- Email: [email protected]
On the flow of granular material in a model blast furnace
Powder
13
Technology, 63 (1990) 13-21
On the flow of granular Cheng-Ken
Ho*,
Ye-Mon
Chen**,
Departwumt of Chemical Engineering,
and Jiing-Ruey
Jeng
Steel & Aluminum
Research
material Chun-i
National
& Development
in a model blast furnace
Lint
Taiwan Institute of Technology,
Department,
Taipei (Taiwan)
China Steel Corporation,
Kaohsiung
(Taiwan)
(Received December 8, 1988; accepted May 11, 1990)
Abstract Experimental studies on the flow of granular material in a l/lOth-scale model blast furnace of a commercial unit were conducted. The velocity distribution of the particulate flow, wall stresses, and the shape of the dead-man formation at the bottom of the furnace were measured. It was found that the particulate material is in an active state in the upper portion of the furnace (above the belly) and a passive state in the lower portion (below the belly). Consequently, the behavior of the particulate flow, wail stresses and dead-man formation can be reasonably described according to the aforementioned failure states.
Introduction The discharge of granular material from a silo or a hopper and the corresponding stress distribution associated with the flow have been the object of active research in the past few decades [ l-31. Several uncertainties concerning the granular material render a general theoretical approach difficult; these include whether the material should be regarded as a continuum (plasticity theory) [4] or whether its motion is merely kinematic (kinematic theory) [5, 61, the constitutive relation and the boundary conditions [ 71. The motion of granular material in a blast furnace is further complicated by several factors: the divergence and convergence geometry of the furnace, more than two granules, gas flow and gas-solid reactions. Based on the observation of a two-dimensional furnace, Sato et al. [S] reported that the angle of inclination *Present address: Steel & Ah.tminnm Research & Development Department, China Steel Corporation, Kaohsinng (Taiwan). **Present address: Westhollow Research Center, Shell Development Company, Houston, TX 77251 (U.S.A.). +To whom correspondence should be addressed.
0032-5910/90/$3.50
of the dead-man, i.e. the stagnant coke located at bottom of the furnace, increased with increased air flow but decreased with increased solid descending velocity. Nishio et al. [ 91 also employed a two-dimensional model furnace and observed that the peak of the dead-man formation could reach into the shaft. Shimizu et al. [ 10, 111, using a three-dimensional model furnace, however, found that the peak of the dead-man did not reach the shaft, and its shape could be well predicted by the locus of passive failure. They also observed plug flow movement of solids in the region above the belly and funnel flow movement below the belly. The stresses were found to be greater in the regions below the belly than in those above. Khodak and Borisov [ 12 ] employed a three-dimensional model furnace to measure the distribution of horizontal and vertical stresses. It was found that except for a small region in the vicinity of particle discharge, the stress distribution in the rest of the furnace is very similar to that of a vertical cylinder with a peripheral outflow. For the gas distribution, the prediction of the Ergun equation [ 131 was proven satisfactory [14, 151. In the present study, the motion of granular material in a three-dimensional l/10-scale mo-
0 Elsevier Sequoia/Printed in The Netherlands
14
de1 furnace of a commercial unit was investigated. The horizontal stress and dead-man fqrmation were also studied.
Experimental The model
blast furnace
The experimental set-up for the present study of the particulate flow in the model blast furnace is shown schematically in Fig. 1. The dimensions of the model were one-tenth those of a commercial scale furnace currently operated in the China Steel Corporation. The main portion of the shell of the model furnace was constructed of steel sheets. A transparent acrylic plate was placed at the center of the furnace such that the motion of solids within the furnace could be studied visually through the acrylic
A : Hopper 8 : Bell- less Feeder C : Blast Furnace D : Load Cell E : Dead-man F: G: H: I :
Table Throat Shaft Belly
Discharger
J : Bosh K : Hearth
Fig. 1. Schematic diagram of the model employed in the present study.
blast furnace
During the experiments, the particles were fed from above by a rotating distribution chute of a bell-less feeder, similar to the actual loading device of the commercial unit. In each complete rotation of the distribution chute, only half of the particles were charged into the furnace on one side of the acrylic plate. The particles that fell into the furnace on the other side of the acrylic plate were immediately removed through a duct from below. Thus, throughout the experiments only one-half of the furnace was filled with particles. In the vicinity of the acrylic plate, the presence of the plate caused a slight distortion of the charged particle layer and hence the distribution in the furnace was not perfectly axisymmetric. Different burden distributions could be achieved by adjusting the angle of inclination and the rotational speed of the chute, which were controlled by a personal computer. At the hearth level, the model furnace featured elevengates for solid drainage. The solid discharge rate was controlled by the rotational speed of a table discharger, located below the furnace. Six load cells were installed at various levels on the furnace wall to measure the horizontal wall stresses. Each load cell consisted of four U-shaped springs and eight strain gauges, as depicted in Fig. 2. The output signals from the load cells were monitored by another personal computer. Two different particles, granular sintered ore and yellow plastic pellets, were used in the experiments. Their physical properties are listed in the Table. Plastic pellets were used in
(a)
Top
(b)
Cross-sectional
Fig. 2. Structure
4.Sprlng
View
View
of the load cell.
Sheet
15 TABLE Physical properties of the two particles employed in the experiments Properties
Materials Yellow plastic pellets
Average particle diameter (mm) Bulk density (g/cm”) Angle of repose (“)
5 0.86 37
Granular ore particles 3.5 2.1 37
plate. The distribution chute was then activated again to charge the pellets into the furnace to the original level. The procedures of marking the tracers and batch charging fresh pellets were repeated until the tracer particles were being discharged from the bottom. A connection of a tracer particle at different times thus revealed the path line of that particular particle. A similar tracer technique was also employed by Khodak and Borisov [ 121 to measure particle trajectories in a model furnace.
Flow of two diflh-ent place of the granular coke used in an actual system because of two practical difficulties. Coke particles were very dusty and, most importantly, they left smears on the acrylic plate which seriously impede visual investigation. While the bulk density of the plastic pellet, 0.86, is different from that of coke, 0.5, the angle of repose of the plastic pellet, 37”, is about the same as that of coke, 36.5”. Flow of a single granular material Only yellow plastic pellets were employed
in this series of experiments. Two different material distributions, either flat or M-shaped, were studied. The model blast furnace was first filled up with the plastic pellets using the distribution chute. To achieve an M-shaped solid surface, the distribution chute was adjusted to operate at an angle of inclination of 45” and a rotational speed of 19 rpm. The rotational speed of 19 rpm of the distribution chute was chosen to match the linear velocity at the tip of the chute of the commercial unit. For a flat surface, the same charging conditions were also used and the surface was manually flattened by a ruler after each batch charge. When the furnace was full, the distribution chute was shut off and a number of red plastic pellets were placed on the top of the solid surface along the acrylic plate, serving as tracer particles. The red tracer particles have exactly the same physical properties as the yellow plastic pellets. The table discharger was then set to a desirable rotational speed in order to discharge the solids and the monitoring system of the load cells was activated simultaneously to record the stresses. As the top surface descended to a certain level, the time was recorded and the positions of the tracer particles were marked on the acrylic
particles
In this series of experiments, both yellow plastic pellets and granular ore were employed. Except for two charges, the operational procedures were similar to those of the preceding experiment. The distribution chute was now connected alternately to either of two feed bunkers containing plastic pellets and granular ore, respectively, to load alternate layers of the two different particles in different batches into the furnace. In the present experiments, particles descend in the model furnace due only to gravity. The effect of gas flow on the particulate flow was not studied. This is due to the fact that granular material in a blast furnace is relatively coarse. In such a system, gravity is the dominant effect on the particulate flow, especially in the upper part of the furnace. Ho [ 161 indicates that in the actual operation of a blast furnace, the drag force exerted by the gas on the particles contributes only about 12% of the external forces, which is relatively insignificant compared with the gravitational force.
Experimental
results
Flow
granular
of single
and discussions matfzrial
In Fig. 3, the shapes and locations of tracer particles at different times, with the initial surface being flat, are shown by the solid lines. The broken lines in this figure are the connections of individual particle locations at different times which constitute the particle path lines. It was noted that some tracer particles did not survive during the entire descending process, as they have moved away from the acrylic plate and disappeared completely. Consequently, the corresponding path lines had to be terminated before reaching the bottom. Nevertheless, the path lines in Fig. 3 reveal
16
TIME(min1
2I 0
0
Exprrimwtal
-
Theoretical I
35 6.2 9.L 12.4 15.4 18.3 21.3
01 0
26.5 29.0
(a)Z:2lCm
2
1
0
2
1
r/R,
r/R,
33.6
(c)z=220cm
(Throat)
(Belly)
39.8 I#5.8
55.1 61 .l 663 72.9 78.6 61.7
01
90.2
0 0
1
96.0
112.7
Fig. 3. The shapes of the moving front of tracer particles and their path lines.
most of the important characteristics of the granular material flow in the furnace. Note that the moving front of the tracer particles remains almost flat at the top portion, indicating that the major portion of the flow in this region is not affected by the wall and the particulate flow can be approximated by a plug flow. The front is progressively distorted from its original flat shape as tracer particles descend into the shaft, and f!inally,all tracer particles disappear before reaching the dead-man zone. The velocity profiles of particles at different locations can be estimated by taking time derivatives of the particle path lines, shown in Figs. 4(a) and 4(b). The profiles are rather flat at the top, as shown in Figs. 4(a) and 4(b), indicating the insignihcant wall effect and the characteristics of a plug flow. The velocity at the center gradually decreases in the lower portion of the furnace as the particles begin to sense the existence of the peak of the deadman zone. The velocity profiles in Figs. 4(a) and 4(b) indicate that the major portion of the particulate flow at the top portion of the furnace can be
’
I
0
1
2
r/R.
r/R, lb)z=137cm
101.7 107.1
2
ldlz-2L5cm
(Shaft)
(Bosh)
Fig. 4. Velocity distributions of the particulate flow at various levels. (a), z= 20.75 cm (throat); (b), z = 136.95 cm (shaft); (c), z=219.95 cm (belly); (d), z=244.85 cm (bosh).
described as irrotational. Such an assumption was also made by Kuwabara and Muchi [ 141. For an irrotational flow, the particulate stream function 1(,must satisfy the following Laplace equation:
a24J
2
+y-
a
ia+
( 1 --
a~ Y 37
=o
(1)
The particulate stream function of eqn. (1) was solved along with the boundary conditions indicated in Fig. 5. Due to the complex geometry of the furnace, the finite difference method was employed to obtain the numerical solution for the particulate stream function. The vertical component of the local particle velocity was then calculated by J7,lY B
Y aY
(2)
The theoretical velocity profiles, represented by the solid lines in Figs. 4(a) through 4(d), are compared with experimental measurements. As shown in the figures, the prediction of a potential flow reasonably represents the particulate flow at the top portion where the furnace diverges and the center portion where the wall effect is insignillcant. The discrepancy
17
- - -- ExperImental ~
Theoretical
Fig. 6. Comparison of theoretical and experimental ticulate streamlines.
L
par-
Fig. 5. Boundary conditions for the particulate stream function.
between the potential flow theory and the measurement in the near wall region indicates the breakdown of the ix-rotational assumption due to the wall effect. The predictions of the potential flow theory were also compared with the experimental path lines of the tracer particles, shown in Fig. 6. As shown, the predicted path lines follow the experimental ones reasonably well except for the lower portion and near wall region. The path line closest to the center, however, also shows unexpected great discrepancy. Measurements of the local solid flow rate reveal that the flow in the model furnace is not perfectly symmetrical, which may result in the distortion of the path line close to the center. In the study of Khodak and Borisov [ 121, particle path lines similar to Fig. 3 were obtained, but no prediction of particle velocity distribution was attempted. Horizontal flow
stress in the single
material
The time-averaged horizontal stresses measured at six different locations are shown in Fig. 7. As shown in the figure, the averaged horizontal stress first increases as the depth increases from the throat to the shaft, reaches a maximum around the belly, and then de-
Fig. 7. Horizontal stress distribution along the furnace Wall.
creases in the bosh. In Fig. 7, two theoretical stress distributions estimated by the modification of Walter’s theory [8, lo] are also plotted. The solid line in the figure was calculated based on the assumption that the failure of particulate material is passive in the entire furnace, whereas the broken line was based on the assumption of active failure. Details about the calculations of the two theoretical lines are given in the following. In the throat and the belly regions, the furnace walls are vertical and the stress can be estimated in a similar manner. The vertical stress, Er,,in those regions is given [ 8, lo] by (3) where
18
B=
sin 4 cos2 8
+4+k
cos +(l + sir.? 6) + 2k(sin2 6 - sin2 c$)“~ (4) D = cos c$(l + sin2 6) + 2k(sin2 6- sin2 c#$‘~ cos c#I[(~+sin2 8)+2kY
tan+ 2 i 3( tan 6 1
l_[l-(k33i’l”
tan (Ye
= PSg
(7)
and the vertical stress for the converging bosh region is given by K2 tan CY&
da; dz+
Rz-(Z-Q)
tan (y,
(8)
= P&
where ayl and (Ye,and .zl and z2 are the wall angles and the depths of the shaft and bosh regions, respectively. The parameters Kl and K2 are given by K,=2(
l+
2)
and K2=2($
-1)
(10)
where F=
sin s sin 2E--(1 fsin
s cos 2E) tan crl 1 -sin 6 COS(:!E-2cQ)
(11) G=
(13)
Yi =
3(t:..)’ {+-(z2)‘1”1 tan S (15)
and vi is the solution of
Kl tan ala, RI + (z -z,)
sin 6
D _ cos ~(1 + sin2 S) + 2k(sin2 S- sin2 Q)‘~ zcos T~[(1 + sin’ S) + ZkY, sin S]
(6)
where 6 is the angle of repose and dI is the wall friction angle. When using eqn. (3), Ri is equal to the throat radius RI in the throat region, and is equal to the belly radius R2 in the belly region. k is the index for the failure state, k = 1 for an active state and k = - 1 for a passive state. In the shaft region where the furnace wall diverges, the vertical stress can be estimated by modifying the original Walter’s theory [8, lo] to yield +
-
(14)
and 2
sin C$
sin S] (5)
Y=
cos-’
sin 6 Sin(2E-k209 +tan (Y2 1 -sin s COS(2Ef2LY2)
(12)
2~2e=
; +Ti+k
cos-’
(16)
In calculating the theoretical stress distributions, the vertical stress is integrated by taking the initial value of zero vertical stress at the top and using eqn. (3) for the throat region with (Ri=R,), eqn. (7) for the shaft region, eqn. (3) for the belly region (with Ri =Rz) and, finally, eqn. (8) for the bosh region. From the vertical stress distribution, the horizontal stress at each location can easily be obtained. As shown in Fig. 7, the stress measurements follow the predictions of the active state line very well from the throat down to about the belly. The measurement at the lower portion of the furnace, on the other hand, follows the trend of a decreasing stress of the passive state line. This indicate that the actual particulate flow shifts from active failme at the upper portion to passive failure at the lower portion, probably due to the change in the furnace geometry from diverging in the shaft to converging in the bosh. Indeed, the measurements indicate that the transition occurs in between the shaft and the bosh, i.e., somewhere in the belly. Due to the implication of transition from active to passive failure by the measurements, another theoretical stress line is generated accordingly, as shown in Fig. 8. This theoretical line is the same as the active state line in Fig. 7 until z = 203 cm (starting point of the belly), below which it is calculated based on the assumption of passive failure. The sharp increase in the theoretical line in the belly shown in Fig. 8 is due to the assumption of point transition from active to passive failure. The experimental measurements, though showing a similar trend of a decreasing stress as pre-
19 .y
6
Z, z ; F v,
300,
I __
250.
Theoretical
x
Experimental
200.
n
150
0
50
100
150 Z
8. Comparison distributions.
Fig.
T Y
500
s 8
400
$
300
2 z
200
-
200
of theoretical
300
and experimental
stress
Theoretical
x
Experimental
Formation
w 100
x x
E
9
250
(cm)
the figure is the theoretical stress line assuming active failure in the upper portion and passive failure in the lower portion. The average density of the two materials is used to estimate the stress distribution. As shown in the figure, the first three measurements in the upper portion of the furnace follow the theoretical active section very well, but the theoretical passive section only shows the correct trend of a decreasing stress of the measurements in the lower portion. The discrepancy may again be due to the existence of a transition zone for the particles converting from active to passive failure.
x
0 0
50
100
150 z
200
250
300
(cm)
9. Comparison of theoretical and experimental distributions with two dierent particles.
Fig.
stress
dieted in the lower portion, depict a much milder change in the vertical stress. The discrepancy may be due to the fact that in reality a transition zone, instead of a transition point assumed, exists for the particulate flow progressively from active to passive failure changes. Khodak and Borisov [ 121 employed a different technique of floating pressure cells moving with particles to measure the horizontal and vertical stresses in a model furnace. In their measurement of the horizontal stress along the axis, a sharp increase in the horizontal stress near the junction of shaft and belly was shown, which is very similar to the theoretical stress line shown in Fig. 8. This result strongly indicates that a transition from active to passive failure does exist near the belly region. Horizontal
stress in the two-material
flow
Both the average and the fluctuation of the horizontal stress measured with two different materials were found to be greater than those with a single material. The greater average stress is due to the use of denser ore, and the greater fluctuation may be due to the possibility of the load cell contacting different particles at different instants. The time-averaged stresses at various locations are shown in Fig. 9. Also shown in
of dead-man
The shape of the dead-man determined experimentally is shown in Fig. 10. According to Kuwabara and Muchi [ 141, the shape of the dead-man formation can be predicted by integrating the following equation dr - =tan(1! dZ
(17)
where 1
(y’Z____ k6 4
2
2
x tan-’ set 6[tan’ 6-h:r]1’2+k
tan2 6j
(18)
N
260
\
I
1
i
\ x
\
x
\ XX
\
280
\ I
3001
0
20
40
r
10. Comparison man formations.
Fig.
60
e’o
(cm)
of theoretical
and experimental
dead-
20
and
Di
sin s sin[z(E+ IL=
a2) ]
1 +sin 6 cos[2(e+ CQ)]
(19)
Predictions of the dead-man shape by Kuwabara and Muchi’s equation [ 141 are also shown in Fig. 10. The integration of eqn. (17) was performed by choosing the initial value of r to coincide with the experimental value at the wall. The solid line in the figure is the prediction of the dead-man formation based on the assumption of a passive state, whereas the broken line is the prediction based on the assumption of an active state. As shown, the shape of the dead-man is well predicted by the theory assuming passive failure. The implication of passive failure by the dead-man formation is consistent with that found by the stress measurement.
Conclusions
Prom the experiments in the model blast furnace, it is found that the granular material is in an active state above the belly of the furnace and in a passive state below. Consequently, the particulate flow can be reasonably described as an h-rotational flow in the upper portion and a funnel flow in the lower portion. The stress measurements follow the active stress line very well from the top to the belly with an increasing stress, and shift to follow the trend of the passive stress line in the lower portion with a decreasing stress. The measurements also indicate that there exists a transition zone for the particles changing from active to passive state. The dead-man formation is found to be well predicted by the passive failure line, consistent with the stress measurement.
Acknowledgement
The authors wish to thank the China Steel Corporation for its support of this investigation.
List of symbols B
D
defined by eqn. (4) defined by eqn. (5)
F G
g k
Kl K2 1
R RI R2 Ri
defined by eqn. (14), i = 1 or 2 defined by eqn. (11) defined by eqn. (12) gravitational acceleration index for active or passive state, 1 for active state and - 1 for passive state defined by eqn. (9) defined by eqn. (10) length of distribution chute radius of blast furnace radius of throat radius of belly radius of throat or belly, 1 for throat and 2 for belly radial co-ordinate particle velocity in 2 direction defined by eqn. (6) used in eqn. (15), i = 1 or 2 vertical distance, positive downwards distance from top to bottom of throat distance from top to bottom of belly apparent angle of repose angle between shaft wall and vertical axis angle between belly wall and vertical axis angle of repose angle between major principal stress and normal stress on wall defined by eqn. (16), i = 1 or 2 defined by eqn. (19) bulk density of solids mean vertical stress over a cross-section angle of wall friction stream function of particulate flow rotational speed of distribution chute
References 1 S. B. Savage, Brit. J. Appl. Phys., 16 (1965) 1885. 2 K. R. Kaza and R. Jackson, Powder Technol., 33 (1983) 223. 3 Y. M. Chen, J. Chinese Inst. Chem. Eng., 17 (1986) 195. 4 U. Tiiziin, G. T. Houlshy, R. M. Nedderman and S. B. Savage, Chem. E~Q. Sci., 37 (1982) 1691. 5 R. M. Nedderman and U. Tiiziin, Powder Technol., 22 (1979) 243. 6 U. Tfiziin and R. M. Nedderman, Powder Technol., 24 (1979) 257. 7 K. R. Kaza and R. Jackson, C/mm. Eng. Sci., 39 (1984) 96. a H. Sate, T. Sugiyama, M. Nakamura and Y. Ham, Tetsu to Hagam, 20 (1980) S634. 9 H. Nishio, W. Wenzel and H. W. Gudenau, Stahl und E&n, 97 (1977) 867. 10 M. Shimizu, A. Yamaguchi, S. Inaba and K. Narita, Tetsu to Hagam, 68 (1982) 936.
21 11 M. Shim& A. Yamaguchi, S. Inaba and K. Narita, Tetsu to H&me, 20<19&) 5635. 12 L. Z. Khodak and Yu. I. Borisov, Powder Techml., 4 (1970/71) 187. 13 S. Ergun, Ch.em. Eng. B-og., 48 (1952) 89.
14 M. Kuwabara and I. Muchi, ‘Prans. ISIJ., 17 (1977) 330. 15 .I. SzekeIy and M. A. Proposter, D-an-s. ZSZJ, 19 (1979) n* 16 ? K. Ho, M.S. Thesis, Technology, (1986).
National Taiwan Institute
of
13
Technology, 63 (1990) 13-21
On the flow of granular Cheng-Ken
Ho*,
Ye-Mon
Chen**,
Departwumt of Chemical Engineering,
and Jiing-Ruey
Jeng
Steel & Aluminum
Research
material Chun-i
National
& Development
in a model blast furnace
Lint
Taiwan Institute of Technology,
Department,
Taipei (Taiwan)
China Steel Corporation,
Kaohsiung
(Taiwan)
(Received December 8, 1988; accepted May 11, 1990)
Abstract Experimental studies on the flow of granular material in a l/lOth-scale model blast furnace of a commercial unit were conducted. The velocity distribution of the particulate flow, wall stresses, and the shape of the dead-man formation at the bottom of the furnace were measured. It was found that the particulate material is in an active state in the upper portion of the furnace (above the belly) and a passive state in the lower portion (below the belly). Consequently, the behavior of the particulate flow, wail stresses and dead-man formation can be reasonably described according to the aforementioned failure states.
Introduction The discharge of granular material from a silo or a hopper and the corresponding stress distribution associated with the flow have been the object of active research in the past few decades [ l-31. Several uncertainties concerning the granular material render a general theoretical approach difficult; these include whether the material should be regarded as a continuum (plasticity theory) [4] or whether its motion is merely kinematic (kinematic theory) [5, 61, the constitutive relation and the boundary conditions [ 71. The motion of granular material in a blast furnace is further complicated by several factors: the divergence and convergence geometry of the furnace, more than two granules, gas flow and gas-solid reactions. Based on the observation of a two-dimensional furnace, Sato et al. [S] reported that the angle of inclination *Present address: Steel & Ah.tminnm Research & Development Department, China Steel Corporation, Kaohsinng (Taiwan). **Present address: Westhollow Research Center, Shell Development Company, Houston, TX 77251 (U.S.A.). +To whom correspondence should be addressed.
0032-5910/90/$3.50
of the dead-man, i.e. the stagnant coke located at bottom of the furnace, increased with increased air flow but decreased with increased solid descending velocity. Nishio et al. [ 91 also employed a two-dimensional model furnace and observed that the peak of the dead-man formation could reach into the shaft. Shimizu et al. [ 10, 111, using a three-dimensional model furnace, however, found that the peak of the dead-man did not reach the shaft, and its shape could be well predicted by the locus of passive failure. They also observed plug flow movement of solids in the region above the belly and funnel flow movement below the belly. The stresses were found to be greater in the regions below the belly than in those above. Khodak and Borisov [ 12 ] employed a three-dimensional model furnace to measure the distribution of horizontal and vertical stresses. It was found that except for a small region in the vicinity of particle discharge, the stress distribution in the rest of the furnace is very similar to that of a vertical cylinder with a peripheral outflow. For the gas distribution, the prediction of the Ergun equation [ 131 was proven satisfactory [14, 151. In the present study, the motion of granular material in a three-dimensional l/10-scale mo-
0 Elsevier Sequoia/Printed in The Netherlands
14
de1 furnace of a commercial unit was investigated. The horizontal stress and dead-man fqrmation were also studied.
Experimental The model
blast furnace
The experimental set-up for the present study of the particulate flow in the model blast furnace is shown schematically in Fig. 1. The dimensions of the model were one-tenth those of a commercial scale furnace currently operated in the China Steel Corporation. The main portion of the shell of the model furnace was constructed of steel sheets. A transparent acrylic plate was placed at the center of the furnace such that the motion of solids within the furnace could be studied visually through the acrylic
A : Hopper 8 : Bell- less Feeder C : Blast Furnace D : Load Cell E : Dead-man F: G: H: I :
Table Throat Shaft Belly
Discharger
J : Bosh K : Hearth
Fig. 1. Schematic diagram of the model employed in the present study.
blast furnace
During the experiments, the particles were fed from above by a rotating distribution chute of a bell-less feeder, similar to the actual loading device of the commercial unit. In each complete rotation of the distribution chute, only half of the particles were charged into the furnace on one side of the acrylic plate. The particles that fell into the furnace on the other side of the acrylic plate were immediately removed through a duct from below. Thus, throughout the experiments only one-half of the furnace was filled with particles. In the vicinity of the acrylic plate, the presence of the plate caused a slight distortion of the charged particle layer and hence the distribution in the furnace was not perfectly axisymmetric. Different burden distributions could be achieved by adjusting the angle of inclination and the rotational speed of the chute, which were controlled by a personal computer. At the hearth level, the model furnace featured elevengates for solid drainage. The solid discharge rate was controlled by the rotational speed of a table discharger, located below the furnace. Six load cells were installed at various levels on the furnace wall to measure the horizontal wall stresses. Each load cell consisted of four U-shaped springs and eight strain gauges, as depicted in Fig. 2. The output signals from the load cells were monitored by another personal computer. Two different particles, granular sintered ore and yellow plastic pellets, were used in the experiments. Their physical properties are listed in the Table. Plastic pellets were used in
(a)
Top
(b)
Cross-sectional
Fig. 2. Structure
4.Sprlng
View
View
of the load cell.
Sheet
15 TABLE Physical properties of the two particles employed in the experiments Properties
Materials Yellow plastic pellets
Average particle diameter (mm) Bulk density (g/cm”) Angle of repose (“)
5 0.86 37
Granular ore particles 3.5 2.1 37
plate. The distribution chute was then activated again to charge the pellets into the furnace to the original level. The procedures of marking the tracers and batch charging fresh pellets were repeated until the tracer particles were being discharged from the bottom. A connection of a tracer particle at different times thus revealed the path line of that particular particle. A similar tracer technique was also employed by Khodak and Borisov [ 121 to measure particle trajectories in a model furnace.
Flow of two diflh-ent place of the granular coke used in an actual system because of two practical difficulties. Coke particles were very dusty and, most importantly, they left smears on the acrylic plate which seriously impede visual investigation. While the bulk density of the plastic pellet, 0.86, is different from that of coke, 0.5, the angle of repose of the plastic pellet, 37”, is about the same as that of coke, 36.5”. Flow of a single granular material Only yellow plastic pellets were employed
in this series of experiments. Two different material distributions, either flat or M-shaped, were studied. The model blast furnace was first filled up with the plastic pellets using the distribution chute. To achieve an M-shaped solid surface, the distribution chute was adjusted to operate at an angle of inclination of 45” and a rotational speed of 19 rpm. The rotational speed of 19 rpm of the distribution chute was chosen to match the linear velocity at the tip of the chute of the commercial unit. For a flat surface, the same charging conditions were also used and the surface was manually flattened by a ruler after each batch charge. When the furnace was full, the distribution chute was shut off and a number of red plastic pellets were placed on the top of the solid surface along the acrylic plate, serving as tracer particles. The red tracer particles have exactly the same physical properties as the yellow plastic pellets. The table discharger was then set to a desirable rotational speed in order to discharge the solids and the monitoring system of the load cells was activated simultaneously to record the stresses. As the top surface descended to a certain level, the time was recorded and the positions of the tracer particles were marked on the acrylic
particles
In this series of experiments, both yellow plastic pellets and granular ore were employed. Except for two charges, the operational procedures were similar to those of the preceding experiment. The distribution chute was now connected alternately to either of two feed bunkers containing plastic pellets and granular ore, respectively, to load alternate layers of the two different particles in different batches into the furnace. In the present experiments, particles descend in the model furnace due only to gravity. The effect of gas flow on the particulate flow was not studied. This is due to the fact that granular material in a blast furnace is relatively coarse. In such a system, gravity is the dominant effect on the particulate flow, especially in the upper part of the furnace. Ho [ 161 indicates that in the actual operation of a blast furnace, the drag force exerted by the gas on the particles contributes only about 12% of the external forces, which is relatively insignificant compared with the gravitational force.
Experimental
results
Flow
granular
of single
and discussions matfzrial
In Fig. 3, the shapes and locations of tracer particles at different times, with the initial surface being flat, are shown by the solid lines. The broken lines in this figure are the connections of individual particle locations at different times which constitute the particle path lines. It was noted that some tracer particles did not survive during the entire descending process, as they have moved away from the acrylic plate and disappeared completely. Consequently, the corresponding path lines had to be terminated before reaching the bottom. Nevertheless, the path lines in Fig. 3 reveal
16
TIME(min1
2I 0
0
Exprrimwtal
-
Theoretical I
35 6.2 9.L 12.4 15.4 18.3 21.3
01 0
26.5 29.0
(a)Z:2lCm
2
1
0
2
1
r/R,
r/R,
33.6
(c)z=220cm
(Throat)
(Belly)
39.8 I#5.8
55.1 61 .l 663 72.9 78.6 61.7
01
90.2
0 0
1
96.0
112.7
Fig. 3. The shapes of the moving front of tracer particles and their path lines.
most of the important characteristics of the granular material flow in the furnace. Note that the moving front of the tracer particles remains almost flat at the top portion, indicating that the major portion of the flow in this region is not affected by the wall and the particulate flow can be approximated by a plug flow. The front is progressively distorted from its original flat shape as tracer particles descend into the shaft, and f!inally,all tracer particles disappear before reaching the dead-man zone. The velocity profiles of particles at different locations can be estimated by taking time derivatives of the particle path lines, shown in Figs. 4(a) and 4(b). The profiles are rather flat at the top, as shown in Figs. 4(a) and 4(b), indicating the insignihcant wall effect and the characteristics of a plug flow. The velocity at the center gradually decreases in the lower portion of the furnace as the particles begin to sense the existence of the peak of the deadman zone. The velocity profiles in Figs. 4(a) and 4(b) indicate that the major portion of the particulate flow at the top portion of the furnace can be
’
I
0
1
2
r/R.
r/R, lb)z=137cm
101.7 107.1
2
ldlz-2L5cm
(Shaft)
(Bosh)
Fig. 4. Velocity distributions of the particulate flow at various levels. (a), z= 20.75 cm (throat); (b), z = 136.95 cm (shaft); (c), z=219.95 cm (belly); (d), z=244.85 cm (bosh).
described as irrotational. Such an assumption was also made by Kuwabara and Muchi [ 141. For an irrotational flow, the particulate stream function 1(,must satisfy the following Laplace equation:
a24J
2
+y-
a
ia+
( 1 --
a~ Y 37
=o
(1)
The particulate stream function of eqn. (1) was solved along with the boundary conditions indicated in Fig. 5. Due to the complex geometry of the furnace, the finite difference method was employed to obtain the numerical solution for the particulate stream function. The vertical component of the local particle velocity was then calculated by J7,lY B
Y aY
(2)
The theoretical velocity profiles, represented by the solid lines in Figs. 4(a) through 4(d), are compared with experimental measurements. As shown in the figures, the prediction of a potential flow reasonably represents the particulate flow at the top portion where the furnace diverges and the center portion where the wall effect is insignillcant. The discrepancy
17
- - -- ExperImental ~
Theoretical
Fig. 6. Comparison of theoretical and experimental ticulate streamlines.
L
par-
Fig. 5. Boundary conditions for the particulate stream function.
between the potential flow theory and the measurement in the near wall region indicates the breakdown of the ix-rotational assumption due to the wall effect. The predictions of the potential flow theory were also compared with the experimental path lines of the tracer particles, shown in Fig. 6. As shown, the predicted path lines follow the experimental ones reasonably well except for the lower portion and near wall region. The path line closest to the center, however, also shows unexpected great discrepancy. Measurements of the local solid flow rate reveal that the flow in the model furnace is not perfectly symmetrical, which may result in the distortion of the path line close to the center. In the study of Khodak and Borisov [ 121, particle path lines similar to Fig. 3 were obtained, but no prediction of particle velocity distribution was attempted. Horizontal flow
stress in the single
material
The time-averaged horizontal stresses measured at six different locations are shown in Fig. 7. As shown in the figure, the averaged horizontal stress first increases as the depth increases from the throat to the shaft, reaches a maximum around the belly, and then de-
Fig. 7. Horizontal stress distribution along the furnace Wall.
creases in the bosh. In Fig. 7, two theoretical stress distributions estimated by the modification of Walter’s theory [8, lo] are also plotted. The solid line in the figure was calculated based on the assumption that the failure of particulate material is passive in the entire furnace, whereas the broken line was based on the assumption of active failure. Details about the calculations of the two theoretical lines are given in the following. In the throat and the belly regions, the furnace walls are vertical and the stress can be estimated in a similar manner. The vertical stress, Er,,in those regions is given [ 8, lo] by (3) where
18
B=
sin 4 cos2 8
+4+k
cos +(l + sir.? 6) + 2k(sin2 6 - sin2 c$)“~ (4) D = cos c$(l + sin2 6) + 2k(sin2 6- sin2 c#$‘~ cos c#I[(~+sin2 8)+2kY
tan+ 2 i 3( tan 6 1
l_[l-(k33i’l”
tan (Ye
= PSg
(7)
and the vertical stress for the converging bosh region is given by K2 tan CY&
da; dz+
Rz-(Z-Q)
tan (y,
(8)
= P&
where ayl and (Ye,and .zl and z2 are the wall angles and the depths of the shaft and bosh regions, respectively. The parameters Kl and K2 are given by K,=2(
l+
2)
and K2=2($
-1)
(10)
where F=
sin s sin 2E--(1 fsin
s cos 2E) tan crl 1 -sin 6 COS(:!E-2cQ)
(11) G=
(13)
Yi =
3(t:..)’ {+-(z2)‘1”1 tan S (15)
and vi is the solution of
Kl tan ala, RI + (z -z,)
sin 6
D _ cos ~(1 + sin2 S) + 2k(sin2 S- sin2 Q)‘~ zcos T~[(1 + sin’ S) + ZkY, sin S]
(6)
where 6 is the angle of repose and dI is the wall friction angle. When using eqn. (3), Ri is equal to the throat radius RI in the throat region, and is equal to the belly radius R2 in the belly region. k is the index for the failure state, k = 1 for an active state and k = - 1 for a passive state. In the shaft region where the furnace wall diverges, the vertical stress can be estimated by modifying the original Walter’s theory [8, lo] to yield +
-
(14)
and 2
sin C$
sin S] (5)
Y=
cos-’
sin 6 Sin(2E-k209 +tan (Y2 1 -sin s COS(2Ef2LY2)
(12)
2~2e=
; +Ti+k
cos-’
(16)
In calculating the theoretical stress distributions, the vertical stress is integrated by taking the initial value of zero vertical stress at the top and using eqn. (3) for the throat region with (Ri=R,), eqn. (7) for the shaft region, eqn. (3) for the belly region (with Ri =Rz) and, finally, eqn. (8) for the bosh region. From the vertical stress distribution, the horizontal stress at each location can easily be obtained. As shown in Fig. 7, the stress measurements follow the predictions of the active state line very well from the throat down to about the belly. The measurement at the lower portion of the furnace, on the other hand, follows the trend of a decreasing stress of the passive state line. This indicate that the actual particulate flow shifts from active failme at the upper portion to passive failure at the lower portion, probably due to the change in the furnace geometry from diverging in the shaft to converging in the bosh. Indeed, the measurements indicate that the transition occurs in between the shaft and the bosh, i.e., somewhere in the belly. Due to the implication of transition from active to passive failure by the measurements, another theoretical stress line is generated accordingly, as shown in Fig. 8. This theoretical line is the same as the active state line in Fig. 7 until z = 203 cm (starting point of the belly), below which it is calculated based on the assumption of passive failure. The sharp increase in the theoretical line in the belly shown in Fig. 8 is due to the assumption of point transition from active to passive failure. The experimental measurements, though showing a similar trend of a decreasing stress as pre-
19 .y
6
Z, z ; F v,
300,
I __
250.
Theoretical
x
Experimental
200.
n
150
0
50
100
150 Z
8. Comparison distributions.
Fig.
T Y
500
s 8
400
$
300
2 z
200
-
200
of theoretical
300
and experimental
stress
Theoretical
x
Experimental
Formation
w 100
x x
E
9
250
(cm)
the figure is the theoretical stress line assuming active failure in the upper portion and passive failure in the lower portion. The average density of the two materials is used to estimate the stress distribution. As shown in the figure, the first three measurements in the upper portion of the furnace follow the theoretical active section very well, but the theoretical passive section only shows the correct trend of a decreasing stress of the measurements in the lower portion. The discrepancy may again be due to the existence of a transition zone for the particles converting from active to passive failure.
x
0 0
50
100
150 z
200
250
300
(cm)
9. Comparison of theoretical and experimental distributions with two dierent particles.
Fig.
stress
dieted in the lower portion, depict a much milder change in the vertical stress. The discrepancy may be due to the fact that in reality a transition zone, instead of a transition point assumed, exists for the particulate flow progressively from active to passive failure changes. Khodak and Borisov [ 121 employed a different technique of floating pressure cells moving with particles to measure the horizontal and vertical stresses in a model furnace. In their measurement of the horizontal stress along the axis, a sharp increase in the horizontal stress near the junction of shaft and belly was shown, which is very similar to the theoretical stress line shown in Fig. 8. This result strongly indicates that a transition from active to passive failure does exist near the belly region. Horizontal
stress in the two-material
flow
Both the average and the fluctuation of the horizontal stress measured with two different materials were found to be greater than those with a single material. The greater average stress is due to the use of denser ore, and the greater fluctuation may be due to the possibility of the load cell contacting different particles at different instants. The time-averaged stresses at various locations are shown in Fig. 9. Also shown in
of dead-man
The shape of the dead-man determined experimentally is shown in Fig. 10. According to Kuwabara and Muchi [ 141, the shape of the dead-man formation can be predicted by integrating the following equation dr - =tan(1! dZ
(17)
where 1
(y’Z____ k6 4
2
2
x tan-’ set 6[tan’ 6-h:r]1’2+k
tan2 6j
(18)
N
260
\
I
1
i
\ x
\
x
\ XX
\
280
\ I
3001
0
20
40
r
10. Comparison man formations.
Fig.
60
e’o
(cm)
of theoretical
and experimental
dead-
20
and
Di
sin s sin[z(E+ IL=
a2) ]
1 +sin 6 cos[2(e+ CQ)]
(19)
Predictions of the dead-man shape by Kuwabara and Muchi’s equation [ 141 are also shown in Fig. 10. The integration of eqn. (17) was performed by choosing the initial value of r to coincide with the experimental value at the wall. The solid line in the figure is the prediction of the dead-man formation based on the assumption of a passive state, whereas the broken line is the prediction based on the assumption of an active state. As shown, the shape of the dead-man is well predicted by the theory assuming passive failure. The implication of passive failure by the dead-man formation is consistent with that found by the stress measurement.
Conclusions
Prom the experiments in the model blast furnace, it is found that the granular material is in an active state above the belly of the furnace and in a passive state below. Consequently, the particulate flow can be reasonably described as an h-rotational flow in the upper portion and a funnel flow in the lower portion. The stress measurements follow the active stress line very well from the top to the belly with an increasing stress, and shift to follow the trend of the passive stress line in the lower portion with a decreasing stress. The measurements also indicate that there exists a transition zone for the particles changing from active to passive state. The dead-man formation is found to be well predicted by the passive failure line, consistent with the stress measurement.
Acknowledgement
The authors wish to thank the China Steel Corporation for its support of this investigation.
List of symbols B
D
defined by eqn. (4) defined by eqn. (5)
F G
g k
Kl K2 1
R RI R2 Ri
defined by eqn. (14), i = 1 or 2 defined by eqn. (11) defined by eqn. (12) gravitational acceleration index for active or passive state, 1 for active state and - 1 for passive state defined by eqn. (9) defined by eqn. (10) length of distribution chute radius of blast furnace radius of throat radius of belly radius of throat or belly, 1 for throat and 2 for belly radial co-ordinate particle velocity in 2 direction defined by eqn. (6) used in eqn. (15), i = 1 or 2 vertical distance, positive downwards distance from top to bottom of throat distance from top to bottom of belly apparent angle of repose angle between shaft wall and vertical axis angle between belly wall and vertical axis angle of repose angle between major principal stress and normal stress on wall defined by eqn. (16), i = 1 or 2 defined by eqn. (19) bulk density of solids mean vertical stress over a cross-section angle of wall friction stream function of particulate flow rotational speed of distribution chute
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National Taiwan Institute
of