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Particle motion and mixing in a rotary kiln
Powder Technology, 76 (1993) 241-245
241
Particle motion and mixing in a rotary kiln G e n e R. W o o d l e
a n d J a m e s M. M u n r o
South Dakota School of Mines and Technology, Rapid City, SD 57701 (USA) (Received June 6, 1992; in revised form February 19, 1993)
Abstract The motion and mixing of solid materials within a rotary kiln was studied experimentally by visual observation of tagged particles in a laboratory kiln. Particle mixing rates were evaluated by the time required to achieve complete or randomized mixing of the kiln bed. Experiments were conducted to investigate the effects of particle type, kiln loading, and wall friction on mixing rates in the bed with the bed in either slipping mode or rolling mode. In slipping mode, the bed behaved as a relatively solid mass with little mixing of particles when compared to operation in rolling mode. In rolling mode the following effects were noted: Increasing kiln loading increased the time required to achieve complete mixing; e.g. in one experiment, a 500% increase in kiln loading resulted in a 67% increase in the time to achieve mixing. Particle type was shown to have an effect on mixing time and an empirical relationship was developed to predict kiln mixing times based on the ratio of the coefficient of particle/particle friction to the coefficient of particle/wall friction.
Introduction The motion and rate of mixing of solid particles in a rotary kiln or other rotary mixing equipment can be important in a wide variety of production processes. The basic purpose of a rotary kiln, for instance, is to transfer heat from the kiln gases and walls to the solid particles in the kiln bed. Because the particles on the outside of the bed insulate those on the inside, the rate of heat transfer is directly related to the rate of mixing of the particles within the bed. If some types of particles mix more rapidly than others, the same heat transfer can be accomplished with a higher kiln throughput. In addition, the effects of kiln loading on the rate of mixing and resulting heat transfer rate can also affect kiln throughput. The rate of kiln throughput can be a major factor in the costs of operation. The effects of particle type, loading, wall friction, and particle motion on mixing rates were studied in a simulated rotary kiln which consisted of a short cylinder of clear plastic with one clear plastic end wall. The cylinder was mounted on an axle and could be rotated with a variable speed motor. The simulator is depicted in Fig. 1. The bed and the particles within it could be observed from the top, bottom, and one side. Three types of particles which had different shapes and masses but were similar in size were studied. For each particle type, mixing and particle motion were examined with the bed occupying 3%, 8%, and 15% of the total volume of the simulator. In addition, motion
0032-5910/93/$6.00
Fig. 1. Rotary kiln simulator.
and mixing with all three particle types at all three loading levels (3%, 8%, and 15%) were studied with the inner wall of the simulator cylinder smooth and with 2.4 mm thick strips attached to the inner cylinder wall. The strips increased the friction between the particles and the wall. As indicated in Fig. 2, particles within the bed generally moved along the bottom of the bed in the direction of rotation until they reached the highest point of the bed and then roiled down the inclined top of the bed. There was a relatively slow moving and slow mixing zone in the center of the bed. In general, particles mixed approximately ten times as rapidly with the strips on the cylinder walls as they
© 1993- Elsevier Sequoia. All rights reserved
242 Direction
of
TABLE 1. Physical properties of test particles
Rotation
Particle type
Mass of one piece (g)
Bulk density (g cm -3)
Tube Ovoid Shell
0.22 0.02 0.21
0.44 0.09 0.38
Be
Fig. 2. Path of particle motion. Ovoid
1/2
inch
Shell
1/2
inch
Tube
5/8
inch
Fig. 3. Particle shape and size.
did when the walls were smooth. Without the strips, particle mixing increased at higher loading levels. With the strips, particle mixing decreased as the loading increased. There was also a significant difference in the mixing rate depending upon particle type, with the fastest mixing particles mixing four to six times as rapidly as the slowest, depending upon operating conditions.
Experimental procedure All experimental runs were performed using a similar procedure. The bed was loaded to the desired level, fifty colored particles of the same material were placed in the center of the bed, and the cylinder was rotated at a fixed rotation speed. After rotation commenced the number of colored particles appearing on the top and on the bottom of the bed at fixed time intervals was noted. The three particle types used were classified as the tube, the ovoid, and the shell. Their approximate size and shape are indicated in Fig. 3. The mass of each particle in grams and the bulk density in grams per cubic centimeter are shown in Table 1. Conventional practice is to consider a system of solids as being completely mixed when the particles are ran-
domly distributed [1]. In order to determine when the bed in the simulator was completely mixed, the number of colored particles which could be predicted to appear in either the top or bottom layer with complete mixing was determined. For example, if there were 15 000 total pieces in the bed and 1 000 pieces on the top layer, 6.7% or 3.33 of the 50 colored pieces could be predicted to appear on the top layer when the bed was totally mixed. Of course, some random deviation in the number of colored particles appearing on the top or bottom layer of particles would be expected, i.e. exactly 3.33 particles would not appear at every observation even in a well mixed bed. An example of data taken and calculations performed for one experimental run (shells at 3% loading, 7 s per revolution, and without the strips) is shown in Table 2. After 14 rain, for example, one colored shell was observed on the top of the bed and 17 were observed on the bottom. The number of shells expected to be observed with a well mixed bed was 10.6 on the top and 11.2 on the bottom. The deviation (Dev.) is the absolute value of the difference between the total number observed and the number expected on both the top and bottom of the bed. Data were grouped in pairs (Paired dev.) for determination of mixing time. The paired deviation at 3 min is the average of the total top and bottom deviation at 2 rain and the total top and bottom deviation at 4 rain. Paired deviation versus time was graphed and the results for the data in Table 2 are shown in Fig. 4. The paired deviation decreased with time until a point was reached which showed relatively little deviation in the results observed. The period of relatively small deviation was considered to indicate the random deviation in particle count expected in a well mixed bed. The mixing time was determined as the time for the paired deviation to reach the random deviation level as shown in Fig. 4. In the run shown in Fig. 4, the mixing time is 46 min. Mixing times for the particles tested at all loading levels with and without the strips is shown in Table 3. Column labels such as 3/7 indicate 3% loading and 7 s per revolution. Time is given in minutes.
243 T A B L E 2. Typical data from experimental run
Time
Top
Bottom
Dev.
(mn) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
0 0 3 0 1 2 1 2 5 1 5 5 8 6 5 5 4 7 8 6 6 7 10 10 8 9 12 10 11 9 9 8
0 0 4 8 15 16 17 14 13 16 17 17 12 15 12 12 15 13 9 12 14 13 10 11 10 10 13 10 7 11 9 12
21.8 21.8 14.8 13.8 13.4 13.4 15.4 11.4 7.4 14.4 11.4 11.4 3.4 8.4 6.4 6.4 10.4 5.4 4.8 5.4 7.4 5.4 1.8 0.8 3.8 2.8 3.2 1.8 4.6 1.8 3.8 3.4
T A B L E 3. Elapsed time for complete mixing
Time (min)
Paired
3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63
21.8 14.3 13.4 13.4 10.9 11.4 5.9 6.4 7.9 5.1 6.4 1.3 3.3 2.5 3.2 3.6
@
g>-
~L
4 2-
15/7
16 46 17
17 32 16
13 26 14
With strips Ovoid Shell Tube
1.2 4.5 1.8
~lippir]g
1.4 5.0 2.0
2.0 7.0 2.3
5lumping
Rolling
@ C~scading
Fig. 5. Bed configuration.
wall, the kiln loading, the speed of kiln rotation, kiln diameter, and the characteristics of the particles within the kiln [2]. A cross-section taken perpendicular to the longitudinal axis of a kiln would show that the bed is in one of the following configurations: slipping, slumping, rolling, cascading, cataracting, or centrifuging. Ordinarily, rotary kilns are not operated under conditions sufficient to cause cataracting or centrifuging [2]. The other four configurations are shown in Fig. 5. In slumping mode the portion of the bed in section U periodically slumps down into section L.
Random Deviation
©
Without strips Ovoid Shell Tube
ctive ayer
Decreasing Raired Deviation /
c 1E~ o !614> 1~ o @ (3 1@-
8/7
Direction of Rotation
O
2g}--
3/7
dev.
0
I I J I I I I I I I I ] i 12 2@ 2B 36 4 4 ~ 2
4
I
I 6B
I
I I SB
I
Time in Ninutes Fig. 4. Graph of paired deviation vs. time.
Evaluation of experimental results Bed configuration The motion of a rotary kiln causes the material in the bed to move and to assume one of six shapes or configurations depending upon several variables, including the friction between the bed material and the
Particle movement In the experiments detailed here, the bed was in slipping mode in runs without the strips and in roiling mode in runs with the strips. In slipping mode, the bed acted as a relatively solid mass and slid along the smooth wall. In rolling mode, a definite active layer formed in the bed. The active layer was a fairly uniform thickness of particles which moved rapidly down the inclined top of the bed. The presence of an active layer in similar circumstances has been reported by several other researchers [2] and is shown in Fig. 6. The presence of the active layer in rolling mode explains the faster mixing rate in roiling mode than in slipping mode.
244
Direction
of
Active
P~rticle
Movemen~
Layer
/
T r-~nsil::ion
Fig. 6. Active layer. T A B L E 4. Active layer m e a s u r e m e n t (thickness in centimeters) Ovoid 3% 8% 15%
1.27 1.91 2.87
Shell 44% 33% 30%
0.64 0.97 1.27
Tube 22% 17% 14%
0.97 1.60 2.54
32% 28% 26%
In slipping mode, the particles moved erratically along the bottom of the bed generally in the direction of rotation at varying rates, but occasionally even moved backward. When particles reached the highest point of the bed they rolled slowly down the inclined top of the bed. In rolling mode, particles moved at a relatively constant rate along the bottom of the bed in the direction of rotation. At or near the highest point of the bed, particles entered the active layer and moved with the layer down the top of the bed.
The effects of loading levels In slipping mode, particles mixed more rapidly at higher loading levels. Although a definitive explanation for this phenomenon was beyond the scope of this research, it is possible that increased bed depth counteracted the effect of particle-particle friction. In rolling mode, particles mixed less rapidly at higher loading levels. The thickness of the active layer accounts for this result. Although the active layer thickness increased with increased loading, it did not increase as rapidly as the loading. Active layer measurements are shown in Table 4. For example, at 15% loading with ovoids, the active layer is 2.87 centimeters thick and 30% of the total particles in the bed are in the active layer. For each particle type the thickness of the active layer increased with increased loading, but the percentage of the total bed in the active layer decreased. The effects of particle type Although several researchers have reported the results of mixing studies, [1, 3-5], no studies were found which examined the effects of particle characteristics in detail.
As indicated in Table 3, there was a marked difference in the mixing rates of the three particles tested. The ovoid consistently mixed the fastest and the shell the slowest. The ratio of the coefficient of friction between the particles and the coefficient of friction between the particles and the wall of the simulator was the best predictor of the relative rate of particle mixing. Particle/wall friction was determined using a fiat sheet of simulator wall material. Each of the particle types was placed on the sheet and the angle at which the sheet was inclined when the particles began to slide was noted. The tangent of the angle of inclination was considered the coefficient of friction. This method had been used by other researchers [2]. The static angle of repose is considered to be a good measure of friction between particles caused by size, shape, and roughness [6]. The angle of repose is the angle of the sides of the conical shape which particles assume when poured out onto a fiat surface. The friction between the particles determines how high a cone the characteristics of the particles will support. The tangent of the angle formed by the sides of the cone was considered the coefficient of particle/particle friction. In all cases, the smaller the ratio of the coefficient of particle/particle friction to the coefficient of particle/ wall friction, the shorter the mixing time. This ratio and mixing times for all particles is shown in Table 5. For operation in rolling mode (with attached strips) the relationship of mixing times for different particles can be estimated with the empirical equation:
t fft2 = (R ffR2 ) 1"3 where tl =time of mixing of particle 1, t2=time of mixing of particle 2, R1 = ratio of coefficient of particle/ particle and particle/wall friction of particle 1, and R2 = ratio of coefficient of particle/particle and particle/ wall friction of particle 2. For example, R1 for ovoids is 1.1, R2 for tubes is 1.3, and (RffR2) ~'3 is 0.8. If mixing times for ovoids (tx) are known to be the observed values in Table 5, times for tubes (t2) may be estimated T A B L E 5. Particle mixing times and friction ratios (time in minutes) Loading
Ovoid Time
With strips 3% 8% 15% Without strips 3% 8% 15%
1.2 1.4 2.0 16 17 13
Tube Ratio
1.1 1.1 1.1 1.1 1.1 1.1
Time
1.8 2.0 2.3 17 16 14
Shell Ratio
1.3 1.3 1.3 1.3 1.3 1.3
Time
4.5 5.0 7.0 46 32 26
Ratio
2.8 2.8 2.8 2.8 2.8 2.8
245 T A B L E 6. Estimation of mixing time based upon values for other particles Loading
Ovoid
Tube
Obs.
Obs.
Pred,
Obs.
Pred.
1.2 1.4 2.0
1.8 2.0 2.3
1.5 1.8 2.5
4.5 5.0 7.0
4.0 4.7 6.7
3% 8% 15%
Shell
increase in loading by 500% resulted in an increase in mixing time of only 67%. Similar results were noted for the other two particle types. Although other factors may need to be considered and no results were obtained for loading levels higher than 15%, it appears that it would be advantageous to operate a rotary kiln at the highest loading level possible where maximum throughput is desired.
Rotation speed
Conclusions
Other researchers have determined that the speed of rotation does not appear to have a significant effect on the rate of mixing. The rate is dependent on the number of revolutions regardless of the speed of rotation. That is, doubling rotation speed halves mixing time [4]. It should be noted, however, that this relationship can be accurate only within a particular mode of bed configuration. If the increase in rotation speed caused the bed to change from slipping to rolling mode, for instance, the rate of mixing would change more than the change in rotation rate alone would indicate.
Bed configuration
Differences in particle type
Bed configuration has a significant effect on the speed of mixing of particles in a rotary kiln and particles mix much more rapidly when the bed is in rolling mode than when it is in slipping mode. Henein et al. [7] have developed a mathematical model for predicting the type of configuration a bed will assume, and a bed in slipping mode may be forced into rolling mode by increasing bed/wall friction or rotation speed. However, if equipment were operational, it would appear that bed configuration could be determined with fair accuracy by simple observation. Although other factors may need to be considered, a kiln could be operated much more efficiently with the bed in rolling mode than with the bed in slipping mode.
References
by dividing ovoid times by 0.8. Results from these calculations are shown in Table 6 as well as the results of similar ovoid/shell calculations. The formulas developed appear to model the system used for these experiments quite accurately with the largest margin of error between predicted and expected results equal to 17% and the average margin of error equal to 10%.
Kiln loading Kiln loading also has a significant effect on mixing rates. If a kiln were operated in slipping mode, faster mixing could actually be promoted by increased loading. In rolling mode, the rate of mixing is decreased by increased loading. However, the increase in mixing time is not directly related to the increase in loading. For example, at the same rotation speed, ovoids reached total mixing in 1.2 min at 3% loading and reached total mixing in 2.0 rain at 15% loading. That is, an
Differences in particle types can have a significant effect on mixing time and some particles may mix many times faster than others. Although the exact effects of differences in parameters such as rotation speed and kiln size are not known, the formulas developed here or similar formulas could be used to predict the mixing speeds of various particle types. If the rate of mixing of one type of particle were known, the rate of mixing of other particle types could be predicted through comparison of the coeffÉcients of particle/wall and particle/particle friction.
1 J.B. Gayle and J.H. Gary, Ind. Eng. Chem., 52 (1960) 519. 2 H. Henein, J.K. Brimacombe and A.P. Watkinson, Metall. Trans., 14B (1983) 191. 3 K.W. Carley-Macauly and M.B. Donald, Chem. Eng. ScL, 17 (1962) 493. 4 K.W. Carley-Macauly and M.B. Donald, Chem. Eng. Sci., 19 (1964) 191. 5 R. Rutgers, Chem. Eng. Sci., 20 (1965) 1079. 6 F.C. Franklin and L.N. Johanson, Chem. Eng. Sci., 4 (1955) 119. 7 H. Henein, J.K. Brimacombe and A.P. Watkinson, Metall. Trans., 14B (1983) 207.
241
Particle motion and mixing in a rotary kiln G e n e R. W o o d l e
a n d J a m e s M. M u n r o
South Dakota School of Mines and Technology, Rapid City, SD 57701 (USA) (Received June 6, 1992; in revised form February 19, 1993)
Abstract The motion and mixing of solid materials within a rotary kiln was studied experimentally by visual observation of tagged particles in a laboratory kiln. Particle mixing rates were evaluated by the time required to achieve complete or randomized mixing of the kiln bed. Experiments were conducted to investigate the effects of particle type, kiln loading, and wall friction on mixing rates in the bed with the bed in either slipping mode or rolling mode. In slipping mode, the bed behaved as a relatively solid mass with little mixing of particles when compared to operation in rolling mode. In rolling mode the following effects were noted: Increasing kiln loading increased the time required to achieve complete mixing; e.g. in one experiment, a 500% increase in kiln loading resulted in a 67% increase in the time to achieve mixing. Particle type was shown to have an effect on mixing time and an empirical relationship was developed to predict kiln mixing times based on the ratio of the coefficient of particle/particle friction to the coefficient of particle/wall friction.
Introduction The motion and rate of mixing of solid particles in a rotary kiln or other rotary mixing equipment can be important in a wide variety of production processes. The basic purpose of a rotary kiln, for instance, is to transfer heat from the kiln gases and walls to the solid particles in the kiln bed. Because the particles on the outside of the bed insulate those on the inside, the rate of heat transfer is directly related to the rate of mixing of the particles within the bed. If some types of particles mix more rapidly than others, the same heat transfer can be accomplished with a higher kiln throughput. In addition, the effects of kiln loading on the rate of mixing and resulting heat transfer rate can also affect kiln throughput. The rate of kiln throughput can be a major factor in the costs of operation. The effects of particle type, loading, wall friction, and particle motion on mixing rates were studied in a simulated rotary kiln which consisted of a short cylinder of clear plastic with one clear plastic end wall. The cylinder was mounted on an axle and could be rotated with a variable speed motor. The simulator is depicted in Fig. 1. The bed and the particles within it could be observed from the top, bottom, and one side. Three types of particles which had different shapes and masses but were similar in size were studied. For each particle type, mixing and particle motion were examined with the bed occupying 3%, 8%, and 15% of the total volume of the simulator. In addition, motion
0032-5910/93/$6.00
Fig. 1. Rotary kiln simulator.
and mixing with all three particle types at all three loading levels (3%, 8%, and 15%) were studied with the inner wall of the simulator cylinder smooth and with 2.4 mm thick strips attached to the inner cylinder wall. The strips increased the friction between the particles and the wall. As indicated in Fig. 2, particles within the bed generally moved along the bottom of the bed in the direction of rotation until they reached the highest point of the bed and then roiled down the inclined top of the bed. There was a relatively slow moving and slow mixing zone in the center of the bed. In general, particles mixed approximately ten times as rapidly with the strips on the cylinder walls as they
© 1993- Elsevier Sequoia. All rights reserved
242 Direction
of
TABLE 1. Physical properties of test particles
Rotation
Particle type
Mass of one piece (g)
Bulk density (g cm -3)
Tube Ovoid Shell
0.22 0.02 0.21
0.44 0.09 0.38
Be
Fig. 2. Path of particle motion. Ovoid
1/2
inch
Shell
1/2
inch
Tube
5/8
inch
Fig. 3. Particle shape and size.
did when the walls were smooth. Without the strips, particle mixing increased at higher loading levels. With the strips, particle mixing decreased as the loading increased. There was also a significant difference in the mixing rate depending upon particle type, with the fastest mixing particles mixing four to six times as rapidly as the slowest, depending upon operating conditions.
Experimental procedure All experimental runs were performed using a similar procedure. The bed was loaded to the desired level, fifty colored particles of the same material were placed in the center of the bed, and the cylinder was rotated at a fixed rotation speed. After rotation commenced the number of colored particles appearing on the top and on the bottom of the bed at fixed time intervals was noted. The three particle types used were classified as the tube, the ovoid, and the shell. Their approximate size and shape are indicated in Fig. 3. The mass of each particle in grams and the bulk density in grams per cubic centimeter are shown in Table 1. Conventional practice is to consider a system of solids as being completely mixed when the particles are ran-
domly distributed [1]. In order to determine when the bed in the simulator was completely mixed, the number of colored particles which could be predicted to appear in either the top or bottom layer with complete mixing was determined. For example, if there were 15 000 total pieces in the bed and 1 000 pieces on the top layer, 6.7% or 3.33 of the 50 colored pieces could be predicted to appear on the top layer when the bed was totally mixed. Of course, some random deviation in the number of colored particles appearing on the top or bottom layer of particles would be expected, i.e. exactly 3.33 particles would not appear at every observation even in a well mixed bed. An example of data taken and calculations performed for one experimental run (shells at 3% loading, 7 s per revolution, and without the strips) is shown in Table 2. After 14 rain, for example, one colored shell was observed on the top of the bed and 17 were observed on the bottom. The number of shells expected to be observed with a well mixed bed was 10.6 on the top and 11.2 on the bottom. The deviation (Dev.) is the absolute value of the difference between the total number observed and the number expected on both the top and bottom of the bed. Data were grouped in pairs (Paired dev.) for determination of mixing time. The paired deviation at 3 min is the average of the total top and bottom deviation at 2 rain and the total top and bottom deviation at 4 rain. Paired deviation versus time was graphed and the results for the data in Table 2 are shown in Fig. 4. The paired deviation decreased with time until a point was reached which showed relatively little deviation in the results observed. The period of relatively small deviation was considered to indicate the random deviation in particle count expected in a well mixed bed. The mixing time was determined as the time for the paired deviation to reach the random deviation level as shown in Fig. 4. In the run shown in Fig. 4, the mixing time is 46 min. Mixing times for the particles tested at all loading levels with and without the strips is shown in Table 3. Column labels such as 3/7 indicate 3% loading and 7 s per revolution. Time is given in minutes.
243 T A B L E 2. Typical data from experimental run
Time
Top
Bottom
Dev.
(mn) 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
0 0 3 0 1 2 1 2 5 1 5 5 8 6 5 5 4 7 8 6 6 7 10 10 8 9 12 10 11 9 9 8
0 0 4 8 15 16 17 14 13 16 17 17 12 15 12 12 15 13 9 12 14 13 10 11 10 10 13 10 7 11 9 12
21.8 21.8 14.8 13.8 13.4 13.4 15.4 11.4 7.4 14.4 11.4 11.4 3.4 8.4 6.4 6.4 10.4 5.4 4.8 5.4 7.4 5.4 1.8 0.8 3.8 2.8 3.2 1.8 4.6 1.8 3.8 3.4
T A B L E 3. Elapsed time for complete mixing
Time (min)
Paired
3 7 11 15 19 23 27 31 35 39 43 47 51 55 59 63
21.8 14.3 13.4 13.4 10.9 11.4 5.9 6.4 7.9 5.1 6.4 1.3 3.3 2.5 3.2 3.6
@
g>-
~L
4 2-
15/7
16 46 17
17 32 16
13 26 14
With strips Ovoid Shell Tube
1.2 4.5 1.8
~lippir]g
1.4 5.0 2.0
2.0 7.0 2.3
5lumping
Rolling
@ C~scading
Fig. 5. Bed configuration.
wall, the kiln loading, the speed of kiln rotation, kiln diameter, and the characteristics of the particles within the kiln [2]. A cross-section taken perpendicular to the longitudinal axis of a kiln would show that the bed is in one of the following configurations: slipping, slumping, rolling, cascading, cataracting, or centrifuging. Ordinarily, rotary kilns are not operated under conditions sufficient to cause cataracting or centrifuging [2]. The other four configurations are shown in Fig. 5. In slumping mode the portion of the bed in section U periodically slumps down into section L.
Random Deviation
©
Without strips Ovoid Shell Tube
ctive ayer
Decreasing Raired Deviation /
c 1E~ o !614> 1~ o @ (3 1@-
8/7
Direction of Rotation
O
2g}--
3/7
dev.
0
I I J I I I I I I I I ] i 12 2@ 2B 36 4 4 ~ 2
4
I
I 6B
I
I I SB
I
Time in Ninutes Fig. 4. Graph of paired deviation vs. time.
Evaluation of experimental results Bed configuration The motion of a rotary kiln causes the material in the bed to move and to assume one of six shapes or configurations depending upon several variables, including the friction between the bed material and the
Particle movement In the experiments detailed here, the bed was in slipping mode in runs without the strips and in roiling mode in runs with the strips. In slipping mode, the bed acted as a relatively solid mass and slid along the smooth wall. In rolling mode, a definite active layer formed in the bed. The active layer was a fairly uniform thickness of particles which moved rapidly down the inclined top of the bed. The presence of an active layer in similar circumstances has been reported by several other researchers [2] and is shown in Fig. 6. The presence of the active layer in rolling mode explains the faster mixing rate in roiling mode than in slipping mode.
244
Direction
of
Active
P~rticle
Movemen~
Layer
/
T r-~nsil::ion
Fig. 6. Active layer. T A B L E 4. Active layer m e a s u r e m e n t (thickness in centimeters) Ovoid 3% 8% 15%
1.27 1.91 2.87
Shell 44% 33% 30%
0.64 0.97 1.27
Tube 22% 17% 14%
0.97 1.60 2.54
32% 28% 26%
In slipping mode, the particles moved erratically along the bottom of the bed generally in the direction of rotation at varying rates, but occasionally even moved backward. When particles reached the highest point of the bed they rolled slowly down the inclined top of the bed. In rolling mode, particles moved at a relatively constant rate along the bottom of the bed in the direction of rotation. At or near the highest point of the bed, particles entered the active layer and moved with the layer down the top of the bed.
The effects of loading levels In slipping mode, particles mixed more rapidly at higher loading levels. Although a definitive explanation for this phenomenon was beyond the scope of this research, it is possible that increased bed depth counteracted the effect of particle-particle friction. In rolling mode, particles mixed less rapidly at higher loading levels. The thickness of the active layer accounts for this result. Although the active layer thickness increased with increased loading, it did not increase as rapidly as the loading. Active layer measurements are shown in Table 4. For example, at 15% loading with ovoids, the active layer is 2.87 centimeters thick and 30% of the total particles in the bed are in the active layer. For each particle type the thickness of the active layer increased with increased loading, but the percentage of the total bed in the active layer decreased. The effects of particle type Although several researchers have reported the results of mixing studies, [1, 3-5], no studies were found which examined the effects of particle characteristics in detail.
As indicated in Table 3, there was a marked difference in the mixing rates of the three particles tested. The ovoid consistently mixed the fastest and the shell the slowest. The ratio of the coefficient of friction between the particles and the coefficient of friction between the particles and the wall of the simulator was the best predictor of the relative rate of particle mixing. Particle/wall friction was determined using a fiat sheet of simulator wall material. Each of the particle types was placed on the sheet and the angle at which the sheet was inclined when the particles began to slide was noted. The tangent of the angle of inclination was considered the coefficient of friction. This method had been used by other researchers [2]. The static angle of repose is considered to be a good measure of friction between particles caused by size, shape, and roughness [6]. The angle of repose is the angle of the sides of the conical shape which particles assume when poured out onto a fiat surface. The friction between the particles determines how high a cone the characteristics of the particles will support. The tangent of the angle formed by the sides of the cone was considered the coefficient of particle/particle friction. In all cases, the smaller the ratio of the coefficient of particle/particle friction to the coefficient of particle/ wall friction, the shorter the mixing time. This ratio and mixing times for all particles is shown in Table 5. For operation in rolling mode (with attached strips) the relationship of mixing times for different particles can be estimated with the empirical equation:
t fft2 = (R ffR2 ) 1"3 where tl =time of mixing of particle 1, t2=time of mixing of particle 2, R1 = ratio of coefficient of particle/ particle and particle/wall friction of particle 1, and R2 = ratio of coefficient of particle/particle and particle/ wall friction of particle 2. For example, R1 for ovoids is 1.1, R2 for tubes is 1.3, and (RffR2) ~'3 is 0.8. If mixing times for ovoids (tx) are known to be the observed values in Table 5, times for tubes (t2) may be estimated T A B L E 5. Particle mixing times and friction ratios (time in minutes) Loading
Ovoid Time
With strips 3% 8% 15% Without strips 3% 8% 15%
1.2 1.4 2.0 16 17 13
Tube Ratio
1.1 1.1 1.1 1.1 1.1 1.1
Time
1.8 2.0 2.3 17 16 14
Shell Ratio
1.3 1.3 1.3 1.3 1.3 1.3
Time
4.5 5.0 7.0 46 32 26
Ratio
2.8 2.8 2.8 2.8 2.8 2.8
245 T A B L E 6. Estimation of mixing time based upon values for other particles Loading
Ovoid
Tube
Obs.
Obs.
Pred,
Obs.
Pred.
1.2 1.4 2.0
1.8 2.0 2.3
1.5 1.8 2.5
4.5 5.0 7.0
4.0 4.7 6.7
3% 8% 15%
Shell
increase in loading by 500% resulted in an increase in mixing time of only 67%. Similar results were noted for the other two particle types. Although other factors may need to be considered and no results were obtained for loading levels higher than 15%, it appears that it would be advantageous to operate a rotary kiln at the highest loading level possible where maximum throughput is desired.
Rotation speed
Conclusions
Other researchers have determined that the speed of rotation does not appear to have a significant effect on the rate of mixing. The rate is dependent on the number of revolutions regardless of the speed of rotation. That is, doubling rotation speed halves mixing time [4]. It should be noted, however, that this relationship can be accurate only within a particular mode of bed configuration. If the increase in rotation speed caused the bed to change from slipping to rolling mode, for instance, the rate of mixing would change more than the change in rotation rate alone would indicate.
Bed configuration
Differences in particle type
Bed configuration has a significant effect on the speed of mixing of particles in a rotary kiln and particles mix much more rapidly when the bed is in rolling mode than when it is in slipping mode. Henein et al. [7] have developed a mathematical model for predicting the type of configuration a bed will assume, and a bed in slipping mode may be forced into rolling mode by increasing bed/wall friction or rotation speed. However, if equipment were operational, it would appear that bed configuration could be determined with fair accuracy by simple observation. Although other factors may need to be considered, a kiln could be operated much more efficiently with the bed in rolling mode than with the bed in slipping mode.
References
by dividing ovoid times by 0.8. Results from these calculations are shown in Table 6 as well as the results of similar ovoid/shell calculations. The formulas developed appear to model the system used for these experiments quite accurately with the largest margin of error between predicted and expected results equal to 17% and the average margin of error equal to 10%.
Kiln loading Kiln loading also has a significant effect on mixing rates. If a kiln were operated in slipping mode, faster mixing could actually be promoted by increased loading. In rolling mode, the rate of mixing is decreased by increased loading. However, the increase in mixing time is not directly related to the increase in loading. For example, at the same rotation speed, ovoids reached total mixing in 1.2 min at 3% loading and reached total mixing in 2.0 rain at 15% loading. That is, an
Differences in particle types can have a significant effect on mixing time and some particles may mix many times faster than others. Although the exact effects of differences in parameters such as rotation speed and kiln size are not known, the formulas developed here or similar formulas could be used to predict the mixing speeds of various particle types. If the rate of mixing of one type of particle were known, the rate of mixing of other particle types could be predicted through comparison of the coeffÉcients of particle/wall and particle/particle friction.
1 J.B. Gayle and J.H. Gary, Ind. Eng. Chem., 52 (1960) 519. 2 H. Henein, J.K. Brimacombe and A.P. Watkinson, Metall. Trans., 14B (1983) 191. 3 K.W. Carley-Macauly and M.B. Donald, Chem. Eng. ScL, 17 (1962) 493. 4 K.W. Carley-Macauly and M.B. Donald, Chem. Eng. Sci., 19 (1964) 191. 5 R. Rutgers, Chem. Eng. Sci., 20 (1965) 1079. 6 F.C. Franklin and L.N. Johanson, Chem. Eng. Sci., 4 (1955) 119. 7 H. Henein, J.K. Brimacombe and A.P. Watkinson, Metall. Trans., 14B (1983) 207.