Streamlined Design Of Chutes To Handle Bulk Solids
David Stuart-Dick & T. Anthony Royal
Jenike & Johanson, Inc
Acknowledgements : The Bionic Research Institute, Chute Design Conference 1991
Plant design which results in reliable flow is essential. Unscheduled plant down-time due to problems at transfer chutes is always expensive.
This paper discusses approaches to chute design, and gives formulae for calculating relevant design data
David Stuart-Dick, Vice President of Jenike & Johnson, Inc., holds a degree in Civil Engineering from the University of Natal. He directs the companies research and development effort, and manages the Californian office.
T. Anthony Royal is also a Vice President of Jenike & Johanson, Inc. He actively consults with clients on solids flow problems.
The uses for chutes are wide ranging and varied. Chutes are used to direct the flow of laundry and packages as well as bulk granular solids. The area where "failed" chute designs are normally costly and, consequently, the area where most effort is directed to improve the designs is where large tonnages of bulk materials are handled. This situation exists in most mining and quarrying operations, ship and railcar loading and unloading facilities.
Some of the problems associated with failed chute designs are plugging of chutes, wear on chute surfaces, unacceptable dust generation, excessive belt wear and particle attrition. By far the most severe of these problems is plugging. Wear on chute surfaces is often dealt with by providing rock boxes, dusting by providing a dust collection system, and excessive belt wear by providing skirts to control bouncing of large lumps. In fact all of these problems can usually be eliminated, or at least minimized, by judicious use of chute design principles.
Referring to Figure 1, the velocity of a stream of particles (assuming no bouncing) after impacting a chute relative to its velocity before impact is:
V2 = cosθ - sinθ tanΦ' V1
Also, the impact force normal to a chute surface is :
FN = m V1 sinθ
V2 = velocity after impact
V1 = velocity before impact
θ = angle of incoming stream relative to chute surface
Φ' = kinematic angle of sliding friction (tan Φ' = coefficient of friction)
FN = force normal to chute
m = mass flow rate
There is a particular combination of θ and Φ' that will reduce V2 to zero (θ + Φ' = 90). At this and larger angles of θ, there is no kinematic sliding of the bulk solid on the chute surface, and the angle Φ' is no longer useful in analyzing the chute.
A chute angle test developed at Jenike & Johanson, Inc. measures critical chute angles as a function of impact pressure. These angles can be used to dictate the minimum chute angle at an impact point where the velocity is reduced to zero. The test consists of loading a sample of the bulk granular solid on a representative coupon of the chute surface with a range of loads to represent different impact pressures. After each load is applied for a few seconds, the load is removed and the coupon is raised about a distant pivot point. The minimum angle at which the solid slides is plotted as a function of impact pressure. A typical plot of the test results is shown in Figure 2.
The rate of changing the direction of a flowing stream of material by impact on a chute surface can significantly affect the stream's velocity. Assuming that we want to avoid reducing the velocity to zero, consider an arrangement where a stream of material must be deflected through an angle θ. If the chute can be arranged so that the stream is deflected twice through angles θ/2, we get:
VI = cos θ - sin θ tanΦ' V1 2 2
at the first impact, and
VII = cos θ - sin θ tan Φ' VI 2 2
at the second impact, The ratio of the velocity after the double deflection to the original velocity is:
VII = cos2 θ - sinθ tanΦ' + sin2 θ tan2Φ' V1 2 2
For one single deflection through the angle θ, the ratio of velocities after and before impact is,
V2 = cosθ - sinθ tanΦ' V1
The ratio VII/V2 obtained by dividing the above equations, shows the advantage in terms of maintaining velocity, of a stepped deflector over a single deflector. Figure 3 shows a family of curves of VII/V2 for values of θ as a function of Φ'. As the graph shows, the. advantage is dramatic when the deflection angle θ is greater than 30.
For example, if the kinematic angle of sliding friction is 28 and the stream must be deflected through an angle of 50, the stream velocity after two deflections of 25 each, will be twice what it would be after a single deflection of 50. At twice the velocity, the stream will have half the cross sectional area.
Extending this argument, it is easy to see that in the limit, a curved deflector will slow down a stream the least, and further, the larger the radius of curvature, the better the stream's velocity will be maintained.
When a bulk solid is sliding on a straight chute surface it will accelerate or decelerate, as a function of α and Φ' (see Figure 4) under the influence of gravity alone:
a = g (sinα - cosα tanΦ')
On a curved surface (in a vertical plane) centrifugal forces will add to the normal forces between the material and the chute, (see Figure 5). This introduces another term to the acceleration equation:
a = g (sinα - cosα tanΦ') - V2/R tanΦ'
R is positive as shown in Figure 5 and the material is assumed to be in contact with the chute at all times.
It is interesting to note the angle at which the term in the above equation cancel. Take values of 25 Φ' and 3m for R. When V = 5 m/s (a free fall drop of 1.3 m) the acceleration is zero when the chute angle is 46 from horizontal. When V = 7.5 m/s (a free fall drop of 2.9 m) the acceleration is zero when the chute angle is 79 from horizontal!
As the material accelerates and decelerate through the chute its cross sectional area changes. This will affect the mass of the element being considered and should be taken into account in the calculations.
It is essential in designing a chute to know what the velocity of the flowing stream is at any point. The concept of a 'throat" in a chute is of no practical significance unless the velocity is known, since the mass flow rate is proportional to velocity and cross sectional area.
Cross Section Shape
In order to control the velocity of a stream through a chute (both magnitude and direction) it is often advantageous to slope the chute rather than allow the material to free fall in a vertical section. While the material is sliding on a sloping chute center of gravity should be controlled relative to the chute cross section. This can be done by shaping the chute cross section. A shape like that shown in Figure 6 concentrates and controls the stream very well.
Most chutes in use today have square or rectangular cross sections. There are many valid reasons for doing this. For example; square or rectangular sections are made from flat plates which are easy to visualize, draw, fabricate, modify, line and replace when sections wear. Flat plates can easily be flanged and bolted, and it is easy to mount inspection ports, blocked chute detectors. etc.. However, when the material being handled is sticky and prone to plug the chute, there are significant advantages to having curved surfaces for the material to slide on. In fact, some of the advantages of a curved chute cross section can be argued for other chute problems as well (like dusting or bouncing of large lumps on a receiving belt).
A curved cross section can be used to center me load whereas a square or rectangular section may allow the load to concentrate in a corner or to disperse and entrain air. Concentrating the load in the center of a curved chute allows the momentum of the moving material to keep the chute clean) whereas concentrating it in the comer of a square or rectangular cross section often results in buildup and plugging.
If a flowing material enters a section of chute with horizontal momentum, it is necessary to deal with this momentum or run the risk of not having the load centered at the chute exit. The path that material will follow can vary with material properties and flow rate.
There are various ways to kill the horizontal momentum including rubber curtains) chains, ribs in the chute etc. The best method depends on the material and the chute layout. In these situations, experience is often more useful than mathematical models; however, models are being developed that can predict flow through various geometries fairly accurately.
Abrasive products that are free flowing do not normally not present difficult wear problems. The easy solution is to provide rock boxes to eliminate impact of the flowing stream on a chute surface. However, one of the most difficult chute problems to solve is how to design for a high flow rate of a sticky material that is abrasive. Examples are wet ash and abrasive ore being transported from in-pit crushers. One of two approaches may be used. Firstly, if space allows, the stream of material can be controlled with a surface very close to its natural trajectory. FN (the normal force between the flowing material and the chute surface) is proportional to the sine of the: impact angle θ. Therefore, by reducing the angle θ, wear will be reduced and the velocity of the material after impact maximized. In addition, the mechanism that causes buildup due to sticking is counteracted in two ways: the impact pressures that cause the problem are reduced, and the momentum of the flowing material will keep the chute, surface cleaned off.
An alternative approach is to minimize the amount of chute surface in contact with the material at the impact points. This is done by using ribs in the chute to create mini rock boxes as shown in Figure 8. When using this approach it is essential to concentrate the stream by using a curved surface and to keep the angle between the trajectory and chute surface small. This approach is recommended when materials, like run-of-mine ore, are being handled where the material consists of large lumps mixed with wet fines. Another example is diamondiferous clayey ore where even abrasion resistant liners do not provide an adequate wear life.
The abrasion resistant ribs ore made integral with the shell is divided into elements. The elements are made to simply hook onto a frame so that replacement of worn elements in the field is simple.
Jenike & Johanson. Inc. engineers pioneered the development of a high speed belt-to-belt transfer chute incorporating these features (U.s. Patent 4,646.910).
Dust is created in a chute when the flowing material entrains air. To avoid dusting, it is essential to keep the material in contact with the chute surface, preferably concentrated, to keep impact angles small and, as far as possible, to keep the velocity through the chute constant. In addition, if the material must land on a belt conveyor at the chute exit, it is essential that the material leaving the chute should be traveling in the direction of and close to, or greater than, the velocity of the belt.
By following these guidelines, the amount of dust generated at a transfer chute can be reduced by orders of magnitude, if not eliminated completely. For example, in a job where plugging and dusting at transfer chutes were causing costly cleanup and maintenance problems at a ship loading facility , we were asked to redesign the chutes. After replacing a particularly troublesome transfer chute, air was sucked into the chute at the point where billowing clouds of dust had previously been generated by the old chute. Since the material (like fine coal) was kept under control in the chute, there was no dust generated within the chute and the exit point was also free of dust problems.
The problems of excessive belt wear and lack of control of material landing on a belt are often due to the same phenomenon. Large lumps being accelerated by the belt bounce and roll after impacting the belt normal to its surface. This increases belt wear and requires extended skirts in the acceleration zone to contain the material. By giving the material a velocity in the direction of the belt, both problems can be reduced or eliminated.
The attrition of a friable product as it flows through a chute will be affected by conditions in the chute. Particle attrition is more likely to occur at impact points where the impact pressures are high than on a smooth surface where the product is sliding. Therefore, in most cases, attrition can be minimized by having a chute designed to: minimize the angle between the flowing stream and chute surface at impact points, keep the flowing stream concentrated and in contact with the chute surface, and keep the velocity of the stream through the chute constant.