Looking at individual particle flow patterns shows ways to increase flow rates
PROFILING FLOW OF PARTICLES HROUGH lerlll mmn3PE PENINGS IIUI
d
ROBERT M. LAFORGE BILLY
he general problem of the flow of granular materials i.e., to initiate and maintain continuous flow of cohesive materials, and to determine and control the rate of discharge. In t h i s study, velocity profiles of free-flowing particles show that particles flowing from the sides of a hopper interfere with the main discharge stream. This effect can be minimized by modifying the design of the hopper bottom or of the discharge opening. I t is well known that internal pregsures within the mass of material in a hopper result in the compaction of cohesive materials into solid masses which “arch” over the hopper opening interrupting or stopping flow. These pressures are not uniform throughout the mass, and they are not equal in all directions as in liquids. Research in this area has been concentrated on efforts to prevent an accumulation of pressure within the mass ( I , 3, 5-7). Efforts to bypass the problem have resulted in devices for breaking up compacted material to allow it to flow (discharge) while in a dispersed state. The study of noncohesive materials offers an opportunity to determine the influence of factors which increase the rate of discharge r a t h a than those which retard or stop flow. From a study of the dwcharge rates of grain, Ketchum, an early investigator (S), published a simple bani for the rate of flow as the cube of the orifice diameter: rate of flow = k,8Da in which fl is the unit density of the material in the bin, D is the diameter of the aperture, and k is a constant depending on the units used. This proved to be an oversimplication, primarily because other factors which affect the rate of discharge were not included (9). When material is being discharged through a round hole in the bottom of a bin, the general movement of particles toward the opening is known to be fastest in
Tfrom a hopper divida itself into two parts:
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INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
K. B O R U F F
the mass immediately above the opening. I t was shown by Rudd (77) and Runo (72) that this faster
movement extends upward through the mass over the opening, with lesser velocities for particles located outward from a vertical axis through the opening. When such a bin is allowed to empty, material usually remains in the sida of the bin, forming an inverted conical surface, each element of which makes an angle with the horizontal which approximates the angle of repose of the material. I t has been common practice among analysts to assume that during normal discharge, this conical surface separates the moving material from the static or “dead” material, and that the static material in the hopper (below this conical surface) does not move as long as there is a movement of material within the center cone toward the opening (7, 73). Recent investigators such as Brown (4) and Fkverloo (2) have determined that material flows readily through the center of the actual hopper discharge opening, but that there is a space adjacent to the edge of the aperture through which little if any material flows, and that the width of this annulus does not depend on the sue or the shape of the opening. Another investigator, Zenz (74), has used thii concept of an effective area within the hopper opening to develop an analogy to fluid flow based on the Francis weir equation. To investigate these phenomena, we have studied flow patterns by projecting frame-by-frame moving pictures made through a transparent wall in a bin. I t is possible by this means to trace the movements of individual particles down through the mass of freeflowing granules as each approaches the opening and is discharged. The projected flow patterns for hopper slopa of 0”, 20’ and 60’ are presented in Figures 1, 2, and 3, respectively. Hopper surface in all cases
was polished steel. In Figure 1, for 0", note the triangular shape and large size of the dead area in which little or no particle movement takes place. I t will also be noted, contrary to popular opinion, that this dead area does not extend to the edge of the orifice. In the space within approximately an inch of the orifice periphery, particles move laterally as they progress slowly toward the edge of the hopper wall where they work their way into the flow stream and at last fall free, Movement, of course, is at a very slow rate. Particle A in Figure 1 moved from position AI to position Az, an actual distance of 0.525 inches, in 145 frames, or an elapsed time of 2.42 seconds. This is an average velocity of 0.217 inch per second. In Figure 2, for 20" hopper slope, the area of particle inactivity is substantially smaller and of somewhat different shape than that observed at 0". Movement takes place as far as an inch and a half away from the orifice periphery and at a sharply accelerated rate. Particle B moved from BI to Bzi a distance of 0.925 inches, in only 2.45 seconds. This is an average velocity of 0.378 inch per second, which is 64y0 greater than that noted above for horizontal hopper slope. I n connection with this increase in velocity, extended observation revealed the existence of an area of extreme particle interference on each side of the orifice as shown in Figure 4. I n the indicated areas converging particle flow paths set up activity which can best be described as turbulence. Particles collide and rebound, resulting in erratic movement inward, outward, and upward, as well as downward. This activity produces the bridging effect illustrated in Figure 5. An arch alternately forms through the wedging action of the particles and then breaks loose as the particles quickly move into a new configuration and then fall away through the orifice. This condition noticeably reduces the effective flow area of the orifice. The periodic breaking of a temporary arch formation may explain the "dilatant waves" described by Brown ( 4 ) who also noted a variation in the voidage above the aperture and associated these phenomena with the rate of flow. The typical flow pattern for a hopper slope of sixty degrees is shown in Figure 3. There is no area of particle inactivity. The flow paths converge smoothly near the hopper outlet with little or no evidence of turbulence. Apparently particles moving from the side areas toward the main flow column undergo most of the rearrangement and interference along or near the sloping hopper walls at a point well above the orifice. Figure 6 illustrates flow activity in the region of the hopper outlet and below, a t a hopper slope of 60'. Although this "contracting jet effect'' is present at other slope angles, it appears to be more pronounced at 60". The rapidly moving mass is more or less extruded through the orifice, and the lateral momentum of the converging particles results in further constriction of the cross section of flow after leaving the hopper. A short distance below the orifice, the efflux reaches its minimum cross section, and then particle interaction causes 44
INDUSTRIAL AND E N G I N E E R I N G C H E M I S T R Y
the flow pattern to fan out quickly in a "spray" pattern. A measurable characteristic of a flowing mass closely related to flow pattern is the velocity profile. Sample velocity profiles were constructed for each hopper slope used in this study by tracing particle movement and counting the corresponding number of projected frames. In each case, the projected distance moved was converted to actual distance and divided by the ?lapsed time (from the frame count) to arrive at particle velocity. A sample velocity profile of particle activity at zero degrees is shown in Figure 7 . The sketch is not actual size and thus covers a relatively small area in the vicinity of the orifice. The velocity arrows represent the end points and general direction of particle movement for which each velocity has been calculated. The velocities are bssed on the straight line distance between end points and have the dimensions of feet per minute. The wide variation of velocity in the top segment of each path may be noted with interest. Paths C, D, and E in the center of the main flow7 column have an initial velocity practically triple that of paths B and F, which lie ~ l outside l the column. Next will be noted the rapid acceleration in succeeding segments of flow paths B through G. I t is surprising to find that average velocity doubles in the bottom segment of C and D compared to the velocity in the middle segment of those paths. However, due to the angle of approach to the orifice, path A rather sharply decelerates. This particle slows as it converges with other particles moving at more nearly vertical angles toward the hopper outlet. Particle H is near the dead zone discussed in the preceding section and thus registers an extremely low velocity. Figure 8 is a sample velocity profile of flow a t a hopper slope of 20". I t is significant that the velocities in the top segments are lower in every case than the comparable velocities at 0 ". The differences in the bottom segments are even more significant. The central path, D, of the profile for 20" has a terminal velocity only 70y0 as great as that for 0". The substantially smaller velocities across the profile a t 20" are corroborated in the results of previous investigations which showed that for all materials tested, the efflux rate is lower at a hopper slope of 20" than at 0". Probably of most importance is the magnitude of the particle velocities along the hopper walls. The horizontal momentum of these particles converging on the orifice not only reduces the effective orifice opening but also reduces the velocity of the main flow column. The facts disclosed by a study of velocity profiles thus confirm the conclusions drawn from the comparison of flow patterns. A sample velocity profile for 60" hopper slope is shown in Figure 9. Note that the terminal velocities near the center of the hopper are only slightly higher than those found for a hopper slope of 20". However,
M . Laforge is Professor of Industrial Engineering at University o f Tennessee, Knoxville, T e n n . Billy K . Boriif is an Industrial Engineer at the Alcoa Tennessee W o r k s of Aluminum Co. of America. AUTHORS Robert
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20'
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30-
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40'
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60'
HOPPER SLOPE IN DEGREES
WOPPEI SLOIE IN OEGIEES
Figure 10. Effectof parlicIe silc onpow rate through hoppers with thb conocnrioMlfour sides
Figure 11. Effect of hoppa surface roughms onJ?ow rate through hoppers
particle velocities near the sloping hopper walls are much higher. And since these velocities are more nearly vertical, horizontal momentum is less, turbulence and particle interference are relatively low, and restrictions on the d u x are lower than at either of the other two slope angles. Thus, a greater effective flow area and a higher average mass velocity at the orifice produces a greater flow rate at an angle of 60' than at 0' or 20'. These observations indicate that as the variable hopper walls take on positive slope above the flat bottom bin (Oo), increased lateral particle momentum retards and restricts the main flow column and results in reduced flow rates. As the angle steepens, the vertical momentum of particles moving along the sloping walls increases until its helpful effects arrest the restrictive influence of the inmasing lateral momentum. The m i n i u m flow occurs between 20" and 40" slope angle, depending on the material. As the hopper slope increases beyond this point, vertical momentum continues to increase with a corresponding sharp increase in flow rate. The influence of particle movement along the plane of the hopper resulting in turbulence or at least having a restricting influence on the rate of flow was shown not to be confined to angles between the horizontal and ZOO. Figure 10 shows the rates of flow of various materials in cubic feet per minute through the same opening using hopper slopes from -50" to +50°. I t is significant to note that all the curves have the same general shape even though the particle shape and surface characteristics of plastic cubes are quite different from those of the other materials. Since all the runs were made with an essentially constant orifice size, the relative position of
the curves demonstrates the effect of panicle size on the flow rate of bulk materials. As the particle size decreases, the gravity flow rate increases. Figures 10 and 11 portray results using the same hopper opening as the previous figures (square, 1.241inch side). Materials used were:
Maferial Austrian pea seed Vetch seed Turnip seed Plastic globules
Average Particle Diamefer, In. 0.2009 0.1195 0.0463
0.0227
Sfandard Deviafion,
In. 0.0214 0.018
0.0023 0.0062
Bulk Density, Lb./Cu. FI. 50.1 49.4 41 8 53.4
The stimulating effect of the change of hopper slope can be attained by modifying the periphery to the desired angle for only a short distance from the opening. Most of the influence can be achieved by changing the slope within less than one inch. This means that a flat bottom bin with a round orifice could attain the flow rate for a 40" sloping hopper by merely adjusting the edge one inch back from the opening to be a 40' slope. By using negative slopes (40' to 50') it is possible to use a flat bottom bin and get rates of flow comparable to bms with +50" sloping bottoms, and not increase the overall height. Similar increase in flow results from change in hopper surface roughness. The flow rate was first measured for several materials using sloping hopper surfaces of polished steel at angles from 0' to +60". These surVOL 56
NO. 2
FEBRUARY 1 9 6 4
45
Figure 72. Test apparatus 7-Feeding 2-Flow
bin 3- Test hopper control slide 4-Clear plastic hopper face
faces were then coated with coarse sandpaper and the runs repeated with each material (Figure 11). Illogical as it may appear, the results show that in general rough hopper walls yield significantly greater flow rates than smooth surfaces, other factors remaining the same. Further, only a relatively small area of rough surface near the orifice periphery produces the difference in discharge rate. For all practical purposes the influence of hopper surface roughness is confined to a threequarter-inch band immediately adjacent to the hopper outlet. The rate of discharge with a vertical wall (constructed to observe flow patterns) was greater than for conven46
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
tional four-sided or pyramidal hoppers. Using the vertical wall as a basis for better bin flow characteristics, we have developed a corner hopper bin having two contiguous vertical walls and sloping walls adjustable to make angles of 20’, 40’, 50°, and 60’. Flow rates for Austrian peas, vetch seed, and turnip seed were measured at each of these positive slopes and showed that the corner hopper produces flow rates 25 to 35y0greater than those observed for a conventional pyramidal hopper having four sides and a center opening. From these observations it appears that the movement of particles prior to and during gravity discharge is apparently a series of individual particle motions caused by the attraction of gravity and influenced by (1) interference of other adjacent moving particles, ( 2 ) friction between adjacent particles, (3) impact of particles pressing or falling from above, (4) shape of particles, and (5) friction between particles and the bin or hopper surfaces close to the opening. This research also serves to support and partially explain why the area of ineffective flow close to the edge of the opening limits the effective discharge rate as follows : -The ring of ineffective discharge in an opening adjacent to the edge of the hopper is caused by particles entering the vertical discharge stream from the periphery at a slower rate than in the center core. This study has demonstrated a firm basis for this by identifying turbulence at that point. -Because the width of the ring of ineffective discharge is a function of the particle diameter (2, 4, 74) small particles discharge a t faster rates than large particles for a given condition. This was observed in earlier research (4, 70) and confirmed in this work. -The width of the ring of ineffective discharge can also be influenced by degree of turbulence at the hopper lip, which is a measure of the rate at which particles enter the vertical movement of the center core of flow. This is an assumption based on observations in this study. -Factors \\-hich retard this side-entering movement of particles into the central core stream include (1) friction of the particles against the hopper surface, (2) reduced angle (slope) of the hopper near the opening, and (3) friction between particles (as in the case of pressure head within the mass of particles). Results of observations in this study verify these expected results for both surface friction and hopper slope angle. REFERENCES (1) Bauer, Wolfgang., Pzt and Quarry 38 Part 2,78-83 (August 1945). (2) Beverloo, TV. A,, Leniger, H. A., v a n d e Velde, J., Chern. Eng. Sci. 15, 260-9 (1 961). (3) Bovey, Henry T., Engineering h‘ezor 52, 32-4 (1904). ( 4 ) Brown, R. L., Richards, J. C., Tmns. Inst. Chern. E n g . 38, 243-56 (1960). (5) Caughey Robert A. Tooles Calvin W. Scheer 4lfred C., T h c Iowa Sr~ltsCob lege Bulleti; 50, No. 24,’BulletiA 172 ( N o v e k b e r 195i). (6) Fordham, A. A,, Engineering 143, 561-2 (1937). (7) Jenike, A. W., Elsey, P. J., Wooley, R . H., A S T M 60 (1960). (8) Ketchum, Milo S., “ T h e Design of Walls, Bins, and Grain Elevators,” 3rd Ed., p. 323, McGraw-Hill, New York, 1919. (9) LaForge, Robert M., Uniu. of Tenn. Eng. Ex#. Sin. Bull., No. 27 (April, 1962). (10) Lee, Yee, Combustion, 20-7 (January 1960). (11) R u d d , John K., RockProdiictr 57,73-4 (March 1954). (12) Rum, W. R., Modern Materials Handling, 90-1 (February 1956). (13) Smith, Julian C., Chemical Engineering 62 Part 2 , 167-8 (Seprember 1955). (14) Zenz, Frederick A,, Perroleurn Refiner 41, 159-68 (1962).
