82 Australian Bulk Handling Review: September/October 2011

TRANSFER CHUTES

AbstractDynamic scale modelling (DSM) of transfer chutes began as a technique in the early 1990s and has been in use continuously since that time. It is based on dimensional analysis and uses the Froude number as the basis of scaling.

The dimensional analysis approach requires that the ratio of the major forces in the system be kept constant. In the case of transfer chutes, which operate in the dense granular flow re-gime, this means the ratio of the inertial forces to the gravita-tional forces.

The theoretical basis of the technique is applicable to co-hesionless materials. Extension into the modelling of cohesive materials requires empirical methods to be adopted, since cohe-sive and adhesive properties of ores do not scale with the Froude number when the size range of an ore is scaled down.

Validation of the technique was conducted during the initial development and has been ongoing. A wide variety of param-eters can be used to provide the basis for validation. Some exam-ples of these are discussed.

IntroductionConveyor belts have been in use for over a century and conveyor transfer chutes have therefore been in use for the same amount of time. Basic design concepts for chutes have been developed and are included as small sections in texts that have been pub-lished on conveyor design, going back to the 1920s. Some theo-retical work has been published since the late 1960s to assist de-sign, but this has had limited application and has involved a two dimensional approach and approximation.

The development of the hood and spoon chutes in the coal industry has represented a significant step forward in chute de-sign, but these chutes are of limited application. Many other ge-neric chute types have evolved to fill the various niches, but it is true to say that transfer chute design is often poorly conceived and executed.

Prior to the development of DSM, it was a common practice of designers to make models of chutes from perspex or card-board and pour material such as vermiculite through them to gain some understanding of how the ore might behave in three dimensional flows. DSM is a formalisation of this ad-hoc approach. It involves the construction of a scale model of the chute, normally in transparent acrylic and the continuous cir-culation of material through the chute. Chute performance can be visualised using this technique, and design modifica-tions can be explored quickly and cheaply before a final de-sign is selected.

Theoretical backgroundThe fundamental variables involved in the flow of granular mate-rial through a transfer chute are listed below.Mass Flow m Coefficent of restitution eBulk density Particle shape factor f

s

Belt velocity V Linear scale factor LGravitational acceleration g Particle diameter dAngle of repose

By application of the Buckingham Pi theory to this set of vari-ables, the following groups can be delineated.

Using the relationship that the volume throughput, we can write this last group as the Capacity number:

The Capacity number is merely an expression of the fact that the volumetric capacity of the chute varies with the velocity and the cross sectional area.

Of importance here is to note that none of the groups con-tains a density term. So the flow is independent of density. This is an important point and one which people often find difficult to grasp intuitively.

The Froude number, which appears throughout the litera-ture on granular flow, expresses the ratio of inertial to gravita-tional forces.

The angle of repose, which is an expression of inter-particle friction, can be simply maintained through the scaling process, as can the particle shape factor. The coefficient of restitution of real materials varies over a small range and, as will be shown, is of negligible influence unless it is at the extreme of the range.

Flow regimesWhen modelling granular flow by any means, it is important to recognize that there are different flow regimes occurring within the granular material. There has been much discussion on this topic in the literature, with many theoretical models being put forward, but the two models that dominate the discussion are the Bagnold model and the Coulomb model. These are discussed in turn here in relation to chute flow and the implications for Froude number scaling.

The work of Bagnold (1954)Bagnold, a man who developed his interest in sand by way of his adventures in the deserts of Northern Africa in a model T Ford in the 1930s, was one of the first people to investigate the flow of dry granular materials. Using an annular shear cell and wax spheres suspended in a fluid so as to maintain neutral buoyancy, he defined a new flow regime, known as the inertial regime, and

Dynamic scale modelling (DSM) of transfer chutesBy Peter Donecker, Bulk Solids Modelling

TRANSFER CHUTES

then went on to develop the mathematics to describe that flow. He applied this mathematics to the flow of sand in an inclined chute, amongst other things.

The recognition of the inertial, or grain inertial flow regime, is of prime importance to the understanding of flow in trans-fer chutes. It occurs at higher shear rates and velocities than the quasi-static regime which is used in soil science and in hopper flow theory and the effective friction varies with the square of the velocity or shear rate, while in the quasi-static regime the coefficient of friction is constant.

In the inertial regime, the particles are separated from each other and undergo energy interchange by collision. We get this type of flow when granular material moves over the surface of an existing deposit or a surface that has been intentionally made rough, such as by the addition of wear bars.

Bagnolds theoretical analysis led him to predict the flow ve-locity in an inclined chute to be given by the expression:

This gave him results that were of the order of 50% too high, which was not unexpected, but they did show the correct trend. He records that, in his experiments, there remained a fixed bed of constant depth in the chute after all runs. Though un-fortunately he does not record this thickness, his flow height is measured above this fixed bed, which provided a rough surface. So his results are all comparable with other tests conducted on chutes with rough surfaces.

If we look carefully at Bagnolds expression, for the case of linear scaling, we can say that Dy and we can re-arrange the terms to come to the result:

So we find that, coming from a purely theoretical approach, which is then compared with experiment, the flow is described by the condition of constant Froude number.

There have been many subsequent tests carried out on flow down inclined chutes of varying surface roughness and inclina-tion, and examination of the results of these investigations always reveals the underlying Froude number relationship. The presence of granular jumps, analogous to hydraulic jumps, has been shown by Savage (1979) to be dependent on the Froude number also.

Brennen & Sabersky (1989) explored flows in smooth in-clined chutes using a continuously recirculated system of glass beads. They showed that the effective friction was a function of the Froude number. At low values of the Froude number, cor-responding to the quasi-static regime, the effective friction was close to constant, while at a critical value of the square form of the Froude number, corresponding to the transition to the dense inertial flow regime, the effective friction rose vertically. Thus the effective friction serves to hold the system to a constant Froude number. These results for two different particle sizes are shown in figure 1.

Coulomb frictionThe other model of flow in a chute is the classic friction ap-proach of Coulomb. The Coulomb friction model forms the basis of the well known analysis of Roberts (2001), which is used to describe the flow in hood and spoon style chutes, so commonly used in the coal industry. A diagram showing the force balance in the spoon section of such a chute is shown in figure 2.

It can be seen from the diagram that most of the slip is hap-pening at the chute interface and this fits with the concept of

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84 Australian Bulk Handling Review: September/October 2011

Coulomb friction. Roberts therefore defines an equivalent fric-tion that he relates to the chute geometry. By assuming that this friction is constant over the spoon section of the chute, he derives the following expression for the velocity in the chute, as a function of the angle , which it can be seen from inspection, is equal to the position around the curved element, starting from where it is vertical.

We can declare a local value of v in realtion to .

Taking the square of both sides and re-arranging, we get:

We can clearly see that the LHS represents the Froude num-ber, and that this is a constant for any given position around the curve, independent of the scale. So, Froude number scaling works nicely for curved chutes.

TrajectoriesAnother form of motion in chutes that is not so strongly corre-lated with friction is the trajectory from the head pulley. There are numerous versions of this calculation, but we will take as an example that of Booth (1934).

He expresses the flow condition as a function of the depar-ture angle from the head pulley, after considering friction. He arrived at the expression below:

From this, we can clearly see that the LHS of the equation is the Froude number, in this case related to the variable , the departure angle. Since the RHS of the equation does not contain any quantities that depend on the size of the system, the Froude number serves as a scaling criterion for geometrically similar sys-tems involving trajectories.

Similar Froude number relationships for cohesionless granu-

lar flows can be found in many other geometries, such as flow from hoppers, flows in rotating drums, flows in high speed shear cells etc.

The effect of material parametersIf we look at the above expressions for the motion of granular material, we do not see any terms involving such parameters as density, coefficient of restitution, rolling friction, shape fac-tor, or particle to particle friction coefficient. The closest we come is the lumped equivalent friction value in Roberts equa-tion, which is in itself an estimate. How then, we might ask, can any of this work have any meaning? The answer perhaps lies in the fact that these parameters are of relatively minor importance in the types of flow we are seeing. Furthermore, the range of these variables for real particles is small.

In the case of DEM modelling these values represent pa-rameters that can be adjusted to make the model fit some de-sired outcome such as replicating a scale model of a particu-lar flow regime, but any cursory perusal of the literature will reveal that a wide range of these values is applied for similar materials and that the actual value does not necessarily cor-respond with a real physical measurement. Furthermore, the real world values of these parameters do not change as the flow regime changes, as DEM requires.

In a comprehensive review of laboratory tests and comput-er simulations of flow in inclined chutes, the Groupement De Recherche Milieux Diviss (G. D. R. Midi) (2004) investigated the influence of the coefficient of restitution and the inter-particle friction on the velocity profiles in flows in inclined chutes in the dense flow regime and came to the interesting conclusion that the flows did not depend on the coefficient of restitution for values of e

Where is the thickness of the material that is left be-hind when a granular material is allowed to flow down a rough plane at any given angle of inclination. His single parameter

carries all the variables associated with the particles and is a simple measurement to conduct, providing that the par-ticle size range is not too great. His expression is strikingly similar to Bagnolds equation and is yet another example of Froude number scaling.

These results confirm the practical results on dynamic scale chute modelling that began 20 years ago. They explain why it is possible to use simple synthetic materials to model chute behaviour. These materials need only be selected on the basis of their particle size and shape and angle of repose, dis-regarding other parameters. There is no need or justification in using scaled samples of the actual ore. We are, after all, us-ing perspex chutes.

Cohesive flowThe DSM technique was developed for cohesionless granular solids. Extension of the technique to cohesive ores would re-quire that the cohesive and adhesive forces in the circulating material be kept in a constant ratio with the inertial forces. It is not possible to simply crush up a sample of ore, maintaining constant moisture content and expect cohesion and adhesion to scale.

These forces will tend to be grossly overstated and very misleading results can be obtained by such an approach. In-stead, it has been found by experience that it is possible to formulate mixtures that simulate the behaviour of cohesive ores very effectively, displaying such behaviour as avalanch-ing flow, cohesive build-up and slow adhesive accumulation of fines.

By varying the proportions of the components in the mix, it is possible to simulate a range of properties from free-flowing to highly cohesive. Once the model is constructed and mount-ed, it can be challenged with a range of materials very quickly. It is rare for testing to take more than a day. By this means, chute behaviour under a wide range of conditions, such as is frequently found in the real world, can be quickly evaluated.

The complexity of cohesive granular materials means that even the behaviour under quasi-static conditions is not well defined in a mathematical sense. The behaviour under inertial flow conditions is even less well defined (Mitarai & Nori, 2006).

The importance of inertial effects can be appreciated by anyone who has observed the simple fact that a sticky ore con-taining large particles is easier to handle than one w hich is comprised entirely of fines. Translation of results from tests conducted in the quasi-static regime into the dynamic domain is clearly not a viable approach in this case.

ValidationAn important consideration in any modelling technique is to be able to validate the test model results against the full scale chute results. There exist a large number of parameters that can be used for verification and some of these are listed in table 1.

Validation example 1The first dynamic scale model tested was an iron ore chute at Hamersley Iron in 1992. A view of this chute, looking from the discharge end of the v-feeder is shown in figure 4.

In the case of this chute, information about the perfor-mance in two configurations was known. The first configura-tion incorporated a v-feeder that was 100mm wider than the second configuration. It was known that this change in width led to a complete alteration of the flow pattern from choked flow in the first case, to free flow in the second case at a flow rate of 7200tph.

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Investigation by modelling, using cracked wheat as the ore, showed the same transition from choked to free flow happening at the same equivalent tonnage. By removal of the liner plates in the v-feeder, it was possible to determine the flow streams against the surface by overlaying the liners with transparent film and marking the direction of the wear scratches on the liner surfaces, which served as flow vectors.

The flow pattern in the full scale chute and the model chute were shown to be identical. A third feature in both cases was the existence of a fast flowing stream on the surface of the ore, which was evidenced by accentuated localised wear in the full scale chute and could be observed through the transparent model chute. So, three separate parameters provided validation between model and full scale.

It is noted here that the wear surfaces in this chute, when examined by scanning electron microscope, did not show a predominance of micro-cutting as one might expect, but in-stead had the appearance of being hammered by millions of small blows, leading to a surface fatigue wear mechanism. This is consistent with the concept of inertial energy transfer be-tween the rocks and the liner surfaces.

Validation example 2In May, 1995, a chute handling washed bauxite for a stacker was modelled, again using cracked wheat. The model is shown in figure 5.

In this case, the model predicted that the ore would flow down the cylindrical section of the chute with a bias to one side, before stagnating in the inverted conical section and then bifurcating as it loaded onto the outgoing belt. A flow bias from to the far side of the belt was predicted.

When the full scale chute was commissioned, the effects shown in the model were duplicated exactly, despite the fact that

the cracked wheat was slightly more angular than the washed bauxite. So, in this case, the overall flow patterns together with the belt loading indicate the validity of the model.

Another factor not mentioned in table 1 was back-spill. Simi-lar back-spill issues were shown to exist in the model and the full scale chute, depending on the angle of the belt representing the boom. These effects are difficult to quantify.

Validation example 3In 2009, a large bifurcated chute handling primary crusher product was modelled. This project involved two phases. The first was modelling of the existing chute and the second was the modelling of the proposed design revision.

In figure 6, the model of the existing chute is shown. This image is taken from a video clip, so the clarity is less than optimal, but it is enough to show that the two outgoing belts are showing biased loading due to segregation of lump to one side. The inset clarifies this segregation.

This is the same effect that was observed in the full scale chute. Of interest in this case is that the chute was modelled else-where using a sample of crushed ore and the segregation issue was not identified. In figure 7 the segregation is quite clear. That material used in this case for the large lumps was dog biscuits!

Validation example 4

In 2011, a chute handling copper ore was modelled using a proprietary mixture of materials including attapulgite and wood flour. The model chute is shown in figure 7.

The chute comprised an inclined rear wall covered in ledges to prevent wear by retaining a coating of ore. The belt was a slow belt case, the most difficult of trajectories to predict.

This was a chute designed to replace an existing chute, so there was information from the existing chute regarding the trajectory as well as the considerable cohesive and adhesive build-up that was occurring. Stage one of the modelling process was to duplicate the effects seen in the existing chute. These details will not be gone into here, but suffice to say, the effects in the existing chute were verified, as was the trajectory.

TRANSFER CHUTES

Figure 4: Iron ore chute, 1992.

Figure 5: Chute handling washed bauxite, modelled using cracked wheat, 1995.

Figure 6: Model of bifurcated chute, showing segregation on outgoing belts (2009).

Table 1 - Parameters that can be used for model validation.

Wear scratches Choked flow condition Ore trajectory Adhesive build-up

Cohesive build-up Segregation effects Surcharge angle Loading bias

Wear pattern Dust effects Free surface shape Wash line

87Australian Bulk Handling Review: September/October 2011

The trajectory was critical in this case, and careful position-ing of the model of the revised design was used to work out how far to move the head pulley so that the deflector was not needed and the flow could be sufficiently centred to load the outgoing belt without bias. In DSM we can set the transition geometry up to match the actual belt. DEM packages at this stage do not allow this feature, allowing only the one simple transition geometry where the head pulley is in the plane of the troughing idlers. This is an uncommon configuration in the real world and does not allow accurate trajectory prediction.

When the chute was built, the flow patterns were seen to match the full scale chute perfectly. However, perhaps the most impressive feature of the validation in this case was the duplication of the form of the adhesive build-up on the back wall over time. A comparison of this build-up in the model and the full scale chute is shown in figure 8.

There are many other examples that could be used to illus-trate the validation techniques mentioned in table1, but there is not space here to provide more. The four cases shown illus-trate not only how well validated the modelling method is, but how long ago the validation process was achieved and how it applies even to complex features seen in chutes handling highly variable and cohesive ores.

This is far in advance of what we are seeing published on DEM at present, with validation still lingering within the realm of tentative laboratory scale bench tests, beginning to extend into meso-scale tests and being confined almost exclu-sively to hood and spoon style chutes.

ConclusionDynamic scale modelling of transfer chutes has been in suc-cessful, validated operation for nearly 20 years in Australia and

has been applied to a wide variety of ores, both free-flowing and cohesive as well as the full range of chute designs. It is not necessary to use scaled down versions of the actual ore. In fact the relevant ore properties do not scale in the cohesive case. Instead, synthetic ores can be made from a variety of mixtures of materials and these can be used to successfully model the flow of ores in full scale chutes.

References Bagnold RA, 1954, Experiments on a Gravity-Free Disper-

sion of Large Solid Spheres in a Newtonian Fluid under Shear. Proc. R. Soc. Lond. A, 225, 49-63.

Brennen CE , Sabersky RH, 1989 Shear Flows of Rapidly Flowing Granular Materials Trans ASME,.J. Applied Mechan-ics, Vol 54, 801-805.

G. D. R Midi, 2004, On dense granular flows, Eur. Phys. J. E, 14, 341-365.

Mitarai N, Nori F,2006, Wet granular materials, Advances in Physics, Vol 55, Nos 1-2, 1-55.

Roberts AW, 1969, An Investigation of the Gravity Flow of Non-cohesive Granular Materials through Discharge Chutes, Trans. A.S.M.E,.,J Engrg. Ind.,91,373.

Roberts AW, 2001, Chute Design Considerations for Feed-ing and Transfer, Proceedings of the BeltCon 11 conference, Randburg, Republic of South Africa.

Savage, SB. 1979, Gravity flow of cohesionless granular materi-als in chutes and channels, J. Fluid Mech, vol. 92, part 1, 53-96.

Booth, E.P.O.1934 Trajectories from conveyors - method of calculating them corrected. Engineering and Mining Journal, Vol. 135, No. 12, pp. 552-554.

TRANSFER CHUTES

Figure 7: Model of chute handling copper ore.

Figure 8: Comparison of adhesive build-up on back wall between model, left, and full scale chute, right (with permission from Gulf Conveyor Systems).

Contact: Peter Donecker, email bulksm@q-net.net.au