Effect of port configuration on discharge from a HICOM® mill

Minerals Engineering 69 (2014) 113–119

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Effect of port configuration on discharge from a HICOMÒ mill Phil J. Owen, Paul W. Cleary ⇑ CSIRO Computational Informatics, Private Bag 33, Clayton South 3168, Australia

a r t i c l e

i n f o

Article history: Received 10 May 2014 Accepted 22 July 2014

Keywords: DEM HICOM mill Mill discharge Comminution Charge transport

a b s t r a c t The discharge behaviour of different port configurations in a HICOM mill is investigated using DEM simulation. The charge in the mill is strongly sheared and circulates rapidly but has a free surface shape that is constant and which rotates with the mill rotation. The horizontal cross-sectional area of the charge decreases with increasing height. Particles within the mill discharge when the rotating charge flows over and is pushed towards the discharge ports. DEM enables the prediction of transient and steady state mass flow rates from each of the individual discharge ports. Twelve discharge ports at different locations in the mill are used here to explore the optimality of the various size and location options and to explore if there is any interaction in the discharge between adjacent ports. This provides information relevant to the operation of this type of mill, guidance for port selection and provides a general demonstration of how DEM can be used to predict transport and discharge behaviour of mills. Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.

1. Introduction The Discrete Element Method (DEM) has become a popular tool to predict the motion of media within tumbling grinding mills. Mishra and Rajamani (1992, 1994) were the first to do this with two dimensional models of just media within ball mills. Cleary (1998, 2001a,b) then included coarse feed into more detailed two dimensional ball mill models. Cleary and Sawley (2002) used a slice model in three dimensions to explore the same type of coarse feed ball mill. Djordevic (2003, 2005) used similar models to estimate the effect of charge size distribution and liner variations on power draw. The first use of DEM for SAG mills was by Rajamani and Mishra (1996). This was followed by Cleary (2001a,c), Herbst and Nordell (2001) and Morrison and Cleary (2004, 2008). Cleary (2004) presented a complete dry pilot scale SAG mill model with 95% of the rock size distribution represented in the DEM model. Cleary et al. (2008) and Cleary (2009a) have presented large three dimensional DEM models of SAG and ball mills. Many authors (such as in the special issue edited by Cleary and Morrison (2008)) have since used DEM for simulating tumbling mills. Modelling of stirred mills with DEM has also been performed by Sinnott et al. (2006) and Cleary et al. (2006) with power draw, flow structure, energy utilisation, wear and particle transport efficiency being explored for tower and pin mills. Yang et al. (2006) studied the flow of grinding media in a simplified Isamill using DEM. Cleary et al. (2008) then studied the flow and segregation of rock ⇑ Corresponding author. Tel.: +61 3 9545 8005. E-mail address: [email protected] (P.W. Cleary). http://dx.doi.org/10.1016/j.mineng.2014.07.016 0892-6875/Crown Copyright Ó 2014 Published by Elsevier Ltd. All rights reserved.

particles within the charge in a periodic slice model of an Isamill. Jayasundara et al. (2008, 2009) then extended their model to multiple discs for studying grinding performance. More recently, Morrison et al. (2009) has used DEM to compare the performance of lab scale tower and ball mills configured to produce the same product size. DEM has also been used to model high intensity agitated mills. These are able to reach or exceed the energy intensity of stirred mills but take the approach of moving the entire grinding vessel at high speeds in order to produce high accelerations and strong grinding intensities. The centrifugal mill is a long established example of such a mill (Hoyer, 1984, 1985). Several researchers have used DEM to study such mills: Inoue and Okaya (1996), Cho et al. (2006) and Lee et al. (2010). Cleary and Hoyer (2000) compared DEM simulation results to experimental results. Their predicted charge profiles were in very close agreement with high speed photographs taken during the experiments. Very good agreement was also achieved with power draw predictions and experimental values for various mill speeds. Transport and discharge are often important elements of mill performance but ones that are rarely included in DEM models of mills. Cleary (2006) examined the axial transport and discharge of coarse rock in a ball mill using a very simple permeable wall to represent the effect of a grate. Coarse particle flow through the grate of a dry SAG mill into the pulp chamber was simulated by Cleary (2004) and slurry discharge by Cleary and Morrison (2012). Rajamani et al. (2011) also demonstrated simulation of flow of slurry within the pulp chamber. Significant challenges still remain in predicting and understanding transport.

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The article by Weerasekara et al. (2013) reviewed 153 research papers giving a general overview of the application of computational techniques to the study of comminution. The authors state that: ‘‘Over the last two decades the DEM has become an important tool for understanding comminution fundamentals and providing information for the design, optimisation and operation of comminution devices’’. The HICOM mill is a high intensity fine grinding mill which has unusual transport and discharge characteristics arising from multiple discharge ports around the mill. Its usual operation involves discharge of both grinding media and dry product powder. The earliest modelling of this mill was by Hoyer and Boyes (1990). Recently Cleary et al. (2010) presented full three dimensional modelling of media flow in a HICOM mill and demonstrated the development of a suitable wear model able to predict the liner life cycle. In this paper, we use DEM to simulate media flow within a HICOM mill and to provide steady state predictions of the mass flow rates from its discharge ports. Twelve discharge ports at different locations in the mill and with different diameters are used to explore the optimality of the various size and location options. This provides information relevant to the operation of this type of mill, guidance for port size and location and a demonstration of how DEM can be used to predict transport and discharge behaviour of mills. Key questions that are explored include the relationship between port open area and discharge rate, the effect of location (both height and azimuthal) on flow rates and whether proximity of ports leads to some form of interaction in the discharge flows.

2. Mill configuration and charge specification The HICOM mill is a cylindrically symmetric vessel that is smaller in diameter at the top, increasing to around 1/3 from the bottom and then decreasing on approach to the closed bottom, see Fig. 1(a). There is a narrow cylindrical neck at the top through which feed material enters. The liner has eight vertical lifters running from the neck to the base. Ports in the form of circular

openings are located between the ribs of the mill liner in the lower section of the grinding chamber, see Fig. 1(b). These allow finely ground and/or large ore particles or media to discharge. Typically such a mill will be operated in closed circuit with media being separated from the discharge stream and returned to the mill. Alternatively fine grates can be placed over the ports to retain media while permitting finer particles to exit. The grinding chamber is inclined at an angle of 4.75° from the vertical, and moves with a nutating motion at a frequency of 380 rpm. In performing this motion, the nutation point remains stationary, while points on the chamber below describe circles around the vertical axis having diameters increasing with distance below the nutation point. The nutating mill was filled through the central feed opening with media particles to a specified fill level of 50% by volume. This was achieved for this mill by feeding in new material at the top at a rate that matches the discharge rate, so maintaining the weight of the particles in the charge constant at 2318 kg. The operating conditions are summarised in Table 1. Thirteen sampling planes are used in these simulations to measure the discharge behaviour. These are computational planes that record the attributes of particles passing through them allowing calculation of mass flow rates. There is one located in the neck of the mill to monitor the feed rate and there is one sampling plane located across each of the twelve ports in order to monitor the discharge rates. The location and dimensions of the discharge ports are given in Table 2. Their locations in two layers, one lower in the mill and one higher in the mill, are shown in Fig. 1(c). The dimensions of the ports were chosen so that the port areas were equal to the effective open areas of the larger grate covered discharge ports that are commonly used during operation of this type of mill. The modelling assumptions used for this study include:  Only grinding media is modelled so there is no ore or powder component to the charge in these simulations.  The particles used represent high-density ceramic media which are genuinely very close to spherical and are therefore modelled as such.

Fig. 1. The geometry of the HICOM 1000 mill: (a) render of the overall shape of the mill, its height is about 2.8 m and its maximum internal diameter is about 1.2 m; (b) render of the lower liner including discharge ports; and (c) diagram showing the locations of the discharge ports (viewed from above, the upper ports are shown in the outer ring and the lower ports are shown in the inner ring).

P.J. Owen, P.W. Cleary / Minerals Engineering 69 (2014) 113–119 Table 1 Mill configuration parameters. Operating speed Grinding chamber inclination Fill level Number of particles Size distribution (mm) Particle density (kg/m3) Total mass of particles (kg)

380 rpm 4.75° 50% 50,000 23.6–26.1 5800 2318

Table 2 Port identification numbers and port diameters and locations. Port identification numbers Port diameter Upper ports Lower port

Ports blocked 3, 5 14, 16

150 mm 1, 11, 15 2, 4, 8

212 mm 7, 9, 13 6, 10, 12

 The particles are nominally mono-disperse, but a small variation of ±5% from the mean diameter has been used to prevent unphysical crystallisation effects occurring in the charge when it is densely packed.  The particle density was 5800 kg/m3.  The particles are dry and cohesionless.  The coefficient of restitution was 0.3 for media–media and media–liner collisions.  The friction coefficient was 0.75 for media–media and media– liner collisions. The DEM code used here has been used and validated extensively for milling applications (see Cleary, 2004, 2009b) for details and examples of milling and other applications). The contact model being used is a linear spring-dashpot model. For details of this contact model and comparison to other models for inelastic collisions see Thornton et al. (2013). The maximum overlap between particles in such a DEM simulation is controlled by the stiffness of the spring in the normal direction and the peak forces produced by the flow which usually scale with the particle mass. Typically, average overlaps of 1% are required to produce accurate solutions that are independent of the spring stiffness choice. For the particle diameters used and the high centrifugal forces occurring in the mill, a spring constant of the order of 106 N/m was required to meet this requirement. The ratio of shear to normal spring stiffness was 0.5.

3. Charge flow pattern in the mill Fig. 2(a) shows two snapshots of the particle motion inside a HICOM 1000 mill (with no discharge ports) at different times, from a side view with the mill chamber cutaway to allow the charge to be visualised. The particles (shaded by speed, blue is 1 m/s and red is 5 m/s) are forced against the interior side wall of the mill by the centrifugal force and are somewhat slumped towards the bottom in response to the comparatively weak gravitational force. This makes the particles form a bed with a steeply angled free surface. The bed is deeper at the bottom and becomes progressively shallower with increasing vertical position in the mill. At the usual operating fill level of 50% the charge almost fills the full height of the chamber, occasionally some loose media bounces around in the neck of the mill. Although the centrifugal force is much lower here (due to the much smaller radius) the charge in this region needs to be managed carefully to ensure that wear is acceptable. The surface of the charge is roughly planar and is inclined with its surface normal moderately above horizontal. As the chamber rotates, the particle circulates around the inside of the mill in a steady pattern. The planar free surface of the bed rotates at the

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same speed as the mill chamber nutates maintaining a constant phase offset with the centerline of the mill. The leading charge particles approach and collide with the next lifter which is then engulfed by the bulk of the bed flowing behind this. There are some high energy impacts during the initial contact of the charge with the lifter but most of the interaction is frictional as the shearing charge mass then slides over the liner. This generates the high shear between particles that results in the high intensity grinding process. The magnitude of normal forces is controlled by the very high G force generated by the high nutation rate. The motion of the particles in the upper section of the mill is more gentle (as indicated by the blue colouring of the particles), since the centrifugal force is much weaker here due to the much smaller radius of the mill at that height. In the lower section, the chamber is wider and its displacement from the vertical (caused by the inclination) is larger, leading to much higher centrifugal force and therefore much higher particle velocities (with the particles coloured red in this region). Fig. 2(b) shows two cutaway views from the top of the mill at the same times as the particle flow pictures above them. The rib or lifter pattern of the mill liner is clearly observed, as is the cross-section shape of the charge. This profile is steady and simply rotates around the mill at the same speed as the nutation. The simplicity of the precession of the constant free surface profile shape does not convey the complexities of the motion of the particles within this charge mass. These follow complex trajectories with particles substantially varying their position within this charge mass. This is due to the strong velocity gradients within the charge mass that lead to very high shear rates. The strong centrifugal force then sculpts the free surface maintaining the constant profile so that the internal granular forces within the charge balance the driving centrifugal force field (whose strength varies with radius). Fig. 3 shows examples of the discharge flow of particles from a smaller HICOM 100 mill with two ports. This smaller mill is used here to demonstrate the discharge process because visualisation is simpler with only two ports. As the bed precesses around the interior of the mill each port moves under the bed and the pressure of the bed against the liner rises due to the centrifugal force. In the region of the discharge port there is no liner to prevent the particles from moving outward in response. So charge starts to flow into the discharge port. Fig. 3(a) shows an example of strong flow along the bottom half of the discharge port when the charge mass fully overlays the port with granular pressure driving the discharge flow. The transit of the particles in this converging flow towards the port is relatively slow and the time available before the charge moves away from the port is short so only a small number of particles are able to complete the full transit of the discharge port tube in time. Some of the slower particles within the port exit the mill after the port has left the bed as shown in Fig. 3b. This dilute flow of particles are those that entered the port when the charge was adjacent but have yet to complete their escape from the mill after the charge mass has moved away from the port. Fig. 3c shows an example where the discharge port is more packed with a larger number of particles having entered the port. Each port exhibits a variant of this discharge behaviour producing a short pulse of discharge with each passage of each port past the bed. Important questions about the port design that affect performance include whether the discharge rate varies with height in the mill, whether there is interaction between the discharge flows if the ports are too close together and how the size of the ports affects the flow rate.

4. Mass balance in mill and steady state operation To ensure that the HICOM 1000 system is in steady state, we measure the total discharge rate through all ports and compare it

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Fig. 2. Views of the particle flow in the HICOM mill at two different times from a (a) side cutaway view, and (b) top cutaway view. The particles are coloured by their speed, blue represents speeds of 1 m/s or less and red is for speeds 5 m/s or more. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Views of the discharge flow of particles from the HICOM mill, (a) strong flow along the bottom half of the discharge port when the charge mass fully overlays the port with granular pressure driving the discharge, (b) dilute discharge flow of particles that had entered the port when the charge was adjacent but have yet to complete their escape from the mill after the charge mass has moved away from the port, and (c) more packed from through a discharge port with the bed pressed against the port. The particles are coloured by size with red being larger and blue being smaller. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to the inflow rate. This is shown in Fig. 4a. The particle inflow rate during the initial filling stage was about 2200 kg/s. After reaching the target fill level of 2318 kg, the mass inflow rate reduces and fluctuates between about 400 kg/s and 1000 kg/s, in order to match the total discharge rate from all of the ports so that the charge level remains constant which is shown by the red curve. The transient

inflow and total discharge rates then match very closely with a very high degree of correlation between their fluctuations indicating that the system is in equilibrium. Averaging these flow rates over about five revolutions of the mill yields the average mass flow rates shown in Fig. 4b. This shows that after filling phase has ended that the average inflow rate matches very closely to the average

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(a) 2500 Total Discharge

Port 2 - dynamic Port 2 - averaged

120

2000

Mass Flow Rates (kg/s)

Mass Flow Rates (kg/s)

Inflow

1500

1000

100 80 60 40 20

500 0 0

-20 0

1

2

3

4

5

6

7

8

0

1

2

3

Time (s)

5

6

7

8

Fig. 5. Mass flow rates from discharge port number 2.

(b) 2500 Average Mass Flow Rates (kg/s)

4

Time (s)

Inflow

Total Discharge

2000

1500

1000

500

0 0

1

2

3

4

5

6

7

8

Time (s) Fig. 4. Mass flow rate into the mill and the total mass discharge rate (both kg/s). After 1.5 s the mill charge is in equilibrium and the average charge mass is constant, (a) measured flow rates showing the periodicity of the individual port discharges, and (b) mass inflow rates smoothed using a filter to remove the mill motion periodicity.

total discharge rate. The steady state average mass inflow and total mass discharge rates are 678 kg/s.

5. Port discharge rates Next we consider the predicted mass flow rates from the individual discharge ports. Fig. 5 shows the dynamic and averaged mass flow rates through port number 2 which is in the lower ring of ports. The dynamic mass flow rate fluctuates in a cyclic manner with a frequency of 6.3 Hz which matches the nutation speed of the mill which is 380 rpm (6.3 Hz) which confirms that there is one discharge burst from each port on each nutation cycle on the mill. The average discharge rate is 34.4 kg/s while the peak discharge rate is more than double this. An interesting observation is that at times the minimum flow rate through this port is slightly negative. This means that there are particles sometimes moving from just outside of the port back inside of the mill. This occurs because discharging particles are often moving quite slowly compared to the mill, particularly at the end of a discharge burst, whilst the mill can be moving much more quickly as it continually changes direction with its nutation and overtakes particles which are then re-captured by the mill. In terms of the particle flow, this behaviour can be seen in animation but cannot be well captured in still images and so is not shown here. The time dependent behaviour of the dynamic and average mass flow rates for all of the discharge ports are very similar manner to that described for port 2a. It is the relative behaviour of the

average mass flow rates for each port that is most useful. These predicted average flow rates are summarised in Table 3. Fig. 6 shows the average mass flow discharge rates for all the lower ports. The six curves fall into two very tight bands. The average mass flow rate for the 150 mm diameter lower ports are virtually indistinguishable from each other and form the lower band. The discharge rates for the 212 mm diameter lower ports are also extremely similar and form the upper band. This shows that the spatial location around the lower port height does not influence the discharge rate. They are only differentiated by the size of the port but not by their port location. The average 150 mm lower port discharge rate was 34.5 kg/s. This compares to a flow rate of 110 kg/s for the 212 mm ports. The area ratio of these two port sizes is 2.0 but the flow rate ratio is 3.19 indicating that the flow rate scales much more strongly than linearly with the open area of the port. This is a consequence of bridging behaviour that occurs for granular materials. On average, the smaller and larger ports have diameter to particle diameter ratios of 6.0 and 8.5 respectively. The ability of the particles to bridge and block is strongly dependent on this ratio, as is often found in hopper discharge flows, Nedderman et al. (1982), Hilton and Cleary (2011). Fig. 7 shows the average discharge rates for the upper ports. They are again clustered into two very tight bands. The discharge rates for the 150 mm diameter upper ports are virtually indistinguishable from each other and form the tight lower band. Unlike all the other ports, there are some small but non-negligible differences between the discharge rates of the 212 mm diameter upper ports. In particular, the uppermost curve representing the discharge rate from port number 9 is consistently slightly higher than the corresponding discharge rates from the other 212 mm Table 3 Discharge port geometry and average discharge rates. Port number

Nearest neighbour diameter (mm)

Average discharge rate (kg/s)

Lower ports, 150 mm diameter

2 4 8

150 0 212

34.4 34.0 35.2

Lower ports, 212 mm diameter

6 10 12

0 212 150

109 110 111

Upper ports 150 mm diameter

1 11 15

150 212 0

19.4 19.6 19.7

Upper ports 212 mm diameter

7 9 13

150 212 0

60.7 64.3 60.8

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other 212 mm diameter ports located in the upper level due to flow enhancement from the larger port below it. Finally, comparing the discharge rates between the upper and lower tiers for the same size ports we see that the upper ports consistently have a discharge rate of only 0.56 times that of the same size port in the lower tier. This is almost independent of port size with the ratio of the average flow rates for the 150 mm ports between layers being 0.568 while the ratio for the 212 mm ports is 0.562. This upper level port discharge rates are lower for a combination of three reasons:

Average Mass Flow Rates (kg/s)

140 120 Lower Ports: 6, 10 & 12 Diameter 212 mm

100 80 60

Lower Ports: 2, 4 & 8 Diameter 150 mm

40 20 0 3

4

5

6

7

8

Time (s) Fig. 6. Average discharge rates through the lower ports.

Average Mass Flow Rates (kg/s)

140 120 100 80

Upper Ports: 7, 9 & 13 Diameter 212 mm

60 40 Upper Ports: 1, 11 & 15 Diameter 150 mm

20

6. Conclusions

0 3

4

5

6

(a) lower dynamic pressures in the charge at the upper tier due to the lower centrifugal force due to the small mill diameter at that height which reduces the driving force and therefore the ability of the charge to push obstructed particles out through the port; (b) the charge cross-section is broader at the bottom thus allowing particles to discharge from the lower ports for a longer period during each revolution; (c) the orientation of the uppers ports allows a larger flow of particles back into the mill; (d) The best discharge rate for the port heights considered here is therefore achieved by placing discharge ports at the height where mill radius is largest. If longer retention times in the mill are required (for example to achieve finer grinding) then this can be achieved by moving the discharge ports either higher or lower to reduce the discharge rate and consequently increase the particle residence time in the mill.

7

8

DEM simulation of the flow within and discharge from a HICOM 1000 mill allows the prediction of

Time (s) Fig. 7. Average discharge rates through the upper ports.

diameter ports at this level. Port number 9 is the 212 mm diameter port in the upper layer that has a 212 mm diameter port directly beneath it in the lower layer. Other combinations of large ports (which are further apart) do not show this behaviour. The flow conditions presented to each row of ports are the same, so this suggests that there is some small amount of interaction between these largest of ports in the two layers when they are very close together. In such situations the upper port has a slightly enhanced discharge rate, but this a quite weak effect. The slight difference in discharge rates between the upper ports 7, 9 and 13 is the only evidence to indicate any interaction between the flow in the vicinity of neighbouring ports. It could reasonanably be anticipated that the degree of interaction may vary with changes in the ratio of the separation distance between ports to the port diameter. The average flow rate for the 150 mm diameter upper layer ports is 19.6 kg/s whilst the average for the 212 mm ports is 61.9 kg/s. The flow rate ratio between these sizes is 3.16 which is extremely close to that found for the lower layer of ports. So although the absolute flow rates are different the ratios between port sizes are independent of location suggesting that this is controlled purely by geometric bridging and obstruction considerations and therefore only by the particle size. Table 3 summarises the diameter of each port, its location (lower or upper level), the diameter of the nearest neighbouring port in the adjacent level and its average discharge rate. Within each port diameter/location group the variation between the average discharge rates are not significant. However, as noted above, the average discharge rate from port 9 is slightly higher than the

 Dynamic and average total mass inflow and total discharge flow rates.  Dynamic and average mass flow rates from each of the individual discharge ports.  A comparison of the discharge behaviour for different port sizes and locations. The behaviour of the discharge flow for the different port design options can be summarised as  The discharge rates from the small ports (150 mm diameter) are independent of their relative location for both upper and lower port rows.  The discharge rates from the large lower ports (212 mm diameter) are independent of their relative location.  The discharge rates from the large upper ports (212 mm diameter) are generally independent of their location, except when located directly over a similar large port in the port layer below. This indicates that there is some potential for weak interaction between these large ports when they are very close together resulting is slightly enhanced discharge for the upper port.  The large ports consistently have a discharge rate per unit area that is 1.6 times higher than that of the smaller ports, independent of the port location (either azimuthally around the mill or its height). This suggests that flow through the larger ports is less obstructed by the converging nature of the discharging flow as particles approach the ports and start to bridge.  The upper ports consistently have a discharge rate that is 40% lower than the lower ports, independent of the size of the port.  The maximum discharge rate can be achieved by locating the discharge ports at a height corresponding to the maximum internal diameter of the mill grinding chamber. There is a strong

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dependence of the discharge rate with distance from this level. This can be used to produce controlled reductions in discharge rate and consequential increases in particle residence time within the mill if these are needed to help in process control.

Acknowledgements The authors would like to thank David Hoyer and Stephen Marshall for their support of this work. We would also like to thank FLSmidth Ludowici Pty Ltd. for agreeing to allow it to be published. HICOM is a registered trademark of FLSmidth A/S and is used in this paper with permission of the owner. References Cho, H., Lee, H., Lee, Y., 2006. Some breakage characteristics of ultra-fine wet grinding with a centrifugal mill. Int. J. Min. Process. 78 (4), 250–261. Cleary, P.W., 1998. Predicting charge motion, power draw, segregation, wear and particle breakage in ball mills using discrete element methods. Min. Eng. 11, 1061–1080. Cleary, P.W., 2001a. Recent advances in DEM modelling of tumbling mills. Min. Eng. 14, 1295–1319. Cleary, P.W., 2001b. Charge behaviour and power consumption in ball mills: sensitivity to mill operating conditions, liner geometry and charge composition. Int. J. Min. Process. 63, 79–114. Cleary, P.W., 2001c. Modelling comminution devices using DEM. Int. J. Numer. Anal. Meth. Geomech. 25, 83–105. Cleary, P.W., 2004. Large scale industrial DEM modelling. Eng. Comput. 21, 169– 204. Cleary, P.W., 2006. Axial transport in dry ball mills. Appl. Math. Model. 19, 1517– 1527. Cleary, P.W., 2009a. Ball motion, axial segregation and power consumption in a full scale two chamber cement mill. Min. Eng. 22, 809–820. Cleary, P.W., 2009b. Industrial particle flow modelling using DEM. Eng. Comput. 26, 698–743. Cleary, P.W., Hoyer, D., 2000. Centrifugal mill charge motion: comparison of DEM predictions with experiment. Int. J. Min. Proc. 59, 131–148. Cleary, P.W., Morrison, R.D., 2008. Editorial. Min. Eng. 21, 743. Cleary, P.W., Morrison, R.D., 2012. Prediction of 3D slurry flow within the grinding chamber and discharge from a pilot scale SAG mill. Min. Eng. 39, 184–195. Cleary, P.W., Sawley, M.L., 2002. DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl. Math. Model. 26, 89–111. Cleary, P.W., Sinnott, M., Morrison, R., 2006. Analysis of stirred mill performance using DEM simulation: Part 2–Coherent flow structures, liner stress and wear, mixing and transport. Min. Eng. 19 (15), 1551–1572. Cleary, P.W., Sinnott, M.D., Morrison, R.D., 2008. DEM prediction of particle flows in grinding processes. Int. J. Numer. Method Fluids 58, 319–353. Cleary, P.W., Owen, P.J., Hoyer, D.I., Marshall, S., 2010. Prediction of mill liner shape evolution and changing operational performance during the liner life cycle: case study of a HICOM mill. Int. J. Numer. Meth. Eng. 81, 1157–1179.

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