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Flow patterns near a solid obstacle in a fluidized bed
Shorter
communications
Table 5. Selection of the optimal recycle concentration
X4
Xl
0.036 0.039 0.042 0.045 0,048
f3(x4, Xl)
0.1180 0.1195 0*1210 0.1225 0*1240
0.1012 0.1017 0,1018 0.1016 0.1009
finally compute the v’s which were desired. The results are given in Table 6. In order to refine and check this solution an independent programme was written to perform a search in three dimensions using a pattern search routine. These results also appear in Table 6. Table 6.
At each stage the maximum was found by a Fibonaceian search since a careful check indicated that the functions were unimodal over the ranges of concentrations covered. It should be noted that ARIS [4] indicated that the functions he encountered were not unimodal and a special search procedure had to be used. AIUS’ [4] solution (no recycling) was checked by this investigator and no such difficulty was found. However, a return of 0.10823 was found while Aris indicated a return of 0.10753. The difference may well be in the values of the equilibrium data and the method of interpolation used. In this work equilibrium values were read-off the curve supplied by ARID [4] and the resulting data was smoothed (Table 1) CHIEN [SJ. Simple parabolic interpolation was used throughout. Acknowledgment-Discussions with Prof. A. ACRIVOS, Prof. D. L. JOHNSTONand Dr. H. CHIEZNare gratefully acknowledged.
The optimal solution
Refined solution (Pattern search) Maximum return = 0.10187
NOTATION X
Solute concentration Flow rate of process stream Profit or objective function Cost ratio Y Concentration of solute in wash stream Flow rate of wash stream Wt Ratio of wash rate to process stream flow rate wt/q Vi r Recycle flow rate
Dynamic programming solution Maximum return = 0.1018
4
n
1 2 3 4
0.04:304 0.055775 0.078218 0.12065
0.2;989 0.32734 0.53028
0.&20 0.0564 0.0790 0.121
0.;74 0.335 0.518
E. M. ROSEN Tables 2, 3 and 4 were extracted from tables generated by an IBM 704 programme for increments of 0.003 for the state variable and parameter xl over the range of possible values.
Applied Mathematics Monsanto Chemical Co. 800 N. Lindbergh St. Louis 66, MO.
REFERENCE.3
JACKSONR., Chem. Engng. Sci. 1963 18 215 RUDD D. F. and BLUME. D., Chem. Engng. Sci. 1962 17 277 MITTEN L. G. and NEMHAUSER G. L., Chem. Engng. Progr. 1963,59 52 ARIS R., RUDD D. F. and AMUNDSONN. R., Chem. Engng. Sci. 1960 12 88.
Chemical Engineering Science, 1964, Vol. 19, pp. 1001-1002. Pergamon Press Ltd., Oxford.
Printed in Great Britain.
Flow patterns near a solid obstacle in a fluidized bed SOLID obstacles may be fitted in fluidized beds for a variety of reasons, e.g., to break up bubbles and so promote “smoother” fluidization, or as heat-exchange pipes carrying steam or cooling water. This note describes some experiments that have been carried out to investigate photographically the flow patterns of particles and of fluidizing fluid near a solid obstacle in a fluidized bed. Two systems have been studied: (i) sand particles (av. dia, 0.01 cm) and air, and (ii) glass (ballotini) spheres (av. dia. 0.05 cm) and water.
EXPERIMENTAL In the sand/air experiments, a cylindrical obstacle (2 cm dia., 1 cm long) was fitted across the thickness of a “2dimensional” bed (approx. 75 cm deep, 30 cm wide, 1 cm thick). The obstacle was placed symmetrically about one quarter of the way up the particle bed from the distributor plate. When the sand particles are fluidized by air at flowrates up to 2-3 times that required for incipient fluidization three distinct flow regimes may be observed near the obstacle:
1001
Shorter communications In the ballotini/water experiments, a cylindrical obstacle (5 cm dia., 1 cm long) was fitted across the thickness of a 2-dimensional bed (approx, 38 cm deep, 30 cm wide, 1 cm thick). The obstacle was placed in the bed as shown in Fig. 2. The water streamlines are made visible by simultaneously injecting seven separate streams of a blue dye, cvanol FF. into the bed. The dark circle on the uhotoarauhs. which appears to surround the obstacle, is part of the back support to the apparatus and has nothing to do with the water streamlines. The superficial velocity of water at incipient fluidization is 0.32 cm/set, and in Fig. 2 (a), (b), (c), (d) the velocities are 0.12, 0.19, 0.35 and 0.37 cm+, respectively. At flow rates distinctly below incipient fluidization [Fig. 2 (a), (b)] the water stream-lines move round the obstacle in ideal fluid flow. In the wake region above the obstacle there is some mixing across the stream-lines, probably due to particle movement. At flow rates approaching incipient fluidization and above it [Fig. 2 (c), (d)] the flow pattern is changed: the streamlines no longer follow a path round the obstacle, but rather curve in towards it. This seems to be due to the circulation of particles in the regions at about 10 o’clock and 2 o’clock with respect to the obstacle. The particle circulation appears to drag water towards the obstacle over much of its lower half. At higher flow rates, up to twice that atincipientfluidization, thereis an apparently defluidized region above the obstacle, and a thin film of water, devoid of particles, below the obstacle. However, neither of these effects appear to be as pronounced as in the sand/air experiments.
8 (9)
(IO)
0 0
Q3
OQ
DISCUSSION
I
FIG. 1 (a) below the obstacle there is a thin film of air of variable thickness. In our experiments the film thickness was very approximately 05 mm. (b) above the obstacle there is little particle movement, and the region is apparently defluidized. The extent of this region is reduced by increasing the air flow rate, but it can extend up to four obstacle diameters above the obstacle when the flow rate is several times that at incipient fluidization. (c) a region approximately at either end of the horizontal diameter of the obstacle in which air from the air film under the obstacle forms into chains of bubbles. Fig. 1 shows tracings taken from ten consecutive frames (at 64 frames/set) of a tine-photograph of the bed in the neighbourhood of an obstacle. The obstacle is shown inthetracings by a dark circle. The flow rate to the bed is 1.75 times the value at incipient fluidization, and the tracings show the formation of a bubble at the obstacle. The 2-dimensional bed is illuminated from both back and front, and bubbles extending across the thickness of the bed appear clear in the tracings. Bubbles against the near bed wall, which do not extend across the whole thickness of the bed, appear as shaded areas of irregular shape. Frame 2 of the sequence shows a pocket of air beneath the obstacle which divides (in frame 4) to right (mainly) and left of the obstacle. Frames 6-10 show the progress of a bubble chain above-but slightly to one side of-the obstacle.
The experiments described refer to fluid flow rates not much in excess of that at incipient fluidization, and it seems likely that the apparently defluidized region above the obstacle is disrupted and broken up at high fluidizing flow rates, and under conditions of particle transport. The observations have important implications for heat transfer between a solid object and a fluidized bed in which the object is placed. If the heat transfer is to be good then the surface of the object needs to be brought into contact as rapidly as possible with fresh particles from regions of the bed away from the surface. Thus an apparently defluidized part of the bed near the object would be detrimental to good heat transfer. Moreover, this suggests that the heat transfer to an object in a fluidized bed will be a function of the orientation of the object in the bed. There is some experimental evidence [l] that this is so: a flat plate, for example, is best arranged vertically in a fluidized bed (rather than at any angle to the vertical) in order to optimize heat transfer from the bed to the plate. Acknowledgemenl-One of us (D.H.G.) is grateful for assistance from the Central Electricity Generating Board during the course of this work. D. H. GLASS D. HARRISON Department of Chemical Pembroke Street Cambridge
Engineering
REFERENCE
111 SINCLAIRR., WRIGHTJ. C. J. and THOMASC. G., BISRA Report PE/A/l0/64.
1002
communications
Table 5. Selection of the optimal recycle concentration
X4
Xl
0.036 0.039 0.042 0.045 0,048
f3(x4, Xl)
0.1180 0.1195 0*1210 0.1225 0*1240
0.1012 0.1017 0,1018 0.1016 0.1009
finally compute the v’s which were desired. The results are given in Table 6. In order to refine and check this solution an independent programme was written to perform a search in three dimensions using a pattern search routine. These results also appear in Table 6. Table 6.
At each stage the maximum was found by a Fibonaceian search since a careful check indicated that the functions were unimodal over the ranges of concentrations covered. It should be noted that ARIS [4] indicated that the functions he encountered were not unimodal and a special search procedure had to be used. AIUS’ [4] solution (no recycling) was checked by this investigator and no such difficulty was found. However, a return of 0.10823 was found while Aris indicated a return of 0.10753. The difference may well be in the values of the equilibrium data and the method of interpolation used. In this work equilibrium values were read-off the curve supplied by ARID [4] and the resulting data was smoothed (Table 1) CHIEN [SJ. Simple parabolic interpolation was used throughout. Acknowledgment-Discussions with Prof. A. ACRIVOS, Prof. D. L. JOHNSTONand Dr. H. CHIEZNare gratefully acknowledged.
The optimal solution
Refined solution (Pattern search) Maximum return = 0.10187
NOTATION X
Solute concentration Flow rate of process stream Profit or objective function Cost ratio Y Concentration of solute in wash stream Flow rate of wash stream Wt Ratio of wash rate to process stream flow rate wt/q Vi r Recycle flow rate
Dynamic programming solution Maximum return = 0.1018
4
n
1 2 3 4
0.04:304 0.055775 0.078218 0.12065
0.2;989 0.32734 0.53028
0.&20 0.0564 0.0790 0.121
0.;74 0.335 0.518
E. M. ROSEN Tables 2, 3 and 4 were extracted from tables generated by an IBM 704 programme for increments of 0.003 for the state variable and parameter xl over the range of possible values.
Applied Mathematics Monsanto Chemical Co. 800 N. Lindbergh St. Louis 66, MO.
REFERENCE.3
JACKSONR., Chem. Engng. Sci. 1963 18 215 RUDD D. F. and BLUME. D., Chem. Engng. Sci. 1962 17 277 MITTEN L. G. and NEMHAUSER G. L., Chem. Engng. Progr. 1963,59 52 ARIS R., RUDD D. F. and AMUNDSONN. R., Chem. Engng. Sci. 1960 12 88.
Chemical Engineering Science, 1964, Vol. 19, pp. 1001-1002. Pergamon Press Ltd., Oxford.
Printed in Great Britain.
Flow patterns near a solid obstacle in a fluidized bed SOLID obstacles may be fitted in fluidized beds for a variety of reasons, e.g., to break up bubbles and so promote “smoother” fluidization, or as heat-exchange pipes carrying steam or cooling water. This note describes some experiments that have been carried out to investigate photographically the flow patterns of particles and of fluidizing fluid near a solid obstacle in a fluidized bed. Two systems have been studied: (i) sand particles (av. dia, 0.01 cm) and air, and (ii) glass (ballotini) spheres (av. dia. 0.05 cm) and water.
EXPERIMENTAL In the sand/air experiments, a cylindrical obstacle (2 cm dia., 1 cm long) was fitted across the thickness of a “2dimensional” bed (approx. 75 cm deep, 30 cm wide, 1 cm thick). The obstacle was placed symmetrically about one quarter of the way up the particle bed from the distributor plate. When the sand particles are fluidized by air at flowrates up to 2-3 times that required for incipient fluidization three distinct flow regimes may be observed near the obstacle:
1001
Shorter communications In the ballotini/water experiments, a cylindrical obstacle (5 cm dia., 1 cm long) was fitted across the thickness of a 2-dimensional bed (approx, 38 cm deep, 30 cm wide, 1 cm thick). The obstacle was placed in the bed as shown in Fig. 2. The water streamlines are made visible by simultaneously injecting seven separate streams of a blue dye, cvanol FF. into the bed. The dark circle on the uhotoarauhs. which appears to surround the obstacle, is part of the back support to the apparatus and has nothing to do with the water streamlines. The superficial velocity of water at incipient fluidization is 0.32 cm/set, and in Fig. 2 (a), (b), (c), (d) the velocities are 0.12, 0.19, 0.35 and 0.37 cm+, respectively. At flow rates distinctly below incipient fluidization [Fig. 2 (a), (b)] the water stream-lines move round the obstacle in ideal fluid flow. In the wake region above the obstacle there is some mixing across the stream-lines, probably due to particle movement. At flow rates approaching incipient fluidization and above it [Fig. 2 (c), (d)] the flow pattern is changed: the streamlines no longer follow a path round the obstacle, but rather curve in towards it. This seems to be due to the circulation of particles in the regions at about 10 o’clock and 2 o’clock with respect to the obstacle. The particle circulation appears to drag water towards the obstacle over much of its lower half. At higher flow rates, up to twice that atincipientfluidization, thereis an apparently defluidized region above the obstacle, and a thin film of water, devoid of particles, below the obstacle. However, neither of these effects appear to be as pronounced as in the sand/air experiments.
8 (9)
(IO)
0 0
Q3
OQ
DISCUSSION
I
FIG. 1 (a) below the obstacle there is a thin film of air of variable thickness. In our experiments the film thickness was very approximately 05 mm. (b) above the obstacle there is little particle movement, and the region is apparently defluidized. The extent of this region is reduced by increasing the air flow rate, but it can extend up to four obstacle diameters above the obstacle when the flow rate is several times that at incipient fluidization. (c) a region approximately at either end of the horizontal diameter of the obstacle in which air from the air film under the obstacle forms into chains of bubbles. Fig. 1 shows tracings taken from ten consecutive frames (at 64 frames/set) of a tine-photograph of the bed in the neighbourhood of an obstacle. The obstacle is shown inthetracings by a dark circle. The flow rate to the bed is 1.75 times the value at incipient fluidization, and the tracings show the formation of a bubble at the obstacle. The 2-dimensional bed is illuminated from both back and front, and bubbles extending across the thickness of the bed appear clear in the tracings. Bubbles against the near bed wall, which do not extend across the whole thickness of the bed, appear as shaded areas of irregular shape. Frame 2 of the sequence shows a pocket of air beneath the obstacle which divides (in frame 4) to right (mainly) and left of the obstacle. Frames 6-10 show the progress of a bubble chain above-but slightly to one side of-the obstacle.
The experiments described refer to fluid flow rates not much in excess of that at incipient fluidization, and it seems likely that the apparently defluidized region above the obstacle is disrupted and broken up at high fluidizing flow rates, and under conditions of particle transport. The observations have important implications for heat transfer between a solid object and a fluidized bed in which the object is placed. If the heat transfer is to be good then the surface of the object needs to be brought into contact as rapidly as possible with fresh particles from regions of the bed away from the surface. Thus an apparently defluidized part of the bed near the object would be detrimental to good heat transfer. Moreover, this suggests that the heat transfer to an object in a fluidized bed will be a function of the orientation of the object in the bed. There is some experimental evidence [l] that this is so: a flat plate, for example, is best arranged vertically in a fluidized bed (rather than at any angle to the vertical) in order to optimize heat transfer from the bed to the plate. Acknowledgemenl-One of us (D.H.G.) is grateful for assistance from the Central Electricity Generating Board during the course of this work. D. H. GLASS D. HARRISON Department of Chemical Pembroke Street Cambridge
Engineering
REFERENCE
111 SINCLAIRR., WRIGHTJ. C. J. and THOMASC. G., BISRA Report PE/A/l0/64.
1002