Literature Cited Abraham, B. M., Fiotow, H. E., Carison, R. D., Proc. lnt. Conf. Peaceful UsesAt. Energy, 7, 166 (1958). Bergman, P. D . , MSChE Thesis, Purdue University, Lafayette, Ind., 1962. Christiansen, E. B., Craig, S. E., Jr., Carter, T. R., Trans. SOC. Rheol., 10, 419 (1966). Christiansen, E. B., Jensen, Gordon E., AlChE J., 15, 504 (1969). Christiansen, E. B., Keisey. S. J., "First Pacific Chemical Engineering Congress," Part I I , pp 289-293, The Society of Chemical Engineers, Japan, Kyoto, Japan, 1972. Christiansen, E. B., Kelsey, S. J., Chem. Eng. Sic., 28, 1099 (1973). Christiansen, E. B.. Ryan, N. W., Stevens, W. E.. AlChE J., 1, 544 (1955). Coleman. B. D . , Noll, W., Ann. N. Y. Acad. Sci., 89, 672 (1961). Fredrickson, A. G., Ph.D. Thesis, University of Wisconsin, Madison, Wis.. 1959. Fredrickson. A. G., Bird. R. B., lnd. Eng. Chem., 50, 347 (1958). Laird, W. M., lnd. Eng. Chem., 49, 138 (1957). Lamb, H., "Hydrodynamics," 6th ed, p 586, Dover, New York, N. Y., 1945. McEachern, D. W., Ph.D. Thesis, University of Wisconsin, Madison, Wis., 1963.
McEachern, D. W.. AlChE J., 12,328 (1966). Neb'rensky, J., Wein. 0.. Ulbrecht. J., Collect. Czech. Chem. Commun., 35, 1964 (1970). Salt, D. L., Ryan, N. W., Christiansen, E. B., J. Colloid. Sci., 6, 146 (1951). Siibar, A,, Pasiay, P. R . , 2. Angew. Math. Mech.. 37, 441 (1957a). Slibar, A.. Paslay, P. R., Petrol. Trans. Am. lnst. Mech. Eng., 210, 310 ( 1957b). Thomas, D. G., "Progress in International Research on Thermodynamic and Transport Properties," J. F. Masi and D. H. Tsai, Ed., pp 704-717, Academic Press, New York, N. Y., 1962. Thomas, D. G., "Solids Dispersed in Liquids," Oak Ridge National Laboratory Report CFN 56-10-35. 1957; also "AEC Reactor Handbook." Vol. IV, 2d ed, S. McLain and J. H. Martens, Ed.. Sec. 1.4.2., pp 2535, Interscience Publishers, New York, N. Y., 1964. Vaughn, R. D., Bergman, P. D., lnd. Eng. Chem., Process Des. Develop., 5 , 44 (1966). Walker, J. E.. Shan, G. A., Rothfus. R. R.. AlChEJ., 3, 484 (1957).
Received for reuiew February 13, 1974 Accepted June 3, 1974
Heat Transfer during a Flash Drying Process Stanley Debrand Philip Morris Research Center, Richmond, Virginia 23267
The particle velocities and flow patterns in a flash dryer have been determined. The slip velocities, Reynolds numbers, and residence times of particles for different pneumatic duct segments were calculated at different applied gas velocities. The relationship between the rate of particle drying and the processing conditions (such as gas velocity and temperature, loading rate, etc.) for a pneumatic flash dryer is discussed. For a typically designed flash dryer, three zones representing a high heat flux between the gas and conveyed particles have been established: the feeding point, the elbows, and the cywas established. clone. The correlation Nu = 0.00076Re'~64Pr0~52
Introduction Fulford (1969), in a major survey of research on drying of solids, comments that drying remains largely an art. This remark seems to apply to flash drying to a larger extent than to any other type of drying. To carry out a flash drying operation, one must be able to form a suspension in a gaseous drying medium either directly or with back mixing. The typical flow system consists of a heater, drying duct, and a separator (cyclone). A modification of this system could include a dispersion mill which is required t o break up the product into an acceptable particle size. In order to establish the heat flux between a drying particle and a gas stream in a flash dryer, it is necessary to determine the gas-particle heat transfer coefficient. The heat transfer coefficient (included in the Nusselt number) depends on the Reynolds number of the particle and this, in turn, is a function of the relative velocity (the difference between the particle and the gas velocity, or the socalled slip velocity). All processing conditions which significantly change the average particle velocity will affect the Reynolds number. For this reason, processing variables such as the geometry and diameter of the pneumatic duct, the loading rate, and the shape and density of the conveyed particles (all of which noticeably change the average particle velocity) have to be taken into account 396
Ind. Eng. Chem., Process Des. Develop., Vol. 1 3 , No. 4, 1974
when considering the heat flux between the gas and the flowing particles. In a published survey of pneumatic drying equipment (McCormick, 1969, 1970), it was suggested that pneumatic dryers are more efficient than rotary dryers. However, this statement was not supported by any technical data. Only a few publications have dealt with the mechanism of drying pneumatic conveying. Elperin (1956) has considered the drying of grain in a suspended state and suggested a pulsated gas stream to intensify the drying process. If we consider drying in a straight duct section during pneumatic conveying, the moisture content in the drying product ( H ) for a given initial moisture level (Ho) varies with the distance ( L s )from the feeding points according to the 1969) relation (Lisovaya, et d.,
H = HoembL, where b is a coefficient depending on the material properties and the drying conditions. A description of the alterations which occur in the flow field about an inverse sphere as the particle Reynolds number increases has been given in the literature (Chang, 1970). In the movement of nonspherical particles, we have sometimes observed (using high-speed photography) rotation of the particles. Turbulence plays a significant role in
determining the boundary layer for such particles (Torobin and Gauvin, 1960). The distribution of particle concentration, mass flow, and velocities in a vertical pipe are other parameters (Soo, et al., 1964) which should be taken into account. For a p-size particle, the concentration increases near the wall of the pipe, whereas mass flow decreases. The drag coefficient appears to depend primarily on the magnitude of the relative turbulence intensity and on the particle Reynolds number. The determination of the particle velocity and the concentration distribution represents a complicated problem for nonspherical particles. One of the recently described methods utilizes stereophotogrammetry (Reddy, e t al., 1969). It has been applied to measure the local mean and turbulence velocity components of the particles in a solid-gas flow in a vertical pipe. In designing a flash dryer, the minimum flow rate for dilute phase solids transportation in a gas stream should be established. A review of the available experimental data (Doig and Roper, 1963) related the Froude number, the loading rate ( L ) ,and the entrainment particle velocity (Vt) according to the equation
v, - 2 log (Fr) = -+ 0 . 2 5 log L 28 This correlation seems to be valid for larger duct diameters. It appears then that a small tube diameter (below 2 in.) results in a marked surface/volume effect upon the saltation behavior. Some equations have been developed (Lappe and Shepherd, 1940) for calculating the path taken by particles undergoing accelerated motion. The fundamentals of particle motion are usually expressed by a plot of the drag coefficient (CD) us. Reynolds number as suggested by Rayleigh. Trajectories have been calculated for particles decelerating in air in the absence and in the presence of a gravitational field. A determination of the drag coefficients in an accelerating field has been attempted by many investigators, but such determinations are difficult and the results show contrary trends. Measurements of the pressure drop of a gas-solid flow for a low loading rate have been investigated. Treating the twophase gas-solid suspension as a continuum, the momentum equation was developed. By use of a model, good agreement with the experimental data including acceleration effects was observed (McCarthy and Olson, 1968). An investigation of the particle slip velocity as a function of the loading ratio and the particle terminal velocity has shown the interrelationship of these parameters for a high turbulent air stream in a vertical pipe (Reddy, et al., 1969). For pneumatic conveying, the average steady (IV)slip velocity correlated by dimensional analysis has been described in the literature (Foeking, 1950) for a very dilute flow. At higher loading rates for conveyed particles (Soo, e t al., 1964) the gravity effect becomes significant for large pipe diameters and large particle concentrations. For the horizontal pipe, the velocity distribution is asymmetric about the pipe axis. In order to determine the heat transfer coefficient in a flash dryer, the correlation between Nu, Re, and Pr numbers should be established. The general form of this correlation (Boothroyd, 1971) is given by the equation Nu = a + bRenPrm. The exponent ( m ) of the Prandtl number is primarily a function of the Reynolds number (Hoffman and Ross, 1972) according to the equation m = 1/3 + 213 exp( -0.85Re0.24). Mass transfer causes a decrease in the convective heat transfer rate. The influence of mass transfer on the heat transfer may be expressed by the equation
Nu = NuoPrmB where B is a function of the Spalding number. During the conveyance of nonspherical particles, a significant fraction of the available kinetic energy is transformed from energy associated with mean flow to energy associated with turbulence and this would increase significantly the exponent of the Re number (Frantz, 1961; Jiracek, et a l , 1972; Moscicka, 1970; Thomas and Fan, 1971; Torobin and Gauvin, 1960). According to several authors (Luikov, 1966; Morgan and Yerazumis, 1967; Smolsky and Sergeyev, 1962), the drying process requires the use of the Gu number equation for the evaporation process. The rate of evaporation of water depends also on the humidity of the heating medium (Yoshida and Hyode, 1970). Reviews of the particle-fluid heat transfer coefficient have been given in the literature (Boothroyd, 1971; Thomas and Fan, 1971). In addition, a substantial portion of the drying process occurs in the cyclone. The phenomena of heat and mass transfer between the particle and the gas stream in the cyclone are related mainly to the field of turbulence (Meline, 1967; Molyneux, 1967). The relationship between the Nu number and the degree and the scale of turbulence has been observed (Moscicka, 1970). The approach given by Burov and Nikolaew (1961) allows one to estimate the residence time during which the turbulent gas remains in contact with the surface of particles. In order to determine the heat transfer between the flowing gas and the particles in a flash drying equipment, the processing conditions and the material properties should be in a range where the external heat transfer controls the drying process. The value of the Biot number determines whether or not these conditions prevail (Luikov, 1966). Objectives This work was undertaken to determine how the heat transfer between gas and particles depends on different processing conditions such as gas velocity, loading rate, etc., in a pneumatic duct for flash drying. The following specific determinations have been made: (1) the conveyed particle velocity along a duct containing two elbows, the resulting residence time of the particle in the pneumatic duct, the gas-particle mean slip velocity for different duct segments, and the particle Re number; (2) the flow pattern and its dependence on the duct configuration; and (3) the drying rate as a function of different processing conditions, the gas-particle average heat transfer coefficient for a flash dryer, and the correlation Nu = f(Re; Pr). Experimental Section Material Used. The basic schemes for representing colloidal porous bodies by models are described in the literature (Luikov, 1966); the tomato leaf belongs to this class of material. Cut tomato leaf (Lycopersicum esculentum) has been used for drying studies. The leaves are cut to li31-in. strips of varying lengths with a thickness in the range of 100 to 120 g. The chemical composition of tomato leaf is described in the literature (Mathan and Cole, 1964). The drying curve (Chang, 1970; Chenikov and Krasivski, 1972) and the thermal diffusivity (Locklair, e t al., 1957) for a leaf having a porous-colloidal structure (Luikov, 1966) have been reported. However, the flow pattern found in a pneumatic duct and resulting slip velocity have rather general character and are factors independent of the properties of the material used. The particle flow pattern has been determined for polyethylene beads (spheres) having an apparent density of 0.6 g/cm3. The material used in these experiments consists of plant leaves with properties similar to those of cut tomato, lettuce, or cabbage leaves. The apparent density of particles to be dried was in the range 0.9 Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4. 1974
397
LOCATION IN A DUCT WHERE THE PARTICLE VELOCITIES WERE DETERMINED.
Figure 1. Scheme of glass tower.
to 1.0 g/cm3. The appearance of the flowing particles is shown in Figures 2a, 2b, and 2c. Apparatus a n d Procedure. A schematic of the 4-in. diameter pneumatic conveying tower constructed of Pyrex glass is shown in Figure 1. The gas velocity was measured using a flow tube and was controlled by adjusting the blower speed. The gas temperatures were measured with high suction thermocouples inserted into the center line of the gas stream. The material was fed to the tower through an air-lock feeder operating at 30 rpm. The material was removed from the gas stream with a cyclone separator fitted with a rotary air-lock discharge valve. The pressure level in the tower was controlled by a throttling valve located downstream from the blower. A Wollensak Optical Co. Model WR-4, 16-mm Fastax camera equipped with a WF-220 Vari-Focus zoom lens was used for taking the high-speed motion pictures. Lighting was provided by four 750-W spotlights arranged to prevent glare and to provide 50,000-65,000 ft candles illumination. Camera distance was 56 in. from the center of the tower. The total filming time was approximately 0.8 sec per reel, and a maximum film speed of approximately 6400 frames per second was used. High-speed motion pictures of the moving particles were taken at different gas velocities at tower locations indicated in Figure 1. A 2-in. r e h e n c e grid was taped to the back of the glass pipe at each location so that the particle travel could be accurately measured. A strobe light operating at 10,000 rpm was focused on an opening cut in the grid pattern to provide timing marks on the film. The stroboscope timing marks were necessary because the film speed was not constant. The camera accelerates continuously over a 100-ft reel of film, so the film speed must be plotted for the entire run. The time intervals between flashes were known (6 msec), and by viewing the film on a stop-action projector, the frame numbers during which the flashes occurred could be recorded (See Figure 2). 398
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4 , 1974
By knowing the number of frames between two stroboscope flashes for a certain film portion and the number of frames during which particles travel the distance of 2 in. (between the two scale lines), we were able to calculate the velocities of the particles. For each tower location (points 1 to 9), the velocities of 100 particles were determined. Knowing the distance along the length of the tower which the particles must travel and their average velocity, we may easily calculate the particles' residence time for each segment of the tower. The amount of heat transferred from the gas to the particles was evaluated by measurements of the amount of water evaporated from the particles plus the calculated heat absorbed during the heat-up period. The oven method (forced heating of the samples at 212°F) was used to determine the initial and final moisture level in the particles (Locklair, et al., 1957). The gas temperature (Walton, et al., 1952) was measured by a high-suction thermocouple. The assumption was made that the particle surface temperature corresponds to 212°F (for 100% stream). Much more needs to be done in order to evaluate the driving force (Atemperature) (Mann and Feng, 1968). Results and Discussion Flow Pattern. In order to calculate values of the particle Re number during the flash drying process, it is necessary to establish the slip velocity for the different sections of the pneumatic duct. The question arises as to how quickly the particles reach their final velocity. This problem is related to the value of the drag coefficient for the accelerated particles. Usually the assumption is made that the drag force which the flowing fluid exerts on the body is due to the inertia of the fluid and is proportional to the square of the slip velocity. A V2 F = C D A p g ~
An empirical expression relating CD and V for a given particle and fluid is as follows
where b is in the range from 0.1 to 0.2 for 10 < Re < 1000. For a steady state (when the accelerating force is zero), the empirical equation derived by Schiller and Nauman (Boothroyd, 1971) fits the experimental data which correlate the drag coefficient and the Reynolds number.
c,
=
24
+ 0. 15Re0.687)
Let us keep in mind that for Re < 0.2, the particle flow regime is laminar, and for Re > 1000, it is fully turbulent. Further, analysis shows that the relationship between CO Re2 us. Re can be established. Knowing the Re number, the value of CO might be found. Let us calculate the acceleration distance needed for the particles to reach 9070 of their final (steady) velocity in an air stream having a velocity of 80 ft/sec. Let us assume that the final slip velocity is 7 ft/sec (equal to the entrainment velocity). Initially, the slip velocity is 80 ft/sec. The slip velocity at any given time is expressed by (80 - Vparticle). It decreases until a particle velocity of 0.9 X 73 = 63.7 ft/sec is reached. A stepwise solution of eq 2 predicts that this velocity will be obtained in a distance of 11.5 ft during a time of
A
I-
C
8
*
00002 sec
F&re 2a. Pictures of the consecutive frames. In picture A observe the timing mark (flush) made on the film by a stroboscope light. Ob. serve the movement of the particles as they move through consecutive framek. A scale with transvene lines at 2-in. intervals is also seen.
A
B
Figure 2b. Pictures of the consecutive frames. Single particle flovv. Observe not only the streamline hut also the rotating movement of the particles as it moves through consecutive frames.
C
D
Figure 2e. Pictures of the consecutive frames. Dense particie flow . (IhseNe not only the streamline but also the tumbling movement of particles as they move through consecutive frames. In picture D 01)serve the timing mark (flush) made on the film by a stroboscope
light. 0.242 sec; application of eq 3 and the relationship CoRe2 us. RE gives a distance of 13-14 ft. Experimental data for particles having the same equivalent diameter which were conveyed in a 4 in. diameter duct showed that the particles were accelerated to a velocity of 65 ft/sec with a distance of 2.5-3.0 ft. When particles were conveyed in a pipe having a bulged section with a larger cross-sectional area, the gas velocity in the bulge was slowed to 7 ft/sec (particle entrainment velocity). The particles entering the bulged section have a n initial velocity of 65 ft/sec; they decelerate to nearly zero velocity within a distance of 2.5-3.0 ft. A comparison of experimental data with those obtained from calculations based on the drag coefficient value for a steady-state condition is not applicable for calculations of the acceleration or (deceleration) pattern of the particles. A typical distribution of the particle velocity (for location l (Figure l) on the duct) is shown in Figure 3. The typical particle velocity (polyethylene heads having yS in. diameter) in the flash drying duct is shown in Figure 3 for an air velocity of 140 ft/sec. An analogous pattern of particle velocity was observed for medium-size particles. The large particles are here defined as the particles which stay on the 10-openinglsq in. screen; the medium size particles which pass through 10-openinglsq in. and are retained on 20-opening sq in. sieve; and short, which pass through 20 and are retained on 30-opening. Figure 4 shows the arithmetic means of the particle velocity as a function of the tower length.
m. m07
2
IO.
r e
The influence of the loading rate on the particle velocity for a gas velocitv of 70 ftlsec is Dresented in Figure 5. , With a higher ga!3 velocity, the velocity differences for two loading rates (sh,own in Figure 5) at tower locations 1, 3, -.."A:-" A-:.?.. "-2 ,"...".I,..rruuwrl -."-~ 1 and 8 (after the 'Lcc'ylLls wnr LalBrl than for other points. The average slip velocities for the consecutive 20-in. segments in the duct and the residence time of the medium-size particles are shown in Table I. A high slip velocity of the gas particles occurs in relatively short duct segments for a distance of 2.5 ft from the feeding point and for a distance of 2.5 ft from the curvature of the elbow. For an applied gas velocity of 70 ft/sec, the average final slip velocity is in the range of 15-20 ft/ ~~~
I
~~~
.
~
~
I
-----
Ind. Eng.
Chem.. Process Des. Develop.. Val. 13, No. 4, 1974 399
teristic dimension of the conveyed particles. For a particle shape such as that of cut tomato leaf, the characteristic dimension (Le., the equivalent sphere diameter) should be established using an experimental approach. The measured entrainment velocity of the particle a t room temperature was about 7 ft/sec. For the laminar-turbulent range of particle flow (Boothroyd, 1971) 0.2 < Re < 1000, the following equation related to the entrainment velocity ( Vt) is applicable
TOWER LENGTH lmearurd fmm Centu of bed tHI IN INCHES
where CD can be found according to eq 3; Re is also given as a function of Vt
Figure 4. Arithmetic means of the particle velocity as a function of the tower length. b GAS VELOCITY 70f1h.c. LOADING RATE 420p/rnn
10 I
0
i
~
20
40
a
no
.
~ IW
,
7
120
~ 1 0 .
~ n O R i Z O N T A ELBOW L ~ VERTICAL
TOWER LENGTH lrneosurcd fmm center
ISO
180
,
~
200
220
~ 240
260
280
l
ELBOW -rtC?cnWlZONT&-6
of bed tee) W INCHES
Figure 5 . Mean particle velocity for two loading rates: top curve, 84 g/r:iin; bottom curve, 840 g/min. sec. For an applied gas velocity of 140 ft/sec, the final slip velocity doubles to about 30-40 ft/sec. The entrainment velocity was about 7 ft/sec for these particles. Therefore, the entrainment velocity cannot be considered as the average final slip velocity during the flash drying process. The average particle velocity at the very dilute loading rate was several feet per second higher than at the denser loading rate. Acceleration of the particles beyond the elbow was more sluggish for the higher loading rate compared to the more dilute loading rate (Figure 5). Particle velocities have also been determined for particles having different sizes, densities, and shapes (see Table 11). The large particles travel faster than small particles having the same density. Flake-shaped particles present the largest resistance to pneumatic conveying. The difference in particle density does not play a very significant role for the types of particles investigated. A study of the flow patterns in the 1.5-D radius-of-curvature elbow has revealed that particle velocities are drastically reduced in traversing the elbows. Therefore, the elbow segment is another region of high slip velocity. The particles tend to merge against the outside curvature forming a dense "column flow" as they exit the elbow (Figure 6). This column is effectively redistributed by the gas turbulence within a distance of approximately 1 ft. For a 4.0-D radius-of-curvature elbow, redistribution of a dense column flow occurs within a distance of 3-4 f t . Redistribution of the particles after the feeding point occurs at a distance of about 1 f t for the small pipe diameters (Figure 6). The observation of a flow pattern in the elbow and feeding point areas reveals the existence of a highturbulence field. By determination of average slip velocity, the Reynolds number can be calculated. However, to establish the Reynolds number, it is also necessary to know the charac400
Ind. Eng. C h e m . , Process D e s . Develop., Vol. 13, No. 4 , 1974
By application of a trial and error method for the solution of these three equations (3, 4, and 5), a value for d of 0.06 cm (equivalent sphere diameter) was determined. The calculated Re number for a particle is presented in Table I. The range of the Re number varies from about 60 to 330, depending on the applied gas velocity and the location in the pneumatic duct. Heat Transfer Coefficient. The heat transfer coefficient is proportional to the Reynolds number, but the ex' ~ I ~ ponent' for the ' Re number depends on many parameters as we have seen above. The heat transferred during the flash drying process might be considered as being the result of the following three different stages: (1) drying during high gas-particle slip velocity which occurs after the feeding point and at each elbow; (2) drying during a nearly steady particle velocity (after the acceleration period) in the straight duct section; and (3) as a result of cyclone performance as a dryer. The total heat transferred between the gas and particles (Q,) during each of these stages may be expressed by the equation Q, = h, (Atemp)(Atime)F; h, = f(Re, Pr) A determination of the particle velocity allows the arithmetic mean of the residence time (in seconds) of the particle in each pipe segment to be obtained (Table I). The driving force (Atemp) is not constant. It is high for the initial heat-up period of drying and then decreases. The surface area ( F ) available for the drying process does not depend only on the properties of the particles but also on the flow density. Another factor related to the rate of drying is the hot gas composition. For a high moisture level in the conveyed particle and for certain conditions of processing, we have observed an increase in the moisture level of the particles exiting the duct (before the cyclone) after applying a steam-air mixture. It is obvious that during the heat-up period, a portion of the heat might be transferred by the condensation process. When the surface temperature is lower than the dew point of the gas, condensation might be observed. The condensation process was not observed for a high degree of steam superheat and high convective heat transfer coefficient. Other authors (Trommelen and Crosby, 1970) observing the drying of drops in superheat vapor have reported a 12.5% increase in weight during the first drying period when the particles were exposed to superheated steam (50°C) at atmospheric pressure. The initial drop in temperature was about 25°C. Let us analyze some of the experimental observations of the drying process and correlate them with the particle
~
L
Table I. A. Average Slip Velocity for Consecutive 20-in. Segments in the 4-in. Glass Tower, Loading Rate 420 g/min Segments measured from the f i r s t elbow-vertical duct; av s l i p velocity. ft/sec
Segments measured f r o m the feeding point-horizontal duct; av s l i p velocity, ft/sec -
Gas velocity 70 f t / s e c Re number Gas velocity 140 ft/sec Re number
-
1
2
3
4
5
6
7
8
38
22
18
24
18
17
16
15
97.9 47
80.1 42
80.1 40
75.7 38
75.0 35
62.3 34
169.2 75 334
187
209
106.8 52 187
178
169
167
152
B. Mean Residence Time of the Particles in the Tower (without Cyclone) Quickest p a r t i c l e s q
Average particles
Slowest particles
0.470 s e c 0.557 s e c Gas velocity 0.640 s e c 70 ft/sec 0.216 s e c 0.256 s e c 0.280 s e c Gas velocity 140 ft/sec a The arithmetic mean of 20% particles (quickest portion). The arithmetic mean of 20% particles (slowest portion),
Table 11. Particle Velocity Gas velocity 70 f t i s e c
Gas velocity 140 f t i s e c
Particle size
Location no. 3
Location no. 7
Location no. 3
Location no, 7
Long s i z e , density 1.0 g/cc Short s i z e , density 1.0 g/cc Flake -shaped particles. density 1 . 1 5 g/cc Long s i z e , density 0.37 g / c c
42.7 40.7 37.1
57.4 53.8 52.0
82.7 81.5 72.2
112.5 107.4 106.5
43.4
58.0
94.5
115.1
velocity and the flow pattern in a pneumatic duct. The heat transfer coefficient is proportional to the Reynolds number and, therefore, to the slip velocity which is about two times higher for a gas velocity of 140 ft/sec, compared to a gas velocity of 70 ft/sec. A comparison of the heat coefficient for different duct segments was performed by using the equation (Frantz, 1961)
Nu = 0.16Re'.3Pr0.67 The velocity and thermal conductivity of the applied gas mixtures have been calculated from the values of pure components using the method published by Bromley and Wilke (1951). The P r numbers of the applied hot gases were 0.743, 0.972, and 1.014. Table III presents the comparison of the average heat transfer coefficient between gas and particles in a consecutive 20-in. segment of the pneumatic duct in a flash dryer for two applied gas velocities of 70-140 ft/sec (Pr = 0.743). With a change in the gas velocity from 70 to 140 ft/sec, the ratio of the heat transfer coefficients at different tower locations (location no. 7 and 9) varied by an order of magnitude. The Nu number for the last segment is 3.5 at a gas velocity of 70 ft/sec, but for the initial segment at gas velocity 140 f t / sec, Nu = 30.8. Table IV shows the total amount of heat transferred from the hot gas to the particles conveyed in the duct and separated in the cyclone. Increasing gas velocity increases
significantly the slip velocity and the related heat transfer coefficient. However, the residence time of particles diminishes the effects of the higher particle slip velocity. Comparing the influence of shorter residence time and higher heat transfer coefficient on the total heat transfer between gas and particles (if we apply higher gas velocity), it was found that the overriding factor is a higher slip velocity. Thus a t higher velocity, the drying process was more effective. Assuming that the cut tobacco leaf particle geometrical dimensions are a = 1.0, b = 0.03125, and c = 0.00433 in., the total surface area of 1 lb was 101.4 ft2. By calculation of the average slip velocity Vav = V,t,/t, (where V, is the average slip velocity for each segment of the dryer and t , = the particle residence time for each segment) an estimation of the overall correlation Nu = (Re)" was feasible. The exponent which was determined for the Re number includes the relatively high field of turbulence existing in the cyclone, the feeding point, and the elbows. The established correlation was Nu = 0.00076Re1.64Pr0.52. In order to determine the exponent of the Re number (Boothroyd, 1971) linear regression was performed on the data according to log Nu = log (Prm) n log Re; m = 0.33 0.66 exp(-0.85Re0.24). The value of the exponent of the Pr number was calculated according to Hoffman and Ross (1972). A calculation of the particle residence time in a pneumatic duct and in the cyclone should also be included. In
+
+
Ind. Eng. Chem., Process
Des. Develop.,
Vol. 13, No. 4 , 1974
401
Table 111. The Heat Transfer Coefficient for Consecutive 20-in. Segments of a 4-in. Tower Gas Velocity 70 ft/sec Horizontal duct
Vertical duct Segment no.
1
4
5
6
7
24 106.8 7.00 201
18 80.1 4.82 139
17 75.7 4.48 129
14 62.3 3.48 100
140 ft/sec 42 42 187.0 231.5 14.51 19.09 131 172
40 178.1 13.61 123
38 169.2 12.72 115
34 151.4 11.08 100
2
3
Average s l i p velocity Re number Nu = 0.016Re'.3Pro*67 h (for a given segment) 100% 11 (for segment no. 8)
38 169.2 12.74 366
Gas Velocity 70 ft/sec 22 18 97.9 80.1 6.25 4.82 180 139
Average s l i p velocity Re number Nu = 0.016Re'.3Pr0*6T h (for a given segment) h (for segment no. 8 ) 100%
75 333.9 30.83 278
Gas Velocity 47 109.2 16.77 155
I5
-
12
-
T-
9 -
SCHEMATIC DIAGRAM OF F L W PATTERN IN THE FEED TEE,O"TOWER
m i
ttl
SCHEMATIC DIAGRAM OF THE FLOW PATTERN IN A HORIZONTAL-TO-VERTICAL I 5 0 RADIUS OF CURVATURE Emow, VOWER
Figure 6. Schematic diagram of flow pattern in the feed tee and elbow.
the cyclone, the particles exhibit a residence time which is pertinent to the heat transfer between the gas and particles. For our consideration, only the residence time which occurs in the region of high turbulence need be taken into account; this is related to the entrance particle velocity and the cyclone diameter. The literature data (Burov, 1961; Meline, 1967) give an indication as to how these estimations might be performed, but much remains to be done in this area. The curve Nu = f(Re) is shown in Figure 7 . Points 1 and 2 refer to the experimental data obtained for a straight 2-in. diameter pipe section (see point B below). Points 3, 4, and 5 refer to the overall gas to particle heat transfer coefficient related to the flash dryer including a cyclone. The broken line represents the data for heating and cooling air flowing normal to a single cylinder as quoted by McAdams (1954). These data have been recently reviewed by Whitaker (1972) and Boothroyd (1971). The higher slope for the obtained curve can be explained by a higher transfer coefficient for a drying process than for 402
Ind. Eng. Chem., Process Des. Develop., Vol. 13, NO.4, 1974
0
1
1
1
1
~
1
1
1
1
1
1
1
1
I1
t
Table IV. Heat Transfer Coefficient (Gas-Particle) in 8-in- Diameter Tower and 3-ft, 4-in. Diameter Cyclone
Run no. 1 1 1 1
2 2 2
2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 6 6 6 6 6 6 a
Heat transferred gas-particle ( A H ) , Btu/lb
Gas velocity, ft/sec
number
183 135 175 120 2 14 215 194 232 220 201 251 252 203 2 67 251 2 10 2 87 281 236 294 286 249 3 15 239 333 259 3 69 331 283 398 3 84 318
157 106 157 106 157 142 106 147 142 106 157 142 106 147 142 106 147 142 106 147 142 106 157 106 147 106 147 142 106 157 142 106
0.972 0.972 1.014 1.014 0.972 0.972 0.972 1.014 1.014 1.014 0.972 0.972 0.972 1.014 1.014 1.014 0.972 0.972 0.972 1.014 1.014 1.014 0.972 0.972 1.014 1.014 0.972 0.972 0.972 1.014 1.014 1.014
Pr
Av Atemp, "F
Total particle residence time, sec
CAV,Ati/CAti = A V
h - Atemp Atime "F F = 101.4 ft2/lb
0.369 0.6 14 0.369 0.614 0.369 0.443 0.614 0.369 0.443 0.614 0.369 0.443 0.614 0.369 0.443 0.614 0.369 0.443 0.614 0.369 0.443 0.614 0.369 0.614 0.369 0.614 0.369 0.443 0.614 0.369 0.443 0.614
83.8 53.9 83.8 53.9 83.8 72.7 53.9 83.8 72.7 53.9 83.8 72.7 53.9 83.8 72.7 53.9 83.8 72.7 53.9 83.8 72.7 53.9 83.8 53.9 83.8 53.9 83.8 72.7 53.9 83.8 72.7 53.9
0.0296 0.0123 0.0285 0.0120 0.0316 0.0266 0.0173 0.0320 0.0267 0.0178 0.0337 0.0278 0.0167 0.0360 0.0279 0.0168 0.0372 0.0304 0.0202 0.0420 0.0339 0.0225 0.04047 0.01873 0.03955 0.01891 0.04503 0.03275 0.02020 0.04565 0.03717 0.02322
165 177
164 160 181 180 180 194 185 181 204 202 195 198 205 201 206 206 188 187 188 178 208 205 223 220 219 225 225 233 230 220
Average slip velocity,
AH
Loading rate 4.75 lb/min. The run number refers to the different moisture level in a fed material.
Table V. Heat Transfer Coefficient (Gas-Particle) in an 11-ftVertical Segment Duct (Pr = 1.014; Loading Ratio = 0.0333 lb of Material/lb of Gas) ~~
Change of the heat transferred. 4 H (Btu /lb) AH = AH, (for 22-ft duct) AH2 (for 11-it duct) Gas velocity, ft/sec Driving force (Atemp). 'F Particle residence time in 11-ft duct/sec Average s l i p velocity A I ' (ft/sec) in 11-ft straight pipe section Heat transfer coefficient (gas- partic le) 12 = 4H/Atime, Atemp surface a r e a , Btu/sec "F f t z Nu = ~ ~ R e ~ p r " . ~ ~
40.9
44.6
100
100
138 0.143
183 0.143
23
23
23
0.0205
0.0168
0.0138 0.0155
iy
77
= 0.035 = 1.15
CY
=
17 =
54.4
0.029 1.15
would be higher than the rate of internal moisture transferred from the interior to the particle's surface. In this case the internal rate of heat and mass transfer might control the resulting rate of water vaporization from the particles (Luikov, 1966). A dried skin is formed on the surface of the particle. The changes in the solubility of water in the skin layer of a particle and/or changes as the
~
~~~~
70.0
34.4
38.0
49.2
60.4
100
100
263 0.143
308 0.143
50 138 0.282
50 183 0.282
50 263 0.282
50 308 0.282
23
11
11
11
11
0.0088
0.00726
0.00595
0.00668
01
= 0.035
17 = 1.15
CY 71
= 0.029 = 1.15
results of thermal degradation could also alter the internal heat and mass transfer coefficient (Trommelen and Crosby, 1970). The phenomena of scorching and toasting the heat sensitive material might also be observed. For this range of conditions the observed rate of drying might be smaller than for the conditions in which a lower entrance gas temperature was applied (Peck and Wason, 1971). Ind. Eng. C h e m . , P r o c e s s D e s . Develop., Vol. 13. No. 4 , 1974
403
The amount of water evaporated would be smaller for a higher heat flux. The same results might be obtained using different hot gas compositions having different Pr numbers. These irregularities (scorching and burning) have been observed experimentally by our use of a hot gas composition having Pr numbers from 0.74 to 1.01 and for a higher entrance gas temperature. However, according to some authors (Kisakurek, 1972) for thin solids (as in our case), the microcapillaries of porous bodies are small, and consequently there is negligible internal resistance to the flow of liquid inside the solid body. Let us analyze some of the processing variables. A . By changing the geometry of a pneumatic duct, we change the average value of the slip velocity, the residence time, and quite often the available contact area for hot gas-particles. B. Radical changes in the material loading rate (pounds of the conveyed material per pound of gas) affect the average value of the temperature difference between the hot gas and surface of the particles because a larger or smaller proportion of the available heat is absorbed by the particles. Also the loading rate influences the average slip velocity and the average particle's residence time. C. A dense flow pattern might cause the diminishing of the available surface area for the heat exchange as compared to a more uniform distribution of the particles in a gas stream. D. By changing the gas velocity we change the mean slip velocity and also the heat transfer coefficient and the residence time of the particles. For any specific change in the conditions of processing such as the temperature of the hot gas, the tower dimensions, the tower geometry, etc., it is necessary to evaluate which of these parameters plays an overriding role in the resulting rate of heat transfer from the gas to the particles. There are three locations in the flash drying equipment in which a high flux is observed between the gas and the particles: (1) the feeding point, (2) the elbows, and (3) the cyclone. The high heat flux at these locations can be explained by a high value of the particle slip velocities and high intensity of the turbulence phenomena. Nomenclature Any consistent set of units may be employed. Those listed are merely illustrative. A = surface area of particles B = the mass transfer shielding; function of the Spalding number Bi = the Biot number, K,S/D, CD = total particle drag coefficient, dimensionless D = the inside diameter of the conduit or tube d = the diameter of the equivalent spherical particle or average diameter of particles D , = diffusivity at interface F = surface area of particle F , = dragforce Fr = the particle Froude number, Vt/(gd)0.5 g = dimensional constant in Newton's law Gu = the Gukhman number ( t o - t,)/To; where t , is the wet bulb temperature and to is the temperature (%:OK) of hot gas stream h, = the average heat transfer coefficient (gas to particles) H o = initial moisture level of a drying product, 7'0 H = moisture level of a drying product at a distance 1 from the feeding point, %
404
Ind. Eng. Chem., Process D e s . Develop., Vol. 13, No. 4 , 1974
k = thermal conductivity K , = mass transfer coefficient L = loading rate, lb of conveyed material/lb of gas m = the exponent of the Prandtl number n = the exponent of particle Reynolds number Nu = the pajicle Nusselt number, dimensionless, h d j k Pr = Prandtl number, dimensionless, c,p/k R = the characteristic particle size measured in the direction normal to the flow direction Re = particle Reynolds number, dimensionless, dAup,/p S = thickness of boundary layer S p = Spaldingnumber V, = gas velocity, ft/sec Vt = entrainment velocity t w = wet bulb temperature Greek Letters pg = densityofgas ps = density of conveyed solid
= viscosityof gas AH = change of the enthalpy Atemp = the driving force, the difference between the gas and particle temperature Ptime = the residence time of particle for a given tower segment A V = the average slip velocity, the difference between the gas and particle velocity p
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Received for reuieu: February 26, 1973 Accepted M a y 24, 1974
