. This will help to resolve the question of whether the temperature indicated by an immersed thermocouple represents the temperature of the particle, that of the gas, or some average of the two. It may also be possible to determine the local heat transfer coefficients and to provide an insight into the mechanism of radial heat transfer in a fluidized bed.
2. PARTICLE
TEMPERATURE
MEASUREMENT
The particles used in a fluidized bed are usually small, of the order of 50 - 200 e in diameter. Small particles have the advantages that temperature gradients inside the particles are eliminated and that they provide a large surface area. The optical system of a conventional pyrometer requires the sample object to have a certain minimum size so that the field of view of the pyrometer is filled. A single particle in a fluidized bed is obscured and produces a very small amount of radiation. However, the temperature of a group of particles in a fluidized bed can be measured by using a sapphire rod to transmit the radiation and a thermistor to measure the quantity of radiation. The light pipe is used as a probe which can be inserted in the column to measure local temperature, and the thermistor is used to measure the radiant energy of the particles. The temperature predicted in this way will be an average over the temperature of the particles contributing to the radiation that is measured and will be taken as the temperature near the end of the probe. 2.1. The characteristics of sapphire and the energy transmitted through the sapphire rod Artificial sapphires are available in a variety of shapes. Their optical behaviour for transmitting radiation has been studied by various workers. As reported by Loewenstein [9],
sapphire is highly transparent to radiation of 0.2 - 5.5 I.trn and is mechanically strong and hard. The transmission through sapphire drops to zero near 90 cm-i. The refractive index of sapphire in the UV and IR regions has been reported by Malitson et al. [lo]. Oppenheim and Even [ 111 have studied the transmittance as a function of temperature from 20 to 1000 “C. Sapphire rods of various lengths have been used as light pipes by Vollmer et al. [ 81, who showed that the effect of side illumination is always small compared with that produced by end illumination. Sapphire is a bad conductor of heat and Lee [12] showed that the amount of heat conducted through sapphire can be neglected. The power transmitted through a light pipe depends on the transmissivity function t(h) of the material. Vollmer et al. [8] have suggested the use of a cut-off wavelength for evaluating the power transmitted through a light pipe: 1 t(X)e,h(T)
dX = /’
e&T)
d);
(1)
0
0
The value of the cut-off wavelength X, for a 6 in sapphire rod has been determined as 4.07 pm. Equation (1) can be multiplied by the geometric transfer function G and the reflection correction function R to obtain the power W, arriving at the thermistor detector. Thus Wt = GR Ice,,(T)
(2)
dX
0
= GR&,(T)
(3)
where @eb(T) = 4 je,,(T) 0
dX = jCe&T)
dh
(4)
0
Lee [12] has shown that the factor GR can be taken as 0.92. 2.2. Thermistor chamcteristics Thermistors are “thermal resistors” with a high temperature coefficient of resistance. The resistance decreases as the temperature increases and vice versa. The resistance of a thermistor is solely a function of the absolute
171
temperature. Since the electrical power dissipated within the thermistor will heat the thermistor and change its resistance, the thermistor circuit must only use a very small amount of power. When a small voltage is applied to a thermistor the small current produced will not generate enough energy to heat the thermistor above the temperature of its surroundings. However, if the voltage is increased the current will increase and the heat generated in the thermistor will finally begin to raise its temperature above that of the surroundings. The resistance will consequently decrease and more current will flow. The voltage-current characteristics of thermistors show [ 131 a maximum and they are usually operated below the peak voltage. Since a thermistor has a certain mass, a finite period of time elapses before it reaches its maximum temperature, this time being a function of the thermistor mass and the applied voltage. Since the voltage is applied to a thermistor and a resistor in series, the magnitude of the current is determined by the voltage and the total circuit resistance. This will heat the thermistor to its maximum temperature and thereafter a constant current will flow. The delay in response can be reduced to 0.001 s by a proper choice of thermistor. The dissipation constant, which is defined as the power required to raise the temperature of the thermistor by 1 “C, is 0.14 mW or the 2000 a G-126 thermistor supplied by Fenwal Electronics. Table 1 shows the resistance-temperature characteristics of the thermistor. 2.3. Heat balance at the sensing element The temperature of the particles in a fluidized bed may vary axially as well as radially. All the particles radiate some energy and a fraction of this energy arrives at the probe. The radiation is incident at different angles and travels through the sapphire rod along different path lengths which are not easy to calculate. Therefore we assume that only particles in the vicinity of the probe contribute to the radiation incident at the probe. These particles are assumed to be at some average temperature. Further, we assume that the following quantities are small and can be neglected for
TABLE 1 Resistance-temperature characteristics of the central thermistor Temperature of the thermistor W)
Resistance @;2)
25.0 25.1 25.2 25.3
2023 2016 2009 2002
25.4 25.5 25.6 25.7
1995 1988 1982 1975‘
25.8 25.9 26.0 26.1
1968 1962 1965 1949
26.2 26.3 26.4 26.5
1942 1935 1929 1922
the purpose of the heat balance: (1) the radiation lost or received through the side of the light pipe; (2) the heat conducted through the sapphire and its supporting tube (cooled by circulating water); (3) the heat generated in the thermistor when the electrical circuit is closed for the resistance measurement; (4) the energy lost by the thermistor to the constant temperature enclosure; (5) the heat lost by thermal conduction through thermistor leads. With these assumptions the heat balance on the sensing element can be written as energy incident on the thermistor = heat lost by radiation and convection Mathematically follows:
this can be expressed as
W,A = osBA,(T4 - T;) + hA,(T - T,,)
(5)
Let
T-T,-,=AT
(6)
By neglecting higher powers of AT/T,,, eqn. (5) reduces to
W,A/A, = (4o,,T$ Therefore,
+ h)AT
(7)
172 TABLE 2 Estimated temperature rise of the central thermistor* Bed temperature (“C)
Percentage 9 of blackbody radiation transmitted through sapphire @I
50 60 70 80
0.50 0.62 0.75 0.95
Total blackbody mdiation eb x 10’ -2 (Wcm 1
Power W, received by the detector x lo4 (Wcm -2 1
Estimated temperature rise AT of the central thermistor W)
6.3 7.0 7.7 8.7
2.898 3.993 5.313 7.604
0.0250 0.0348 0.0463 0.0663
90 100 110 120
1.2 1.4 1.7 2.0
9.7 11.0 12.0 13.4
10.709 14.168 28.768 24.656
0.0933 0.1234 0.1635 0.2148
130 140 150 160
2.3 2.7 3.1 3.6
15.0 16.4 18.0 19.6
31.740 40.738 51.336 64.915
0.2765 0.3649 0.4470 0.5655
170 180 190 200
4.1 4.5 5.1 5.7
21.5 23.5 25.5 28.0
81.098 97.290 119.646 146.832
0.7164 0.8475 1.0422 1.2789
‘Using eqn. (9) and a value of h = 4 Btu ftw2 h-l “F-l as given by ref. 14.
AT=
Wt 16oszT:
+ 4h
By substituting the value of Wt from eqn. (3) into eqn. (8), the following expression is obtained:
highly idealized. For these reasons any attempt to predict particle temperatures in a fluidized bed requires that the temperaturemeasuring device be calibrated.
3. EXPERIMENTAL
AT=
SET-UP
G@%,(T) 160sxT; + 4h
Equation (9) can be used to estimate the rise in temperature of a thermistor that receives the radiation transmitted through the sapphire rod. Table 2 shows the temperature rise of the thermistor corresponding to bed temperatures ranging from 50 to 200 “C (the value of h was taken [14 ] as 4 Btu ftm2 h-l “F-l )* Tables 1 and 2 can be used to construct temperature-resistance characteristics. The broken line in Fig. 1 shows such a plot obtained with the help of eqn. (9) and Tables 1 and 2. We must point out that the plot is not exactly the same as that obtained from packed bed data (Fig. 1). The overall picture is very complicated and our assumptions for arriving at eqn. (9) are
A schematic diagram of the experimental setup is shown in Fig. 2. It consists of a fluidization column and devices for measuring temperature, pressure and flow. The fluidization column was made of four aluminium cylinders, each 6 in in internal diameter. These cylinders were placed one above the other and were held together by an exterior threaded rod in a bracket arrangement to form a column. The top and bottom cylinders were 6 in long and the two central cylinders were 12 in long. One of them had a water jacket and could be placed in either of the central positions. This column had provisions for inserting temperature-measuring devices at various points. A cone was connected at the bottom of the column for gas distribution. The cone was filled with glass balls ‘/4 in in diameter to
173 2040
l-
I
I
I
20
40
60
80 PACKEO
BED
I
I
I
I
I
I
100
120
140
lb0
180
200
TEMPERATURE,
‘C
m
Fig. 1. Calibration curve: 0, experimental data from the packed bed; ----, characteristics from Table 1.
Fig. 2. Schematic diagram of the experimental set-up: 1, fluidization column; 2, two 200-mesh screens; 3, sapphire rod probe; 4, thermometer; 5, two 200mesh screens; 6, thermistor housing; 7, water jacket; 8, manometer; 9, temperature controller; 10, constant-temperature bath; 11, thermometer; 12, heater; 13, stirrer; 14, immersion pump; 15, cooling coil; 16, rotameter; 17, diaphragm valve; 18, heater.
ensure proper distribution of the fluidizing air. Two 200-mesh stainless steel screens were placed between the cone and the column to support the particles. A 500 W heater was placed on top of the screen and was connected to a Variac which allowed the input voltage to the heater to be varied from 0 to 140 V. The resistance of the heater was approximately 25 Q . The air flow rate was measured with a rotameter which was regulated by a diaphragm valve. The air supply line was fitted with a pressure gauge to monitor the line pressure. An air filter removed compressor oil and dirt from the fluidizing air. The pressure drop across the column was
J
given by eqn. (9) and the thermistor
measured with a manometer as shown in Fig. 2. Thermometers and thermocouples were used for calibration of, and comparison with, the radiation pyrometer described below. The pyrometer for measuring particle temperature consisted of a sapphire rod which transmitted radiation from the heated particles to a thermistor. The sapphirethermistor combination is shown in Fig. 3. This consisted of a synthetic sapphire rod, 6 in long and l/s in in diameter, both ends of which were polished. Since sapphire is a delicate material and can break under mechanical stress, it was housed in a % in stainless steel tube. The annulus between the rod and the tube was fitted with Teflon which was machined for a close fit. Steel is a good conductor of heat and therefore the tube can transmit enough heat to affect the detector reading; in order to eliminate this possibility, part of the steel pipe was surrounded by a jacket for water circulation. The radiation transmitted through the sapphire rod was measured with a 2000 R thermistor (Fenwal Electronics type G-126) and a second 2000 Sl thermistor was used to measure the ambient air temperature. The thermistors were mounted on a U-shaped wire as shown in Fig. 3. Fluctuations in the ambient temperature have a considerable effect and make it impossible to reproduce thermistor readings. To eliminate the effect
174
THERMISTORS o.ooiOIA. PT. Ii? WIRE
NI-FE
b
I/;
-4406i
/--
ALLOY
T
I%1
(4
Fig. 3. The thermistor
1 WATER
IN
(b)
(a) and the thermistor
housing (b).
of changes in the ambient temperature, the thermistors were placed in a constant temperature enclosure. The enclosure was cross-shaped. One arm of the cross was fixed to one end of the sapphire rod and the opposite arm held a reflector with a concave surface. The other two arms of the cross, which were perpendicular to the sapphire reflector axis, contained the two thermistors. One thermistor was placed so that the bead of the thermistor was on the sapphire reflector axis and received direct radiation through the sapphire rod. The other thermistor was mounted so that the bead of the thermistor was kept in only one of the arms of the cross and did not receive direct radiation. The entire housing had a constant-temperature water jacket. The temperature of the bath could be controlled to within 0.05 “C. The bath had an on-off controller connected to a small immersion heater, and a cooling coil was immersed in the bath for circulating cold water. The flow could be adjusted manually. A Wheatstone bridge (5430-A, Leeds and Northrup Company) together with an external galvanometer (2430-C, Leeds and Northrup Company) with a sensitivity of 0.005 PA per scale division were used to measure the thermistor resistance.
4. EXPERIMENTAL
‘al
BEAD
PROCEDURE
AND RESULTS
The temperature-measuring device was calibrated with a 6 in bed of 0.00896 in spent cracking catalyst particles. The sapphire rod and the thermometer ends were positioned in the centre of the bed. The material was fed into the column and was heated in the fluidized state by an electric heater. The bed was allowed to settle and the pyrometer
resistance corresponding to the temperature of the immersed thermometer was measured. This process was repeated to obtain a complete calibration plot. Calibration points are shown in Fig. 1. In order to measure the particle temperature in the fluidized bed and to compare it with the bed temperature, thermometer and thermistor readings were recorded (i) by varying the flow rates when the bed was heated to 240 “C and was then allowed to cool down; (ii) with an IR heater introduced at the top during cooling; (iii) for constant flow rates of 8 ft3 min-l with varying input voltages; (iv) at flow rates of 6.2, 7.2 and 8 ft3 min- ’ to study the effect of fluidization velocity on the particle temperature. Figure 4 compares the thermistor resistance with the bed temperature in a packed bed and in a fluidized bed under various conditions. The top line represents the packed bed characteristics. The bottom two lines show the cooling characteristics with and without IR heating. Between these lines are points which represent fluidization at three different velocities.
5. DISCUSSION
The only source of heat for the thermistor is the radiant energy from the particles that is transmitted through the sapphire. This means that the temperature measured by the thermistor is the temperature of the particles. A thermometer immersed in the bed measures the particle temperature in the case of a packed bed and the bed temperature in the case of a fluidized bed. In principle a pyrometer probe at any point in the packed bed receives radiation from all
175
i?
z
c”
1960
I %
I940 1920 20
I
I
I
I
I
i
I
40
60
60
lea
120
I40
160
BED
TEMPERATURE,
1
160
1
200
k
Fig. 4. Temperature-resistance relation for packed and fluidized beds: curve 1, packed bed; curve 2, fluidized bed during cooling; curve 3, fluidized bed during cooling when heated with an IR heater; 0, fluidiz$ bed flow rate 8.0 ft3 min? ; A, fluidized bed flow rate 7.2 ft3 min-’ ; q, fluidized bed flow rate 6.2 ft3 min .
possible directions, but in practice radiation coming from particles at some distance from the top of the probe is liable to be intercepted by particles around the end of the probe. Furthermore, when a heated bed is allowed to cool by itself the maximum temperature will be at the centre of the bed, i.e. near the end of the probe. Based on these arguments we selected a packed bed for the purpose of calibration and we assumed that the temperature so obtained will be the average temperature of the particles around the end of the probe. Figure 1 is the calibration plot and the line obtained using eqn. (9) in conjunction with the temperature-resistance characteristics of the thermistor (Tables 1 and 2). The two lines are seen to be very close. It can be seen from Fig. 4 that the data with and without IR heating are consistent: particle temperatures stay higher during the cooling cycle with IR heating. For a given bed temperature the thermistor readings for the packed bed and the fluidized bed are different, showing that the particle temperature (recorded by the thermistor sapphire pyrometer) differs from the bed temperature (recorded by the thermometer). The particle temperature is given by the intersection of the constant-resistance line that passes through the point of the bed temperature and the R-T curve for the packed bed. Curve 2 in Fig. 4 is the cooling curve for a heated fluidized bed. The cooling process has the advantage that it creates a situation in
which the particles are at a higher temperature than the fluidizing air until the process is complete. The temperature difference was further increased by introducing an IR bulb at the top of the column which heated the particles as the column was being cooled by the fluidizing air. Curve 3 of Fig. 4, obtained for simultaneous heating (by the IR bulb) and cooling, helped us to analyse the character of a fluidized bed for the purpose of predicting the local heat transfer coefficient and of determining the relation between the particle, gas and bed temperatures (eqn. (10)) (see Section 5.1). It has been pointed out that the data with and without IR heating are consistent and that during IR heating the particles are at higher temperatures. Thus we may conclude that in a fluidized bed the particles are at a higher temperature than the bed temperature as measured by an immersed thermometer. This may be why all the fluidized bed points fall below the packed bed line (Fig. 4). However, because of the highly turbulent character of the fluidized bed the difference between bed and particle temperatures is small and this could explain the small scatter of the points in Fig. 4. 5.1. Solid-gas temperature difference during cooling The data of Fig. 4 for a bed cooled at a gas flow rate of 8 ft3 min-’ are replotted in Fig. 5. Here T, is the calibration temperature corresponding to the pyrometer resistance
176
Two time-dependent energy balances may be written for T,(t) and TB(t) during the time t of the cooling process. These are as follows:
210
190
dTi3=
%F*
dt
M,C,
dTs = --MT, - TJ
I70
w,C,(T1
-
T&) + h,(T,
-
Tg) (11)
dt
(12)
150
Initially T,, = T, = 210 “C, and when the cooling process is complete we expect that T,, = T, = Tf = T1 = 25 “C. Equation (10) is used to eliminate TB from eqns. (11) and (12). By eliminating time as a variable the resulting expression can be written
130
I IO
dy 90
d In x
Y
(13)
where y = (T, - T,)/(T, - Tl) and x = T, - T1. The constants are
70
50
,ALB-y
/ ^^ 9”
1
.._ II”
I
130 BE0
A’=a
I
I
I
I
IS0
170
190
210
TEMPERATURE,
T,,%
Fig. 5. Fluidized bed cooling characteristics: particle and gas temperatures vs. bed temperature for a gas flow rate of 8 ft3 min-l . The points are experimental data from Fig. 4. The curve drawn for T, is from eqns. (10) -(12) with a = 0.2 and h, = 1.07 cal s-l “C-l. The line shown for T, is from eqn. (10) with D = 0.2.
and Tb is the bed temperature, i.e. the reading of a thermometer immersed in the fluidized bed. (For example, when T,, is 180 “C the pyrometer resistance is about 1960 a. This resistance corresponds to a calibration value of l’, = 190 “C from the packed bed curve of Fig. 4.) When the calibration curve is applied to a fluid&d bed, T, represents the particle temperature. The bed temperature T,, is determined by T, and the gas temperature Tg. The three temperatures are related, and we postulate that
Tb = UT, + (1 -a)T,
(10)
where 0 < a < 1. The evaluation of (I will give the quantitative relationship between the three temperatures.
B =a2
p+E(l+y-)/ KG+J, Mfhs
(14) (15)
The boundary condition from eqn. (13) is that y = 0 when x = 210 - 25 = 185 “C. Exact solutions can be obtained for eqn. (13) (with different forms depending on the sign of dy/d In x + y) and can be used to deduce the values of A’ and B. A reasonable estimate of the parameters can be obtained from the data points in Fig. 5. The experimental data for the experiment of Fig. 5 were as follows: MS = 976 g; M, = 6 g; C, = 0.21 cal g-l “C-l; C, = 0.24 cal g-’ “C-l; wg = 4.6 g s-l. These values together with the data points of Fig. 5 and eqn. (13) lead to the estimates a = 0.2 and h S= 1 *07 cal s-l “C-l. The last value corresponds to an average particle-gas heat transfer coefficient of 10m6 cal cmw2 s-l “C-l. This is in excellent agreement with previous results (see Fig. 6 in ref. 2: Jh = 0.00105, Re = 3.5, D, = 0.00076). The estimate a = 0.2 suggests that an immersed thermometer measures a bed temperature which can be determined by adding 80% of the particle temperature and 20% of the gas temperature (eqn. (10)). The bottom
177
curve of Fig. 5 shows the variation of Tg as calculated from eqn. (10) with a = 0.2. Any vertical line will give the temperature difference between the particle and the gas. During the cooling process the gas and particle temperatures apparently differ by as much as 70 “C. This is an unexpectedly large difference, suggesting that the well-known uniformity of fluidized bed temperatures may disguise substantial non-uniformities between local particle and gas temperatures.
6. CONCLUDING
REMARKS
c,,G eb ebk G
h h,
M,. M, R t(X) T AT
The pyrometer used in this work to measure particle temperature can be considerably improved. We shall discuss some of the important factors. (i) Vollmer et al. [ 81 have reported the characteristics of sapphire and have shown that the smaller the rod the higher the cut-off wavelength. Equation (1) indicates that the power transmitted through the sapphire will increase for a higher cut-off wavelength. Thus the probe length can be chosen according to requirements. (ii) A thermistor with better sensitivity will give a quicker response. If the thermistor is larger, the power arriving at the thermistor increases but it may take more time to reach the steady state. A compromise between size and sensitivity is necessary to obtain the best performance. (iii) The thermistor housing is the most important part of the equipment. A small change in housing temperature can affect the accuracy of the measurement markedly. Equation (9) shows that the heat loss due to atmospheric cooling is considerable; this can be eliminated by using an evacuated enclosure. (iv) An ideal reflector may also increase the amount of radiation incident on the thermistor.
NOMENCLATURE
:
A’ 4,
B
parameter in eqn. (10) projected area of the thermistor, cm2 defined by eqn. (14) surface area of the thermistor, cm2 defined by eqn. (15)
wg wt X
Y
heat capacity total black-body emissive power, defined in eqn. (4) Planck’s distribution function geometric transfer function heat transfer coefficient average heat transfer coefficient between the particles and the gas multiplied by the particle surface area, cal s- ’ “C- ’ total mass, g reflection correction transmissivity function temperature, “C temperature difference defined in eqn. (6), “C gas input flow rate at temperature T1 power arriving at the thermistor detector, W cmv2 (T, - Tb)/( T, - T,), variable in eqn. (13) T, - T1, variable in eqn. (13)
Greek symbols x wavelength, I.trn A, uSB
d
cut-off wavelength, I.tm Stefan-Boltzmann constant fraction of black-body radiant power below X, = 4.07 /.ull
Subscripts b g :
bed gas solid enclosure
REFERENCES J. J. Barker, Znd. Eng. Chem., 57 (5) (1965) 33. J. R. Ferron and C. C. Watson, Chem. Eng. Prog. Symp. Ser. 58, 38 (1962) 79. M. Leva, Fluidization, McGraw-Hill, New York, 1959. J. S. Walton, R. L. Olson and 0. Levenspiel, Znd. Eng. Chem., 44 (1952) 1474. J. Eichhom and R. White, Chem. Eng. Prog. Symp. Ser., 48 (1952) 11. W. W. Wamsley and L. N. Johanson, Chem. Eng. Bog., 50 (1954) 347. R. W. Astheimer and E. M. Wormser, J.Opt. Sot. Am., 49 (1959) 179. J. Vollmer, G. C. Rein and J. A. Duke, J. Opt. Sot. Am., 49 (1959) 75. E. V. Loewenstein, J. Opt. Sot. Am., 51 (1) (1961) 108.
178 10 I. H. Malitson, F. V. Murphy, Jr., and W. S. Rodney, J. Opt. Sot. Am., 48 (1958) 72. 11 U. P. Oppenheim and U. Even, J. Opt. Sot. Am., 52 (9) (1962) 1078. 12 K. H. Lee, M.S. Thesis, University of Delaware, June 1960. Technical Manual, Fenwal Elec13 Thermistor tronics, 1970. 14 R. B. Bird, W. E. Stewart and E. B. Lightfoot, Transport Phenomena, Wiley, New York, 1960.
(A7) Substituting for dT,/dT, and (Tl - T&l( T, T& in eqn. (A4) from eqns. (A7) and (A6), respectively, yields the following relation after rearrangement: 1
wgc, M,Cs
l+__+_
APPENDIX
MgCg hs
T.s- Tb
T,, = aT, + (1 -a)T,
2
- TB) + h,(T,--
- TJ
T, - Tg
Tg = {Tb - (1 -a)T,}/a
T, .- Tg Differentiating
KC, wg Ts- Tl -M,
h, T,--T,,
MsCs w, Ts- TI --M,
h, T,-T,
(A3)
(A4)
Ts - Tl Ts -Tb eqn. (A5) with respect
=
X
T, - TI
(AlO)
A’=ajl+z
cl+?)\
(All)
and (A5)
Eliminating Tg from ( TI - TJ/(Ts - TB) using eqn. (A5), the following expression is obtained: =1-a-
-
(A91
w&g TI - Tg -1
KC, dT, h, From eqn. (Al)
-’
TJ (A2)
Time is eliminated as a parameter altogether by dividing eqn. (A2) by eqn. (A3) giving
KC, --=-_ dT,
MgCg1
(Al)
dT, = w,Cg(T1 M&B dt dT, = -h,(T, dt
2
-- Ts - TI -’
Derivation of eqn. (13) Starting from eqns. (10) - (12), Tg and the time derivative can be eliminated as follows:
Tl -T3
dT,
KC,
(
=a
M,C,
dTb
Ti - Tb ---T,-TT,
w3) to T,
B =a2
Mscsw,
(A121
M,hs Substituting the values of Y, LX,A’ and B from eqns. (A9) - (A12) into eqn. (AS) leads to the following expression:
dy d In x
=A'?
-y
Y
(A13)
Particle Temperature Measurement in a Gas-Solid Fluidized Bed A. N. SINGH* and JOHN R. FERRON Chemical Engineering
Department,
University
of Rochester,
Rochester
(U.S.A.)
lations which shows a wide variation in the values of heat transfer coefficients. He attributes this variation mainly to the choice of surface area and temperature difference. Whatever may be the flow pattern, the problem of the correct temperature difference has been a matter of great concern in studies of gas-solid heat transfer. This may be because it has not been possible to measure the particle temperature. As pointed out by Leva [3] measurement of particle temperature is difficult because it is not possible to attach a thermocouple without impairing the mobility of the particle. An attempt to measure temperature gradients with a thermocouple has been made by Walton et al. [ 41 but it was not clear whether the thermocouple indicated the true temperature of the solid or that of the gas or some average between them. Eichhom and White [5] were unable to measure the temperature difference between the solid and the gas, although the particle temperature was kept constant by dielectric heating. Wamsley and Johanson [6] and Ferron and Watson [ 21 avoided estimating the temperature of the solids by using unsteady state experimental conditions. All the investigations carried out in the past have involved some compromise in interpreting the measured temperatures. With the advances in IR technology it has become possible to measure small amounts of radiation with great accuracy. Astheimer and Wormser [‘7] have developed a high speed IR radiation pyrometer using a thermistor as a temperature sensing element, and they claim to be able to detect a black-body temperature difference of 0.01 “C!. Sapphire (Also,) has long been used as a window glass to transmit IR radiation in the region 1 -6 pm and also as a light pipe. Window transmission has been reported by Astheimer and Wormser [7]. The
Abstract In this work, particle temperature w.as measured in a gas-solid fluidized bed. We used a pyrometer consisting of a 6 in sapphire rod, $44in in diameter, and two 2000 a thermistors. The sapphire rod transmits radiation from the heated particles and a thermistor is used to detect this radiation. The second thermistor measures the temperature of the enclosure. The pyrometer was calibrated using a packed bed heated to different temperatures. Experiments were carried out in a fluidized bed under heating, cooling and steady state conditions to illustmte the use of this pyrometer. We observed that the tempem ture of the particles in a fluidized bed is substantially different from the tempemture of the bed as measured by an immersed thermometer.
1. INTRODUCTION
Studies of gas-solid heat transfer are necessary to understand the mechanism of addition, dissipation and recovery of heat in a fluidization or packed-bed process with or without chemical reaction. The flow behaviour of a fluidized bed is complex and this is probably the reason for the lack of agreement in the various definitions of gas-solid heat transfer coefficients found in the literature [ 1,2] . The choice of heat transfer coefficient depends on the definitions of the “effective surface area” and the “mean temperature difference” between the particles and the gas. Barker [l] has provided a graphical summary of existing corre*Present address: Chemical Engineering Department, Bihar Institute of Technology, Sindri, Dhanbad, Bihar, India. 169
170
optical characteristics of sapphire rods of various lengths have been investigated by Vollmer et al. [ 81 . By using a sapphire rod as a light pipe and a thermistor as a sensing element we can predict the temperature of solid particles in a fluidized bed. The temperature distribution so obtained can be compared with the temperature distribution obtained by a bare thermocouple. This will help to resolve the question of whether the temperature indicated by an immersed thermocouple represents the temperature of the particle, that of the gas, or some average of the two. It may also be possible to determine the local heat transfer coefficients and to provide an insight into the mechanism of radial heat transfer in a fluidized bed.
2. PARTICLE
TEMPERATURE
MEASUREMENT
The particles used in a fluidized bed are usually small, of the order of 50 - 200 e in diameter. Small particles have the advantages that temperature gradients inside the particles are eliminated and that they provide a large surface area. The optical system of a conventional pyrometer requires the sample object to have a certain minimum size so that the field of view of the pyrometer is filled. A single particle in a fluidized bed is obscured and produces a very small amount of radiation. However, the temperature of a group of particles in a fluidized bed can be measured by using a sapphire rod to transmit the radiation and a thermistor to measure the quantity of radiation. The light pipe is used as a probe which can be inserted in the column to measure local temperature, and the thermistor is used to measure the radiant energy of the particles. The temperature predicted in this way will be an average over the temperature of the particles contributing to the radiation that is measured and will be taken as the temperature near the end of the probe. 2.1. The characteristics of sapphire and the energy transmitted through the sapphire rod Artificial sapphires are available in a variety of shapes. Their optical behaviour for transmitting radiation has been studied by various workers. As reported by Loewenstein [9],
sapphire is highly transparent to radiation of 0.2 - 5.5 I.trn and is mechanically strong and hard. The transmission through sapphire drops to zero near 90 cm-i. The refractive index of sapphire in the UV and IR regions has been reported by Malitson et al. [lo]. Oppenheim and Even [ 111 have studied the transmittance as a function of temperature from 20 to 1000 “C. Sapphire rods of various lengths have been used as light pipes by Vollmer et al. [ 81, who showed that the effect of side illumination is always small compared with that produced by end illumination. Sapphire is a bad conductor of heat and Lee [12] showed that the amount of heat conducted through sapphire can be neglected. The power transmitted through a light pipe depends on the transmissivity function t(h) of the material. Vollmer et al. [8] have suggested the use of a cut-off wavelength for evaluating the power transmitted through a light pipe: 1 t(X)e,h(T)
dX = /’
e&T)
d);
(1)
0
0
The value of the cut-off wavelength X, for a 6 in sapphire rod has been determined as 4.07 pm. Equation (1) can be multiplied by the geometric transfer function G and the reflection correction function R to obtain the power W, arriving at the thermistor detector. Thus Wt = GR Ice,,(T)
(2)
dX
0
= GR&,(T)
(3)
where @eb(T) = 4 je,,(T) 0
dX = jCe&T)
dh
(4)
0
Lee [12] has shown that the factor GR can be taken as 0.92. 2.2. Thermistor chamcteristics Thermistors are “thermal resistors” with a high temperature coefficient of resistance. The resistance decreases as the temperature increases and vice versa. The resistance of a thermistor is solely a function of the absolute
171
temperature. Since the electrical power dissipated within the thermistor will heat the thermistor and change its resistance, the thermistor circuit must only use a very small amount of power. When a small voltage is applied to a thermistor the small current produced will not generate enough energy to heat the thermistor above the temperature of its surroundings. However, if the voltage is increased the current will increase and the heat generated in the thermistor will finally begin to raise its temperature above that of the surroundings. The resistance will consequently decrease and more current will flow. The voltage-current characteristics of thermistors show [ 131 a maximum and they are usually operated below the peak voltage. Since a thermistor has a certain mass, a finite period of time elapses before it reaches its maximum temperature, this time being a function of the thermistor mass and the applied voltage. Since the voltage is applied to a thermistor and a resistor in series, the magnitude of the current is determined by the voltage and the total circuit resistance. This will heat the thermistor to its maximum temperature and thereafter a constant current will flow. The delay in response can be reduced to 0.001 s by a proper choice of thermistor. The dissipation constant, which is defined as the power required to raise the temperature of the thermistor by 1 “C, is 0.14 mW or the 2000 a G-126 thermistor supplied by Fenwal Electronics. Table 1 shows the resistance-temperature characteristics of the thermistor. 2.3. Heat balance at the sensing element The temperature of the particles in a fluidized bed may vary axially as well as radially. All the particles radiate some energy and a fraction of this energy arrives at the probe. The radiation is incident at different angles and travels through the sapphire rod along different path lengths which are not easy to calculate. Therefore we assume that only particles in the vicinity of the probe contribute to the radiation incident at the probe. These particles are assumed to be at some average temperature. Further, we assume that the following quantities are small and can be neglected for
TABLE 1 Resistance-temperature characteristics of the central thermistor Temperature of the thermistor W)
Resistance @;2)
25.0 25.1 25.2 25.3
2023 2016 2009 2002
25.4 25.5 25.6 25.7
1995 1988 1982 1975‘
25.8 25.9 26.0 26.1
1968 1962 1965 1949
26.2 26.3 26.4 26.5
1942 1935 1929 1922
the purpose of the heat balance: (1) the radiation lost or received through the side of the light pipe; (2) the heat conducted through the sapphire and its supporting tube (cooled by circulating water); (3) the heat generated in the thermistor when the electrical circuit is closed for the resistance measurement; (4) the energy lost by the thermistor to the constant temperature enclosure; (5) the heat lost by thermal conduction through thermistor leads. With these assumptions the heat balance on the sensing element can be written as energy incident on the thermistor = heat lost by radiation and convection Mathematically follows:
this can be expressed as
W,A = osBA,(T4 - T;) + hA,(T - T,,)
(5)
Let
T-T,-,=AT
(6)
By neglecting higher powers of AT/T,,, eqn. (5) reduces to
W,A/A, = (4o,,T$ Therefore,
+ h)AT
(7)
172 TABLE 2 Estimated temperature rise of the central thermistor* Bed temperature (“C)
Percentage 9 of blackbody radiation transmitted through sapphire @I
50 60 70 80
0.50 0.62 0.75 0.95
Total blackbody mdiation eb x 10’ -2 (Wcm 1
Power W, received by the detector x lo4 (Wcm -2 1
Estimated temperature rise AT of the central thermistor W)
6.3 7.0 7.7 8.7
2.898 3.993 5.313 7.604
0.0250 0.0348 0.0463 0.0663
90 100 110 120
1.2 1.4 1.7 2.0
9.7 11.0 12.0 13.4
10.709 14.168 28.768 24.656
0.0933 0.1234 0.1635 0.2148
130 140 150 160
2.3 2.7 3.1 3.6
15.0 16.4 18.0 19.6
31.740 40.738 51.336 64.915
0.2765 0.3649 0.4470 0.5655
170 180 190 200
4.1 4.5 5.1 5.7
21.5 23.5 25.5 28.0
81.098 97.290 119.646 146.832
0.7164 0.8475 1.0422 1.2789
‘Using eqn. (9) and a value of h = 4 Btu ftw2 h-l “F-l as given by ref. 14.
AT=
Wt 16oszT:
+ 4h
By substituting the value of Wt from eqn. (3) into eqn. (8), the following expression is obtained:
highly idealized. For these reasons any attempt to predict particle temperatures in a fluidized bed requires that the temperaturemeasuring device be calibrated.
3. EXPERIMENTAL
AT=
SET-UP
G@%,(T) 160sxT; + 4h
Equation (9) can be used to estimate the rise in temperature of a thermistor that receives the radiation transmitted through the sapphire rod. Table 2 shows the temperature rise of the thermistor corresponding to bed temperatures ranging from 50 to 200 “C (the value of h was taken [14 ] as 4 Btu ftm2 h-l “F-l )* Tables 1 and 2 can be used to construct temperature-resistance characteristics. The broken line in Fig. 1 shows such a plot obtained with the help of eqn. (9) and Tables 1 and 2. We must point out that the plot is not exactly the same as that obtained from packed bed data (Fig. 1). The overall picture is very complicated and our assumptions for arriving at eqn. (9) are
A schematic diagram of the experimental setup is shown in Fig. 2. It consists of a fluidization column and devices for measuring temperature, pressure and flow. The fluidization column was made of four aluminium cylinders, each 6 in in internal diameter. These cylinders were placed one above the other and were held together by an exterior threaded rod in a bracket arrangement to form a column. The top and bottom cylinders were 6 in long and the two central cylinders were 12 in long. One of them had a water jacket and could be placed in either of the central positions. This column had provisions for inserting temperature-measuring devices at various points. A cone was connected at the bottom of the column for gas distribution. The cone was filled with glass balls ‘/4 in in diameter to
173 2040
l-
I
I
I
20
40
60
80 PACKEO
BED
I
I
I
I
I
I
100
120
140
lb0
180
200
TEMPERATURE,
‘C
m
Fig. 1. Calibration curve: 0, experimental data from the packed bed; ----, characteristics from Table 1.
Fig. 2. Schematic diagram of the experimental set-up: 1, fluidization column; 2, two 200-mesh screens; 3, sapphire rod probe; 4, thermometer; 5, two 200mesh screens; 6, thermistor housing; 7, water jacket; 8, manometer; 9, temperature controller; 10, constant-temperature bath; 11, thermometer; 12, heater; 13, stirrer; 14, immersion pump; 15, cooling coil; 16, rotameter; 17, diaphragm valve; 18, heater.
ensure proper distribution of the fluidizing air. Two 200-mesh stainless steel screens were placed between the cone and the column to support the particles. A 500 W heater was placed on top of the screen and was connected to a Variac which allowed the input voltage to the heater to be varied from 0 to 140 V. The resistance of the heater was approximately 25 Q . The air flow rate was measured with a rotameter which was regulated by a diaphragm valve. The air supply line was fitted with a pressure gauge to monitor the line pressure. An air filter removed compressor oil and dirt from the fluidizing air. The pressure drop across the column was
J
given by eqn. (9) and the thermistor
measured with a manometer as shown in Fig. 2. Thermometers and thermocouples were used for calibration of, and comparison with, the radiation pyrometer described below. The pyrometer for measuring particle temperature consisted of a sapphire rod which transmitted radiation from the heated particles to a thermistor. The sapphirethermistor combination is shown in Fig. 3. This consisted of a synthetic sapphire rod, 6 in long and l/s in in diameter, both ends of which were polished. Since sapphire is a delicate material and can break under mechanical stress, it was housed in a % in stainless steel tube. The annulus between the rod and the tube was fitted with Teflon which was machined for a close fit. Steel is a good conductor of heat and therefore the tube can transmit enough heat to affect the detector reading; in order to eliminate this possibility, part of the steel pipe was surrounded by a jacket for water circulation. The radiation transmitted through the sapphire rod was measured with a 2000 R thermistor (Fenwal Electronics type G-126) and a second 2000 Sl thermistor was used to measure the ambient air temperature. The thermistors were mounted on a U-shaped wire as shown in Fig. 3. Fluctuations in the ambient temperature have a considerable effect and make it impossible to reproduce thermistor readings. To eliminate the effect
174
THERMISTORS o.ooiOIA. PT. Ii? WIRE
NI-FE
b
I/;
-4406i
/--
ALLOY
T
I%1
(4
Fig. 3. The thermistor
1 WATER
IN
(b)
(a) and the thermistor
housing (b).
of changes in the ambient temperature, the thermistors were placed in a constant temperature enclosure. The enclosure was cross-shaped. One arm of the cross was fixed to one end of the sapphire rod and the opposite arm held a reflector with a concave surface. The other two arms of the cross, which were perpendicular to the sapphire reflector axis, contained the two thermistors. One thermistor was placed so that the bead of the thermistor was on the sapphire reflector axis and received direct radiation through the sapphire rod. The other thermistor was mounted so that the bead of the thermistor was kept in only one of the arms of the cross and did not receive direct radiation. The entire housing had a constant-temperature water jacket. The temperature of the bath could be controlled to within 0.05 “C. The bath had an on-off controller connected to a small immersion heater, and a cooling coil was immersed in the bath for circulating cold water. The flow could be adjusted manually. A Wheatstone bridge (5430-A, Leeds and Northrup Company) together with an external galvanometer (2430-C, Leeds and Northrup Company) with a sensitivity of 0.005 PA per scale division were used to measure the thermistor resistance.
4. EXPERIMENTAL
‘al
BEAD
PROCEDURE
AND RESULTS
The temperature-measuring device was calibrated with a 6 in bed of 0.00896 in spent cracking catalyst particles. The sapphire rod and the thermometer ends were positioned in the centre of the bed. The material was fed into the column and was heated in the fluidized state by an electric heater. The bed was allowed to settle and the pyrometer
resistance corresponding to the temperature of the immersed thermometer was measured. This process was repeated to obtain a complete calibration plot. Calibration points are shown in Fig. 1. In order to measure the particle temperature in the fluidized bed and to compare it with the bed temperature, thermometer and thermistor readings were recorded (i) by varying the flow rates when the bed was heated to 240 “C and was then allowed to cool down; (ii) with an IR heater introduced at the top during cooling; (iii) for constant flow rates of 8 ft3 min-l with varying input voltages; (iv) at flow rates of 6.2, 7.2 and 8 ft3 min- ’ to study the effect of fluidization velocity on the particle temperature. Figure 4 compares the thermistor resistance with the bed temperature in a packed bed and in a fluidized bed under various conditions. The top line represents the packed bed characteristics. The bottom two lines show the cooling characteristics with and without IR heating. Between these lines are points which represent fluidization at three different velocities.
5. DISCUSSION
The only source of heat for the thermistor is the radiant energy from the particles that is transmitted through the sapphire. This means that the temperature measured by the thermistor is the temperature of the particles. A thermometer immersed in the bed measures the particle temperature in the case of a packed bed and the bed temperature in the case of a fluidized bed. In principle a pyrometer probe at any point in the packed bed receives radiation from all
175
i?
z
c”
1960
I %
I940 1920 20
I
I
I
I
I
i
I
40
60
60
lea
120
I40
160
BED
TEMPERATURE,
1
160
1
200
k
Fig. 4. Temperature-resistance relation for packed and fluidized beds: curve 1, packed bed; curve 2, fluidized bed during cooling; curve 3, fluidized bed during cooling when heated with an IR heater; 0, fluidiz$ bed flow rate 8.0 ft3 min? ; A, fluidized bed flow rate 7.2 ft3 min-’ ; q, fluidized bed flow rate 6.2 ft3 min .
possible directions, but in practice radiation coming from particles at some distance from the top of the probe is liable to be intercepted by particles around the end of the probe. Furthermore, when a heated bed is allowed to cool by itself the maximum temperature will be at the centre of the bed, i.e. near the end of the probe. Based on these arguments we selected a packed bed for the purpose of calibration and we assumed that the temperature so obtained will be the average temperature of the particles around the end of the probe. Figure 1 is the calibration plot and the line obtained using eqn. (9) in conjunction with the temperature-resistance characteristics of the thermistor (Tables 1 and 2). The two lines are seen to be very close. It can be seen from Fig. 4 that the data with and without IR heating are consistent: particle temperatures stay higher during the cooling cycle with IR heating. For a given bed temperature the thermistor readings for the packed bed and the fluidized bed are different, showing that the particle temperature (recorded by the thermistor sapphire pyrometer) differs from the bed temperature (recorded by the thermometer). The particle temperature is given by the intersection of the constant-resistance line that passes through the point of the bed temperature and the R-T curve for the packed bed. Curve 2 in Fig. 4 is the cooling curve for a heated fluidized bed. The cooling process has the advantage that it creates a situation in
which the particles are at a higher temperature than the fluidizing air until the process is complete. The temperature difference was further increased by introducing an IR bulb at the top of the column which heated the particles as the column was being cooled by the fluidizing air. Curve 3 of Fig. 4, obtained for simultaneous heating (by the IR bulb) and cooling, helped us to analyse the character of a fluidized bed for the purpose of predicting the local heat transfer coefficient and of determining the relation between the particle, gas and bed temperatures (eqn. (10)) (see Section 5.1). It has been pointed out that the data with and without IR heating are consistent and that during IR heating the particles are at higher temperatures. Thus we may conclude that in a fluidized bed the particles are at a higher temperature than the bed temperature as measured by an immersed thermometer. This may be why all the fluidized bed points fall below the packed bed line (Fig. 4). However, because of the highly turbulent character of the fluidized bed the difference between bed and particle temperatures is small and this could explain the small scatter of the points in Fig. 4. 5.1. Solid-gas temperature difference during cooling The data of Fig. 4 for a bed cooled at a gas flow rate of 8 ft3 min-’ are replotted in Fig. 5. Here T, is the calibration temperature corresponding to the pyrometer resistance
176
Two time-dependent energy balances may be written for T,(t) and TB(t) during the time t of the cooling process. These are as follows:
210
190
dTi3=
%F*
dt
M,C,
dTs = --MT, - TJ
I70
w,C,(T1
-
T&) + h,(T,
-
Tg) (11)
dt
(12)
150
Initially T,, = T, = 210 “C, and when the cooling process is complete we expect that T,, = T, = Tf = T1 = 25 “C. Equation (10) is used to eliminate TB from eqns. (11) and (12). By eliminating time as a variable the resulting expression can be written
130
I IO
dy 90
d In x
Y
(13)
where y = (T, - T,)/(T, - Tl) and x = T, - T1. The constants are
70
50
,ALB-y
/ ^^ 9”
1
.._ II”
I
130 BE0
A’=a
I
I
I
I
IS0
170
190
210
TEMPERATURE,
T,,%
Fig. 5. Fluidized bed cooling characteristics: particle and gas temperatures vs. bed temperature for a gas flow rate of 8 ft3 min-l . The points are experimental data from Fig. 4. The curve drawn for T, is from eqns. (10) -(12) with a = 0.2 and h, = 1.07 cal s-l “C-l. The line shown for T, is from eqn. (10) with D = 0.2.
and Tb is the bed temperature, i.e. the reading of a thermometer immersed in the fluidized bed. (For example, when T,, is 180 “C the pyrometer resistance is about 1960 a. This resistance corresponds to a calibration value of l’, = 190 “C from the packed bed curve of Fig. 4.) When the calibration curve is applied to a fluid&d bed, T, represents the particle temperature. The bed temperature T,, is determined by T, and the gas temperature Tg. The three temperatures are related, and we postulate that
Tb = UT, + (1 -a)T,
(10)
where 0 < a < 1. The evaluation of (I will give the quantitative relationship between the three temperatures.
B =a2
p+E(l+y-)/ KG+J, Mfhs
(14) (15)
The boundary condition from eqn. (13) is that y = 0 when x = 210 - 25 = 185 “C. Exact solutions can be obtained for eqn. (13) (with different forms depending on the sign of dy/d In x + y) and can be used to deduce the values of A’ and B. A reasonable estimate of the parameters can be obtained from the data points in Fig. 5. The experimental data for the experiment of Fig. 5 were as follows: MS = 976 g; M, = 6 g; C, = 0.21 cal g-l “C-l; C, = 0.24 cal g-’ “C-l; wg = 4.6 g s-l. These values together with the data points of Fig. 5 and eqn. (13) lead to the estimates a = 0.2 and h S= 1 *07 cal s-l “C-l. The last value corresponds to an average particle-gas heat transfer coefficient of 10m6 cal cmw2 s-l “C-l. This is in excellent agreement with previous results (see Fig. 6 in ref. 2: Jh = 0.00105, Re = 3.5, D, = 0.00076). The estimate a = 0.2 suggests that an immersed thermometer measures a bed temperature which can be determined by adding 80% of the particle temperature and 20% of the gas temperature (eqn. (10)). The bottom
177
curve of Fig. 5 shows the variation of Tg as calculated from eqn. (10) with a = 0.2. Any vertical line will give the temperature difference between the particle and the gas. During the cooling process the gas and particle temperatures apparently differ by as much as 70 “C. This is an unexpectedly large difference, suggesting that the well-known uniformity of fluidized bed temperatures may disguise substantial non-uniformities between local particle and gas temperatures.
6. CONCLUDING
REMARKS
c,,G eb ebk G
h h,
M,. M, R t(X) T AT
The pyrometer used in this work to measure particle temperature can be considerably improved. We shall discuss some of the important factors. (i) Vollmer et al. [ 81 have reported the characteristics of sapphire and have shown that the smaller the rod the higher the cut-off wavelength. Equation (1) indicates that the power transmitted through the sapphire will increase for a higher cut-off wavelength. Thus the probe length can be chosen according to requirements. (ii) A thermistor with better sensitivity will give a quicker response. If the thermistor is larger, the power arriving at the thermistor increases but it may take more time to reach the steady state. A compromise between size and sensitivity is necessary to obtain the best performance. (iii) The thermistor housing is the most important part of the equipment. A small change in housing temperature can affect the accuracy of the measurement markedly. Equation (9) shows that the heat loss due to atmospheric cooling is considerable; this can be eliminated by using an evacuated enclosure. (iv) An ideal reflector may also increase the amount of radiation incident on the thermistor.
NOMENCLATURE
:
A’ 4,
B
parameter in eqn. (10) projected area of the thermistor, cm2 defined by eqn. (14) surface area of the thermistor, cm2 defined by eqn. (15)
wg wt X
Y
heat capacity total black-body emissive power, defined in eqn. (4) Planck’s distribution function geometric transfer function heat transfer coefficient average heat transfer coefficient between the particles and the gas multiplied by the particle surface area, cal s- ’ “C- ’ total mass, g reflection correction transmissivity function temperature, “C temperature difference defined in eqn. (6), “C gas input flow rate at temperature T1 power arriving at the thermistor detector, W cmv2 (T, - Tb)/( T, - T,), variable in eqn. (13) T, - T1, variable in eqn. (13)
Greek symbols x wavelength, I.trn A, uSB
d
cut-off wavelength, I.tm Stefan-Boltzmann constant fraction of black-body radiant power below X, = 4.07 /.ull
Subscripts b g :
bed gas solid enclosure
REFERENCES J. J. Barker, Znd. Eng. Chem., 57 (5) (1965) 33. J. R. Ferron and C. C. Watson, Chem. Eng. Prog. Symp. Ser. 58, 38 (1962) 79. M. Leva, Fluidization, McGraw-Hill, New York, 1959. J. S. Walton, R. L. Olson and 0. Levenspiel, Znd. Eng. Chem., 44 (1952) 1474. J. Eichhom and R. White, Chem. Eng. Prog. Symp. Ser., 48 (1952) 11. W. W. Wamsley and L. N. Johanson, Chem. Eng. Bog., 50 (1954) 347. R. W. Astheimer and E. M. Wormser, J.Opt. Sot. Am., 49 (1959) 179. J. Vollmer, G. C. Rein and J. A. Duke, J. Opt. Sot. Am., 49 (1959) 75. E. V. Loewenstein, J. Opt. Sot. Am., 51 (1) (1961) 108.
178 10 I. H. Malitson, F. V. Murphy, Jr., and W. S. Rodney, J. Opt. Sot. Am., 48 (1958) 72. 11 U. P. Oppenheim and U. Even, J. Opt. Sot. Am., 52 (9) (1962) 1078. 12 K. H. Lee, M.S. Thesis, University of Delaware, June 1960. Technical Manual, Fenwal Elec13 Thermistor tronics, 1970. 14 R. B. Bird, W. E. Stewart and E. B. Lightfoot, Transport Phenomena, Wiley, New York, 1960.
(A7) Substituting for dT,/dT, and (Tl - T&l( T, T& in eqn. (A4) from eqns. (A7) and (A6), respectively, yields the following relation after rearrangement: 1
wgc, M,Cs
l+__+_
APPENDIX
MgCg hs
T.s- Tb
T,, = aT, + (1 -a)T,
2
- TB) + h,(T,--
- TJ
T, - Tg
Tg = {Tb - (1 -a)T,}/a
T, .- Tg Differentiating
KC, wg Ts- Tl -M,
h, T,--T,,
MsCs w, Ts- TI --M,
h, T,-T,
(A3)
(A4)
Ts - Tl Ts -Tb eqn. (A5) with respect
=
X
T, - TI
(AlO)
A’=ajl+z
cl+?)\
(All)
and (A5)
Eliminating Tg from ( TI - TJ/(Ts - TB) using eqn. (A5), the following expression is obtained: =1-a-
-
(A91
w&g TI - Tg -1
KC, dT, h, From eqn. (Al)
-’
TJ (A2)
Time is eliminated as a parameter altogether by dividing eqn. (A2) by eqn. (A3) giving
KC, --=-_ dT,
MgCg1
(Al)
dT, = w,Cg(T1 M&B dt dT, = -h,(T, dt
2
-- Ts - TI -’
Derivation of eqn. (13) Starting from eqns. (10) - (12), Tg and the time derivative can be eliminated as follows:
Tl -T3
dT,
KC,
(
=a
M,C,
dTb
Ti - Tb ---T,-TT,
w3) to T,
B =a2
Mscsw,
(A121
M,hs Substituting the values of Y, LX,A’ and B from eqns. (A9) - (A12) into eqn. (AS) leads to the following expression:
dy d In x
=A'?
-y
Y
(A13)