Tower Mill Rotation Speed

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Minerals Engineering 19 (2006) 1551–1572

Analysis of stirred mill performance using DEM simulation:Part 2 – Coherent flow structures, liner stress

and wear, mixing and transport

Paul W. Cleary a,*, Matt Sinnott a, Rob Morrison b

a CSIRO Mathematical and Information Sciences, Private Bag 33, Clayton, Vic 3169, Australiab Julius Kruttschnitt Mineral Research Centre, The University of Queensland, Brisbane, Australia

Received 7 June 2006; accepted 11 August 2006

Abstract

Stirred Mills are becoming increasingly used for fine and ultra-fine grinding. This technology is still poorly understood when used inthe mineral processing context. This makes process optimisation of such devices problematic. 3D DEM simulations of the flow of grind-ing media in pilot scale tower mills and pin mills are carried out in order to investigate the relative performance of these stirred mills. Inthe first part of this paper, media flow patterns and energy absorption rates and distributions were analysed to provide a good under-standing of the media flow and the collisional environment in these mills. In this second part we analyse steady state coherent flow struc-tures, liner stress and wear by impact and abrasion. We also examine mixing and transport efficiency. Together these provide acomprehensive understanding of all the key processes operating in these mills and a clear understanding of the relative performanceissues.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Discrete element modelling; Simulation; Comminution; Fine particle processing

1. Introduction

Stirred media mills are being increasingly used in min-eral processing, as increasingly fine-grained ores containingbase and precious metals need to be ground finer to pro-duce liberation. Traditional ball mills cease to be econom-ically viable below 30 lm, whereas stirred mills have muchhigher energy efficiency in this size range and are beingdeployed for ultra-fine grinding (<10 lm) applications.Models for understanding stirred mill design and processoptimisation have not yet matured. A lab scale study ofvariables affecting fine grinding in vertically stirred millshas been made by Jankovic (2003). Weller et al. (2000) usedsolid and liquid tracers to investigate slurry transport and

0892-6875/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.mineng.2006.08.013

* Corresponding author. Tel.: +61 3 9545 8005; fax: +61 3 9545 8080.E-mail address: [email protected] (P.W. Cleary).

particle breakage. PEPT studies of media motion havebeen made by Conway-Baker et al. (2002) and Barleyet al. (2004). A micro-hydrodynamics model for stirredmedia mills has also been suggested by Eskin et al. (2005).

Recently (in Sinnott et al. (in press)), we presented thefirst part of a comprehensive study using the Discrete Ele-ment Method (DEM) of two vertically stirred dry pilotmills, namely a 1.5 kW tower mill and a 7.5 kW pin mill,(described in detail in Jankovic (1999)). DEM is a computa-tional technique that allows particle flows in various typesof equipment to be simulated. It has been used extensivelyin the simulation of mills (Cleary, 1998, 2001a,b,c, 2004;Cleary et al., 2003; Morrison et al., 2001). DEM simulationinvolves following the motion of every particle (coarserthan some cut-off size) in the flow and modelling each colli-sion between the particles and between the particles andtheir environment, such as the mill liner, grate or pulp lift-ers. This has the advantage of being able to simulate

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1552 P.W. Cleary et al. / Minerals Engineering 19 (2006) 1551–1572

equipment under very tightly controlled conditions and tobe able to make detailed predictions of specific outputswhile providing insight into the flow patterns and breakageprocesses. The general DEM methodology and its variantsare well established and are described in review articles byCampbell (1990), Barker (1994), and Walton (1994). Herewe use a conventional linear spring and dashpot variantof DEM which is described in detail in Cleary (1998, 2004).

In Sinnott et al. (in press), we investigated the mediadynamics within these two mills. The tower mill is charac-terised by a large, vertical double-helical steel screw agita-tor, whereas the pin mill employs a vertical shaft withembedded sets of pins. The interaction between the agitatorand charge generates motion within a media of steel orceramic balls leading to size reduction of the feed that flowsthrough between the media. DEM was used to investigatethe internal bed dynamics for each mill using ceramicmedia. Analysis of the performance of each mill was madethrough consideration of the global flow patterns, powerdraw, the spatial distribution of energy dissipation, andthe nature of the collisional environment producing thefeed comminution using energy spectra.

The tower mill was found to have a strong swirling flowaround the axis of the screw and a strong axial recircula-tion with media moving in the direction of the screw in acentral core and then returning more slowly downward ina thin outer annular region adjacent to the mill chamber.This makes almost all flow and grinding behaviour cylin-drically symmetric around the mill and independent ofthe axial position in the mill. The outer edge of the screwgenerates the largest speeds, pressures and media energyabsorption rates (and therefore grinding), which decreasewith both increasing and decreasing radii. A substantialfraction of the media in this mill is able to contribute simul-taneously to the size reduction process and so this mill hasa good media participation rate.

In the pin mill, the passage of the pins generates intensehigh pressure zones in surrounding media and on the pinsand some nearby parts of the shaft. The pin spacing is farenough apart that their effects are independent and theoriesrelying on intersection of compression and/or shear effectsfrom adjacent pins are not supported. The media flow inmiddle and upper regions of the mill involves particlesmoving on circular trajectories with only small vertical ran-dom walk style variations. Energy absorption by the mediadecreases strongly with height and is highly localised to thevicinity of the pins. The largest contribution comes fromthe small regions surrounding the two pins closest to thebase plate. This mill has a very poor participation ratefor the media with most of the charge volume contributinglittle to comminution.

In this second part of this paper, we present a moredetailed analysis of the coherent flow structures of themedia using three different DEM analysis methods. Linerstress and wear from abrasion and impact are also exam-ined. Finally the mixing and transport efficiency of thetwo mills are explored since they have significant impact

on comminution performance. Together these all providea comprehensive understanding of the operation andpotential of these two mills.

2. Understanding the nature of the coherent media flow

structures

Three different DEM analysis methods are used here tohelp to understand the nature of the media flow and thecoherent steady state flow structures that are generated inthese two mills.

2.1. Force chains

Collisional forces in a packed granular medium manifestthemselves as an elaborate network of force chains linkingeach pair of contacting particles. Through these networks,particles are ‘loaded’ by forces transmitted from the rest ofthe granular bed. Visualisation of the force network in a sys-tem is a powerful technique for identifying and understand-ing these force structures. This has been commonly used inquasi-static problems in two dimensions, but has rarely beenused in three dimensions for dynamic problems. Here, weare particularly interested in force configurations that mayhelp shed light on the mechanisms of breakage in mills.

Networks of force chains are shown for the tower and pinmills in Fig. 1. In three dimensions, the force chains are hererepresented as cylindrical segments between each contactingpair of particles. The particles have been shrunk to smallspheres that represent nodes in the force network so thatthe force cylinders can be seen. The colour and diameterof the cylinders are proportional to the magnitude of forcebetween the pair. The normal and tangential force compo-nents have been displayed separately. For each mill the net-works of each component are substantially similar with onlyminor variations at the individual particle pair level.

The tower mill shows ‘rays’ of high force transmittedupward and radially outward from the surface of the screw.This results from the upward pushing on the charge by therotating helical screw. Some particles are in strong loadbearing chains, whilst many are in weak secondary chainsand some particles which are in free motion do not partici-pate in force chains at all. The screw generates an aniso-tropic and coherent directional stress field in the particlebed that leads to strong upward and swirling motion ofthe bed. A cylindrical layer of balls slides downwards overthe cylindrical layer of balls being raised by the screw. Thistype of grinding action with layers of balls sliding across oneanother is not unlike the action in a ball mill and is very dif-ferent form the action in the pin mill which is described next.

In the pin mill, the pins drive into the bed and generatestrong stress chains radiating forward as they compressthe particle bed. The spreading of these force chains toeither side is weak so the force remains focused within a rel-atively small solid angle in front of the pin. The very strongcompressive forces generated in these forward directed fanshaped regions extend between 2 and 3 pin diameters into

Fig. 1. Typical force chain networks for (a) the tower mill, and (b) for the pin mill. The colour and diameter of each cylindrical segment is a proportionalto the magnitude of an interaction force between each pair of particles. Shaft rotation is from right to left at the front of the shaft.

P.W. Cleary et al. / Minerals Engineering 19 (2006) 1551–1572 1553

the particle bed before they become dispersed through theforce network and fade towards the background force level.This distance is much smaller than the distance between thepins, so the compression effects of each pin do not interactwith that of any other pin. One existing theory for breakagein the pin mill is that pressure waves from adjacent sets ofpins (positioned vertically above each other) intersect inthe region between these pins resulting in compressive frac-ture. Since the direction of force transmission from each pinis predominantly forward and the distance between pins islarger than the length of the compressed region, the pineffects do not interact and this theory would appear to beunsupported. The bed is constantly in shear and, as such,it is not possible for any portion of the bed to maintain astable, coherent network of force over a long enough time-scale to initiate this type of breakage.

2.2. Particle paths

One of the strengths of DEM is its ability to interrogatethe entire collision history for any given particle. The par-ticle path or trajectory of a single particle shows where theparticle spends most of its time in the system and the localvelocities, forces and energy exchanges that it experiencesthroughout its journey. This provides additional informa-tion for understanding particle motion and mixing throughthe use of virtual ‘tracer’ particles.

Fig. 2 shows two examples of particle trajectories foreach mill. The particle path is coloured by total cumulative

energy absorption. For the tower mill, the trajectory shownin Fig. 2a is representative of the downward spiral of a par-ticle descending down the outer part of the charge near themill chamber wall. The pitch of this spiral trajectory is sig-nificantly larger than the pitch of the screw impeller. Thelevel of energy absorption for the particle increases as itdescends towards the base of the screw. The particle inFig. 2c begins quite close to the shaft of the screw and isconveyed upwards in a tight spiral trajectory at a constantradial position. The pitch of the trajectory is the same asthat of the screw during this upward part of the particlemotion. As it moves upwards it absorbs energy steadily.When it reaches the free surface of the particle bed, it thentravels radially outward along the bed surface before beingentrained back into the bed to spiral downwards nearthe outer wall of the mill. Again the pitch of the slow out-ward spiral is much larger than that of the upward innerspiral. This difference in the pitch of the spiral trajectoriescontributes to the shear interactions between layers. Thisclearly shows the nature of the media circulation in thetower mill.

In contrast, the pin mill shows very little radial or verti-cal displacement of the particles. The particle shown inFig. 2b spends its entire time constrained to a region adja-cent to the shaft with a small amount of vertical movement.The amount of energy absorption is low. Fig. 2d shows aparticle located at a much larger radius from the mill axis.Its motion is circular and almost periodic with only a verysmall vertical drift. This particle experiences a much greater

Fig. 2. Particle paths are shown as a single trajectory of a lone DEM particle in each picture for (a) and (c) tower mill, and (b) and (d) pin mill. Each pathis shaded by the level of energy absorption which evolves from grey (low) to white (max) as it accumulates.


degree of energy absorption. From these trajectories, it isclear that the transport of media within this mill is very

poor and one suspects that this will also apply to the finerfeed material as well.


2.3. Isosurfaces

The motion of the charge in a stirred mill is highly three-dimensional and standard visualisation techniques providelimited insight regarding flow structures within packedbeds. Isosurfaces are three-dimensional surfaces deter-mined by where a given variable or parameter attains agiven constant value. Isosurfaces for bed density, velocity,force, and power provide an important way for betterunderstanding the dynamics within the charge.

To do this, a cylindrical grid is constructed over the bedand rotates with the agitator. Local averages for particleforce and motion data are first collected on this co-movinggrid over time. Due to the different dimensions of each milland different media sizes, the collection grid used for eachmill is slightly different. The details of the grid for each millare summarised in Table 1. This Eulerian representation ofthe DEM particulate data allows the generation of isosur-faces for variables of interest. This is a useful tool for iden-tifying flow characteristics inside densely packed movingmaterial. In this report we examine isosurfaces of bulk den-sity, flow velocity, collisional force and collisional power.

Bulk density isosurfaces for the tower and pins mills aregiven in Fig. 3. In the tower mill, the bulk density increasesmonotonically with radius and shows little variation eitherwith height or with azimuthal position in the mill. The den-sity isosurfaces are concentric open cylinders that extendfrom the bottom of the mill up to the free surface of themedia. The region of highest density is therefore adjacentto the walls. The centrifugal force generated by the screwforces the particles outwards and they become most com-pact near the walls of the mill. At intermediate radii, theshear between the upward moving core material and thedownward moving outer material dilates the charge andthe pressures from the centrifugal force are lower so thecharge density declines. Near the shaft (at small radii) thecentrifugal force generated pressures are relatively verylight so the charge is most mobile and least dense. The low-est bulk density indicates zones of maximum charge dila-tion due to the media being forced across one another inlayers and is therefore, probably a region of maximumcomminution. The high density zones are the least dilatedand are likely to be the least active, except where the chargeis compressed by the ‘toe’ or leading edge at the bottom ofthe screw. This density variation will have strong implica-tions for cases where this mill is run wet. Slurry will flowpreferentially in the core because it has the highest poros-

Table 1The details of the cylindrical grids used for collecting and averaging the parti

Tower mill

Radial Azimuthal Axial

No. of cells 5 30 25Grid size 0.12 m 6.283 rad 1.2 mCell size 0.024 m 0.209 rad 0.048 m

The number of cells, grid dimensions, and cell dimensions are listed for each

ity, but the screw will try to pump the slurry up the corewhile gravity will push it down. On the outside the slurrywill be less mobile and will be forced to more strongly fol-low the media on its downward spiral.

For the pin mill (bottom panel of Fig. 3), the bulkdensity distribution is much more complex and is fullythree-dimensional. The density isosurfaces are closed andconcentric, that is, one isosurface is entirely enclosed withinthe next which is enclosed within the next. The maximumdensity occurs in the spaces between the vertical rows ofpins and at a radial distance comparable to the locationof the tips of the pins. This structure extends from the sec-ond row of pins from the top down to just above the discbase. These regions are paired, with each of the high den-sity regions in each pair connected by a high density bridgerunning around the bottom pin separating these regions.These high density regions are produced by the strong com-pression fronts generated by each of the pins. These regionsare not necessarily good for comminution since fine particlemobility will be lower between the media and there will belower shear. The lower density contours follow the samepattern, concentrically expanding from the inner high den-sity one. There is little sign of radial density stratificationproducing the centrifugal force. The media distribution iscompletely dominated by the disruptive effects of the pins.The peak bulk density of the charge in the pin mill isslightly higher than for the tower mill.

Isosurfaces of bed velocity are shown in Fig. 4 for towerand pin mills respectively. The velocity components areexpressed in cylindrical coordinates. For the tower millall the velocity components are very close to cylindricallysymmetric. The tangential (azimuthal) velocity is struc-tured as closed, concentric surfaces where the peak valueoccurs at the edge of the screw as shown by the red isosur-face. The tangential velocity decreases with radial distanceas one moves inward or outward away from the screwedge. The peak tangential velocity is essentially constantalong the axial length of the screw. There is a very weakexpansion of the lower speed isosurfaces with heightreflecting the gentle decrease on bed density with heightwhich slowly increases particle mobility allowing the parti-cles higher in the bed to move a little faster. The two con-tours of vertical velocity shown correspond to ±0.03 m/s.The inner surface is positive indicating that the materialclose to the screw is all rising together. The strong symme-try of this isosurface indicates that there is little spatial var-iation and that particles at a given radius rise at a rate that

cle motion and force data are described here for each mill

Pin mill

Radial Azimuthal Axial

10 30 250.14 m 6.283 rad 0.8 m0.014 m 0.209 rad 0.032 m

of the radial, azimuthal and axial directions.

Fig. 3. (Top) Isosurfaces of bulk density are shown for the tower mill. The orange isosurface corresponds to a density of qb = 1200 kg/m3, the green one to1400 kg/m3 and violet one is 1450 kg/m3; (left) the agitator is included for reference; (middle) shows just the isosurfaces with the violet and green onesclipped to show the orange one, and (right) just the highest bulk density isosurface by itself. (Bottom) Isosurfaces of bulk density are shown for the pinmill. The orange isosurface corresponds to a density of qb = 1400 kg/m3, the green one to 1500 kg/m3 and violet one is 1560 kg/m3; (left) the agitator isincluded for reference; (middle) shows just the isosurfaces with the violet and green ones clipped to show the orange one, and (right) just the highest bulkdensity isosurface by itself with no clipping is shown in order to see the full 3D structure.


is independent of the vertical or azimuthal position withinthe mill. The combination of the axial flow and the strongtangential swirl combines to give the spiral trajectoriesobserved earlier (see Fig. 2 for examples).

The radial velocity behaviour is more complex, with theradial velocity isosurfaces being closed, concentric surfaceswhose peak occurs at the outer edge of the screw and nearthe base of the mill. The red isosurface shows that theradial velocity decreases as one moves both inwards andoutwards from the edge of the screw. It also decreases asone rises higher in the mill. This indicates that the edgeof the screw pushes particles just outside the screw awayfrom the screw and pushes particles, that are just insidethe outer edge of the screw, further inwards towards theshaft of the screw. This edge effect of the screw decreasesas the free surface of the charge is approached. Note that

the peak tangential velocity of the charge is around ninetimes higher than the vertical migration rates of the parti-cles and these are in turn about three times higher thanthe radial speeds. The very small radial speeds are respon-sible for the strong cylindrical symmetry of all the otherattributes of the charge (including velocity and density).

Media in the pin mill are observed to follow substan-tially circular paths around the mill chamber with gradualvertical drift generated by the passage of the pins (see Fig. 2for examples). The tangential velocity isosurfaces in Fig. 4(bottom, centre) form complex, closed, concentric surfacesthat are quite different to those found in the tower mill. Thepeak tangential velocities are found in vertical regionsbetween the columns of pins. The high tangential speedregions extend into the gaps between pins in each column.Since the rows of pins are staggered, this leads to a some-

Fig. 4. Isosurfaces of velocity, with the colouring scheme being blue for low, green for medium and red for high speed, for (top) tower mill with isosurfacesof (left) radial velocity for Vrad = 0.005, 0.01 and 0.0125 m/s, (middle) tangential velocity for Vtang = � 0.1, �0.15 and �0.275 m/s, and (right) verticalvelocity for Vz = �0.03 and 0.03 m/s. (Bottom) Pin mill with isosurfaces of (left) radial velocity for Vrad = 0.06 and 0.12 m/s, (middle) tangential velocityfor Vtang = � 0.5,�0.8 and �1.1 m/s (where outer two isosurfaces have been clipped to show the inner isosurface structure), and (right) vertical velocity forVz = �0.025 and 0.025 m/s.


what zig-zag like structure. For the relatively high speedred isosurface, there is some bridging of these ‘bubble like’regions across the pin columns. The high tangential veloc-ity isosurface does not extend down to the lower pins, nordoes it reach the free surface, indicating that the highestsuch speeds are reached in the middle of the mill. This isconsistent with what was shown by the one-dimensionalprofiles of tangential velocity with height in part 1 of thispaper (Sinnott et al., in press). The radial and verticalvelocities are small compared to the peak tangential veloc-ity with the peak radial velocities being around 9 timessmaller and the peak vertical velocities around 40 timessmaller. Note that this is the opposite order to that found

in the tower mill where the radial velocities were smallest.The passage of the pins generates reasonable radial distur-bances whereas the screw generates little radial movement.Conversely, the pins generate little coherent vertical move-ment, whereas the screw generates consistent moderate ver-tical motion (and therefore strong vertical recirculation).

Not only are the magnitudes of the radial and verticalvelocities different for the two mills, but the distributionsare also quite different. For low radial velocities, ellipsoidalisosurfaces form around the tip of each pin. This reflectsthe high compression zone in front of each pin observedin the bulk density which inhibits particle motion leading tolow radial speeds. At the 0.06 m/s speed, these isosurfaces


merge to form undulating columns of particles movingradially at this speed. The 0.12 m/s radial velocity isosur-face shows interesting structure at the bottom of the mill.There are two triangular shaped higher radial speed regionson either side of the agitator rising from the base plate justin front of the two lowest pins. This indicates a coherenthigher speed motion of media into the mill shell in theseregions. Looking at the vertical velocity isosurfaces in thesame region, we observe a large negative velocity bubblesurrounding and trailing the two lowest pins. These stretchback to and under the lowest pin on the following columnof pins. There are matching positive isosurface bubblesstarting underneath these lowest pins in the followingcolumn of pins.

Combining these three coherent velocity structures wecan deduce that as the lowest pins approach, the particlesare forced radially outward and vertically upward in orderto pass around these pins. These pins are too close to thebase plate to allow easy passage under these pins, so theyhave to flow around the pins generating the triangularradial and upwards vertical isosurfaces bubbles. After pass-ing these pins, the particles flow downwards and pass underthe lowest pin of the following column of pins, which is off-set by half a pin spacing higher than on the preceding col-umn. Here the distance from the base plate is large and theparticles flow more easily through the gap under these pins.After passing underneath, the particles then rise back up totheir original level as they approach the next column ofpins. Comparing this to the bulk density distribution wherewe found a high density bridge under the higher pair ofbottom pins, we see that this compression corresponds tothe regions where the particles are directed to flow underthe second column of pins. So the media near the bottomof the mill undergoes complex wave like oscillatory motionflowing over the lowest pins of the pin columns set close tothe base plate and then under the lowest pins of the pin col-umns that are offset higher. So even though the agitator hasfour pin columns, the velocity and density fields have onlytwo-fold symmetry with a pairing of the low and high offsetpin column.

These types of coherent structures in the velocity anddensity distributions can be identified by these time aver-aged quantities collected on co-moving Eulerian grids.These are structures that are very hard to identify by look-ing at individual particle trajectories since it is not a prioriclear where to look for them and the signal to noise ratio ispoor.

Isosurfaces of normal and tangential collisional force forthe tower and pin mills are shown in Fig. 5. Both the nor-mal and tangential force isosurfaces are closed and concen-tric for both mills. For the tower mill, they are also broadlycylindrically symmetric. The innermost surface indicatesthat the peak normal force occurs halfway up the lengthof the mill and at the outer radial edge of the screw. Glanc-ing collisions with high tangential force are observed alongthe full axial length of the screw in the region betweenscrew and wall. Media experiencing collisions of low

normal or tangential force tend to be concentrated at theinner radii close to the shaft, in the stagnant zone underthe screw and on the free surface. Overall, the forcedistributions are remarkably uniform in space and inmagnitude.

The distribution of collisional force in the pin mill is rad-ically different with strong dependence of force on depthinto the bed. The red isosurfaces showing the regions ofhigh force are elongated bubbles with their centres in frontof the lowest pins on the two pin columns that are locatedclosest to the base plate and extending up to a compressedregion in front of the pin directly. There are much smallerhigh force isosurfaces in front of the lowest pins on thehigher offset following columns of pins. The average nor-mal force decreases monotonically with distance from thesehigh force peaks. At intermediate force levels, the expand-ing isosurface bubbles from the four rows of pins merge toform a sharply peaked structure. Here, moderate force isexerted on the particles in front of most of the pins andthen declines rapidly with distance. This causes the isosur-faces to rise sharply in the vertical direction in the region inadvance of the pins and then to descend strongly in theregions between pin columns. There is a very clear depres-sion around the shaft where forces remain low at locationsalong the shaft. The low normal force isosurface reachesalmost to the free surface near the pins but still falls sharplyin the regions between pins and at smaller radii. So thereare large fractions of the bed material that are not sub-jected to high force at any given time in this mill. The tan-gential force distributions are very similar in structure tothe normal forces but have a much lower magnitude. Thenormal forces load the particles, whilst the shear forcesactually lead to the attrition of the feed material.

Collisional forces in the tower mill depend predomi-nantly on the radial position and are relatively independentof height and substantially independent of azimuthal posi-tion. For the pin mill the force depends strongly on depthinto the bed and proximity to the lower pins. The lower off-set pins create the largest bed forces which have two-foldsymmetry around the mill.

It is also useful to understand the distribution of energyconsumption within the mill. This can be done by examin-ing the isosurfaces of normal and tangential energy dissipa-tion by the particles. Fig. 6 shows their distribution in thetower mill. Peak energy dissipation occurs in a cylindricalshell centred on the outer edge of the screw and extendingfrom near the bottom of the mill to only one flight from thetop of the screw. The red (high energy dissipation) isosur-face is a closed surface surrounding this peak region. Themedium and low energy dissipation regions have similarshapes but occur at further distances from the edge ofthe screw, and specifically closer to the shaft of the screwand closer to the free surface. There is clearly very littledependence of the energy dissipation on the depth intothe bed and a good fraction of the grinding media are inthe high energy dissipation region indicating good mediaparticipation in this mill.

Fig. 5. Isosurfaces of normal and tangential collisional force, with colours blue (low), green (medium) and red (high), for (top) tower mill; (left) theagitator is included for reference in identifying the isosurfaces with the bed for the normal force; (middle) isosurface values are Fnormal = 0.3, 0.4 and0.45 N, and (right) isosurface values are Ftang = 0.075, 0.1 and 0.125 N. (Bottom) Pin mill; (left) the agitator is included for reference in identifying theisosurfaces with the bed for the normal force, (middle) isosurface values are Fnormal = 0.25, 0.5 and 0.8 N, and (right) isosurface values are Ftang = 0.1, 0.2and 0.25 N.


The energy dissipation isosurfaces for the pin mill areshown in Fig. 6. The highest energy dissipation rates arefound in the regions in front of the two lowest pins andthen in front of the lowest pins on the higher offset follow-

ing columns and then the second lowest pins on the firstcolumns of pins and so on. This leads to reasonable sizered isosurface bubbles in front of these lower pins. Theenergy dissipation isosurfaces are closed and concentric.

Fig. 6. Isosurfaces of normal and shear energy dissipation, with colouring of blue (low), green (medium) and red (high), for (top) tower mill; (left) normalpower with the agitator is included for reference, (middle) isosurfaces of normal power are Pnormal = 0.5, 1.0 and 1.5 lW, and (right) isosurfaces of shearpower Pshear = 1.0, 3.0 and 5.0 lW. (Bottom) Pin mill; (left) normal power with the agitator is included for reference; (middle) isosurfaces of normal powerPnormal = 7.5, 10.0 and 20.0 lW, and (right) isosurfaces of shear power Pshear = 7.5, 20.0 and 40.0 lW.


With decreasing energy dissipation levels, the isosurfaceregions expand predominantly vertically. The lowest nor-mal energy isosurface extends all the way up in front of

each column of pins almost to the free surface but increasesonly very slightly in the radial direction. This indicates thatthe energy dissipation is very closely concentrated around


the compressed and flowing media in front of the pins.Media elsewhere do not really participate in energy dissipa-tion and therefore will not contribute to grinding. Theshear energy absorption levels (resulting in attrition andabrasion) are higher than that of the normal energy (result-ing in impact breakage) and so the regions of high sheardissipation are spatially somewhat larger than for the nor-mal dissipation.

3. Wear/stress distribution

Time-averaged surface velocities and stresses, as well ascollisional power are accumulated on the elements of theboundary mesh throughout the course of the simulation.From the distributions on the boundary mesh, we can inferlocal details about loading of the mill components andidentify regions of high collisional power density leadingto damage of the agitator or the chamber wall.

Surface velocities are shown for each mill in Fig. 7. Theslip velocity at the wall of the tower mill decreases withheight as the bed pressure increases and presses the parti-cles more firmly against the walls. On the upper surfaceof the screw the slip velocity increases with radius. Thehighest speed is found on the outer radial edge of the screw,where media exhibit the highest velocities. These velocitiesare much smaller than the edge speed of the screw (0.73 m/s).Peak wall velocities for the pin mill are much greater (fourtimes) than the tower mill and are concentrated on the edgeand outer parts of the top surface of the disc base of theagitator. Many stirred mills do have this base disk –perhaps for good reason. Moderate velocities also appear

Fig. 7. Surface velocity distribution on the chamber wall and agitator for each mwhere red represents a speed of 0.25 m/s.

on the outer radial tips of the pins. Again these velocitiesare much less than the pin tip speed (2.6 m/s).

Normal and shear stress predictions are shown in Fig. 8.The tower mill experiences large stresses at the outer radiiof the screw’s top helical surface. This is due to a combina-tion of high media speed on the screw surface coupled tothe lift generated by the screw. The shear stresses have avery similar distribution to the normal stresses on thescrew. Their magnitude is up to half the magnitude of thenormal stresses. The shear stress is limited to half the nor-mal stress. This only occurs if all the particle-wall contactsare fully sliding, because the particle-wall friction coeffi-cient used in the simulation was 0.5. The shear stress onthe chamber wall is significantly less than the normal stressindicating a much lower level of particle slip at the wall.The pressure distribution on the chamber wall and screware axially symmetric, hence there is no asymmetric loadingof mill components. There is also a region of very high nor-mal and shear stress visible at the ‘toe’ of the screw. Thearea of high normal stress extends over the outer half ofthe leading face of the toe while the shear stress is concen-trated in the lower triangular region extending from thebottom corner of the leading edge of the screw.

In contrast, the pin mill shows pressure on the chamberwalls and the agitator shaft increasing with bed depth.Shear stress on the agitator also increases with bed depth.Very high normal stresses are found on the forward facingsurfaces of the pins, on the shaft above and below each pinand a little in advance of the pin. These are produced as acompressed zone of particles is pushed and compressed bythe pin presses hard against the shaft and pin surfaces.

ill, (a) tower mill where red represents a speed of 0.08 m/s, and (b) pin mill

Fig. 8. (Top) Normal stress (pressure) on the chamber wall and agitator. (Bottom) shear stress, (left) stresses for the tower mill with red being 6 and 3 kPafor the normal and shear stress; (right) stress for the pin mill with red being 10 and 6 kPa for the normal and shear stress.


Quite low normal stresses are found on the backs of thepins and on nearby parts of the shaft. The disc base expe-riences very high pressures on its outer surface and in twolarge regions on the top surface of the disc starting fromeach of the two lower pins and extending forward a sub-stantial distance. This results from the high compressiongenerated by the bottom pins as they force media intothe small gap between these two pins and the base plate.The disc edge and the floor of the chamber beneath the discboth experience great pressure due to its motion.

The shear distribution is similar to that of the normalstress. In the highest pressure regions on the pins, the shearstress is around half that of the normal stress. This indi-cates that most particle contacts are sliding on the mill sur-face. On the shaft and on the mill shell, the shear stress issignificantly lower than the normal stress. Even on the baseplate, the shear stress is quite a bit lower with only moder-ate levels on the outside surface and on much of the top

surface. Looking closely at the lower pins, we observe thatthe normal stress on the top half and the bottom half aresymmetric, but the shear stress on the curved cylindricalsurface is not. The shear stress is higher on the upper sur-faces than on the lower ones. This reflects the local downflow direction of the media recirculation in this region.

The normal stress distribution on the disc top surfaceand on the shaft suggests asymmetric loading of the agita-tor shaft. This loading is probably sensitive to rotationalvelocity and thus there are obvious implications for milloperation and mechanical damage, particularly if the load-ing results in a ‘wobble’ of the agitator. This irregular load-ing of the agitator and pins could lead to gross failure dueto metal fatigue if the mechanical design did not take theseinto account.

The rates of energy absorption by mill surfaces are keymeasures of wear. The normal and shear distributionsreflect the rates of impact damage and abrasion of the mill


and are shown in Fig. 9 for both mills. In the tower mill,the normal power is small relative to the shear power. Thusimpact damage is predicted to be mild and concentrated onthe outer edge of the screw and moderate in a concentratedtriangular region of the leading front face of the ‘toe’ of thescrew with its peak at the bottom outer corner where thescrew digs into the grinding media. The level of shearenergy absorption indicates that abrasion dominates wearin this machine. The screw experiences strong abrasivewear on the outer radial edge of the top surface of thescrew. This will result in a progressive rounding of this edgeover time. The abrasive wear is strongest on the outer frontsurface of the toe of the screw with the entire end cornereroding over time. In full-scale application, a tungsten car-bide shoe is commonly installed to protect the toe regionfrom such damage.

Fig. 9. (Top) Impact damage (as predicted using normal energy absorption) ofthe shear energy absorption) of the mill surfaces. The same colour scaling isrepresents an energy absorption rate of 100 W, and for the pin mill, red repre

For the pin mill, the larger agitator speed and more vio-lent action of the pins with the media produce much greaterlevels of energy absorption than the tower mill. Again, theshear energy absorption (measuring abrasion) is substan-tially higher than the normal energy (measuring impactdamage). The modest impact damage is concentrated onthe leading edges of the pins and there is some impact dam-age on the outside of the base plate. There is negligibleimpact damage on the backs of the pins, on the agitatorshaft or the mill chamber. The shear energy absorptionindicates that there will be significant abrasive wear onall parts of the pins, but most strongly concentrated onthe front faces, the edge of the end of the pin, and on theback of the pin near the ends. This will cause roundingof the end of the pins and flattening of their leading sur-faces. Almost the entire base plate (outer faces and top

the mill chamber and agitator. (Bottom) Abrasion wear (as predicted usingused for normal and shear work for each mill. For the tower mill, red

sents 800 W. For both mills dark blue is zero.


surface) is also subject to significant abrasive wear. Moder-ate abrasive wear is observed on the remainder of the backsof the pins and patchily on the shaft in regions of eitherhigh shear force or high surface velocity. This is strongestunderneath the lowest pins in the two columns that are off-set upwards from the base plate allowing significant mediaflow under these pins. The regions of the shaft behind thepins are well protected and experience little abrasion. Themill chamber experiences moderate wear in the middleand upper sections. This results from increased wall slipthat is experienced higher in the bed where the bed pres-sures are lower and the charge is therefore more mobile.The high pressures at the base of the mill press the chargemore firmly against the wall and produce lower wall slip.This helps protect the lower part of the mill chamber fromabrasion.

Fig. 10. Progress of axial mixing for the tower mill, (left) clipped 3D view shocentral slice of the bed shown from a side view at four different times (in scre

It is clear that the vertical offsetting of the pins betweencolumns has a number of deleterious effects. These includea complex oscillating flow for the media alternating overone pin and then under the next, strong asymmetric stressesin the agitator, and uneven wear patterns on the shaft.Without modelling an agitator that has no such offset itis not possible to predict if the grinding is or is notimproved by this pattern, but there is an open questionabout whether this is a useful design option.

4. Mixing and transport of media within the stirred mills

The existence of stagnant, non-mixing regions has directimplications for uniform size reduction throughout a milland also for overall mill performance. Each mill containsregions of high and low energy transfer from media to feed

wing the initial classification of the bed into horizontal strata, (right) a 2Dw revolutions) showing the extent of mixing.


material. Media trapped in low energy regions are unlikelyto generate much size reduction but at the same time theyare unlikely to interfere with the overall flow. It is useful tounderstand the mixing of media inside the mills and toexplore what this means for feed and product materialtransport within the mills.

4.1. Mixing of media – horizontal strata

Mixing behaviour can be predicted by colouring the par-ticles in various patterns according to their initial positionsand then observing the mixing of these different colours.The methodology for quantitatively measuring mixingusing these colours is given in Cleary et al. (1998). Herewe will classify the particles in the bed into horizontaland annular coloured regions in order to explore both axialand radial mixing and transport.

Fig. 10 shows the mixing predictions for the horizontalstrata case for the tower mill, where the particles aredivided into five horizontal bands of equal thickness. Theinitial particle colouring is shown in the sectioned three-

Fig. 11. Progress of axial mixing for the pin mill, (left) clipped 3D view showcentral slice of the bed shown from a side view at four different times (in scre

dimensional plot on the left of the figure. Since this flowis substantially axi-symmetric, a clear visualisation of theprogress of the mixing can be achieved by looking at justa narrow two-dimensional vertical slice through the millcentre. These are shown in the right columns of Fig. 10for four different times. The tower mill shows strong axialflow along the core screw. At 5 revolutions, material fromeach of the strata has moved upwards by two full stratathicknesses. More modest downward movement is alsoobserved around the outer layers of the charge near thewalls of the mill chamber. Each of the strata interfaceshas moved downward and clear intrusions of red materialinto the lowest blue level can be seen near the outer edgeof the screw. Material is pulled into the screw from thesides near the bottom. This demonstrates that a strongrecirculatory flow has been established with material risingin a cylindrical region near and inside the screw radius, andthen flowing back down the outside of the mill.

After 10 revolutions of the screw, the bottom layer ofdark blue material has reached the second top flight ofthe screw. Pink/violet material from the top strata has

ing the initial classification of the bed into horizontal strata, (right) a 2Dw revolutions) showing the extent of mixing.


moved downward and is now located only in an annularregion between the second top flight of the screw and abit below the middle of the mill. At the bottom, all the darkblue material accessible by the screw has been removedleaving only a stagnant region below the base of the screw.By 20 revolutions, the initial strata are becoming much lessdistinct. There is significant mixing of the colours repre-senting particles from initially very different parts of themill. The pink/violet material has maintained the highestlevel of coherence, but there is quite a lot of other materialinter-mixed.

After 30 revolutions, the bed is substantially well mixed.The stagnant dark blue region below the screw remains rel-atively unperturbed throughout. Above the screw, theshape of the surface of the bed is flat indicating the centrif-ugal forces are not dominant (compared to gravity) or elsethe free surface would become angled and in the form of aninverted cone. This levelness of the free surface is furtherassisted by maintaining a fill level well above the top ofthe helical screw.

The tower mill is clearly very effective at mixing themedia in around 30–35 revolutions. This will be positivefor maintaining a genuine steady process for the feed mate-rial as it will be rapidly distributed throughout the mill andground product will also be rapidly circulated allowing it tobe effectively removed. These mixing attributes and theflow pattern that can be deduced from the mixing patternare very consistent with the coherent media velocity distri-

Fig. 12. (Top) time evolution of the axial mixing state, (bottom) corresponding(Left) tower mill, and (right) pin mill.

butions observed in the velocity isosurfaces shown inFig. 4.

Fig. 11 shows the mixing predictions for the horizontalstrata case for the pin mill, where the particles are againdivided into five horizontal bands of equal thickness. Theinitial particle colouring is shown in the sectioned three-dimensional plot on the left of the figure. For visualisingthe mixing, we again show just a narrow two-dimensionalvertical slice through the mill centre. These are shown inthe right columns of Fig. 11 for four different times.Despite the highly energetic nature of the pin interactionswith the bed, they do not generate consistent coherent ver-tical motion (see bottom panels in Fig. 4). This means thatthere is only slow, local diffusion of particles across theinterfaces between colour regions, but there is no globalconvective transport. This can be seen by the very slowprogress of the mixing. After 50 revolutions, the strata stillremain substantially coherent.

The pin mill produces violent disruption of the bed sur-face as shown in Fig. 11. This is due to a combination of amuch higher centrifugal force (resulting from the muchhigher mill rotation speed) and to the smaller bed massabove the top pins which limits damping of the pressurewaves propagating to the free surface. Media centrifugesand piles up at the wall, allowing voids to propagate downthe shaft to as far as the first layer of pins.

The classification of bed regions into ‘coloured’ verticalstrata allows us to make global estimates of the degree of

time-dependent mixing rate calculated as the gradient of the mixing state.


mixing and the mixing rate as a function of time. A three-dimensional cylindrical grid is first superimposed over themedia bed. The grid cells then store estimates of the localaverage bed ‘colour’ at regular intervals which can be usedto calculate a mixing state and a rate of mixing. Thismethod is well described in Cleary et al. (1998).

The time-dependent mixing state (as % mixed) and thecorresponding mixing rate for axial mixing are plottedfor both mills in Fig. 12. The very strong axial mixing ofthe tower mill is confirmed. The mixing begins slowly withmixing of predominantly of particles within each colourstrata. Once the strata begin to mix, there is a sustainedperiod (around 12 revolutions) with a linear increase inmixing. This corresponds to the time taken to lift mediafrom the floor of the mill to the top free surface as shownin Fig. 10. The mixing slows after 20 revolutions (and

Fig. 13. Progress of radial mixing for the tower mill, (left) clipped 3D view shcentral slice of the bed shown from a side view at four different times (in scre

above 70% mixed) as the mixing saturates and it becomeharder to mix the remaining amount of material. By 30 rev-olutions nearly 90% of the bed is mixed. Considering thataround 5% of the bed is stagnant below the bottom ofthe screw, this means that the mill has almost reached theperfect mixing limit in only 30 revolutions.

In contrast, the axial mixing in the pin mill is signifi-cantly slower than for the tower mill. After 60 revolutions,the particles have only been mixed to around 8%. So mix-ing in the tower mill is around 20 times faster than for thepin mill. This reflects the much higher efficiency of convec-tive mixing compared to purely diffusive mixing. For thepin mill, there is no certainty that the diffusive mixing willbe able reach a fully mixed state. It could saturate wellbefore this and remain substantially unmixed. The bestcase is that the mixing is very slow.

owing the initial classification of the bed into annular strata, (right) a 2Dw revolutions) showing the extent of mixing.


4.2. Mixing of media – annuli

Next we investigate the quality of radial mixing in thesemills by colouring the bed into annular regions of equalvolumes. Fig. 13 shows initial annular strata and the subse-quent mixing of these strata for the tower mill at the sametimes as used for the axial mixing. By 5 revolutions, there isquite significant disruption of the annular layers. Thisoccurs from both diffusive axial mixing and at the endsfrom the axial transport by the screw. In the middle regions(well away from the areas affected by the axial flow, manyparticles can be seen well away from their initial radialpositions. This indicates that the mill is also effective atmixing in a purely radial direction. By 10 revolutions, bluematerial (originally in the core) has now occupied the tophalf of the mill and the pink/violet outer layer is now mixedthroughout the lower half of the mill. By 30 revolutions,there is little remaining of the initial colour distributionsand the material is fairly well mixed. There are even signsof radial mixing in the relatively stagnant zone under thescrew (material which is not exposed to the axial mixing

Fig. 14. Progress of radial mixing for the pin mill, (left) clipped 3D view showinslice of the bed shown from a side view at four different times (in screw revol

or axial transport). Fig. 15a shows the quantitative mixingstate of the media throughout the simulation. The annularcoloured particles mix very rapidly at first and achieve a50% mixed state by about 8 revolutions. The mixing slowsafter this but reaches an 85% mixed state at 33 revolutions.This is close to the asymptotic limit of mixing. This demon-strates that the tower mill is also effective at mixing in theradial direction, perhaps only 10% slower than the veryeffective axial mixing.

Fig. 14 shows the progress of radial mixing in the pinmill. After 10 revolutions, the bed above the top pins isvery well mixed. This results from the energetic collisionsof the pins and the low bed weight above which gives theparticles very good mobility in this region. Below this thereis reasonable mixing in the region inside the radii of thepins. This results from the strong perturbing force of thepins passing through the bed and the much lower bed pres-sures at low radii resulting from the much lower centrifugalforce. The annular layers are increasingly well preserved asthe radius increases from the ends of the mill out to thechamber radius. There is a large unmixed region below

g the initial classification of the bed into annular strata, (right) a 2D centralutions) showing the extent of mixing.

Fig. 15. (Left) Time evolution of the mixing state for the tower mill as % mixed is given in the top picture. Below this is the corresponding time-dependentmixing rate. These describe mixing in the radial regime. (Right) The degree of mixing and the mixing rate are similarly given for the pin mill.


the bottom plate of the agitator indicating that there is noflow here.

By 20 revolutions, the good mixing in the top of the bedhas extended down to about the top third of the bed. Thereis little sign of increased mixing for the media outside of thepins. Media migration across the annular interfaces pro-ceeds via the pin interactions with a highly packed bed.Each pin pushes particles in front to the sides but alsoout to larger radii. Once the pin has passed, particles flowinto the void behind the pin. These come from above andbelow and also from the compressed bed at larger radii.This is a random walk type process which is inherently dif-fusive and leads to radial mixing. This mechanism does notgenerate radial mixing beyond the short distance of thecompression that the pin generates and so is not effectiveat mixing particles at larger radii. The mixing state is littlechanged at either 30 or 50 revolutions (shown in Fig. 14).

The radial mixing rate for the pin mill (see Fig. 15b)starts off fairly high, but still only half the rate of the towermill. This rate is significantly faster than the rate of axialmixing for the pin mill. The mixing state variation is para-bolic in shape and the rate of mixing steadily drops withthe passage of time. By 60 revolutions the extent of radialmixing has just passed 50% and the mixing is clearly satu-rating. The asymptotic limit appears to be around 60%, sothe radial mixing is faster than the axial mixing, but it is farfrom perfect.

5. Conclusions

DEM models of dry pilot-scale tower and pin mills havebeen used to explore the dynamics of these two mills. Theflow patterns are very different in the two mills, as are theirdistributions of energy absorption, their mixing and trans-port properties, and their wear characteristics. For bothmills, the average rate of shear energy absorption is abouta factor of three higher than for the normal energies, indi-cating that comminution is dominated by attrition andabrasion. Again for both mills, the power is less than therated power of the mills since they are not being operatedat the maximum agitator speed or with the maximummedia density suggested by the mill specifications. Detailedwear predictions on the mill shells and agitators providesclear indications as to the manner in which these two typesof mills will wear and how this wear differs between the twotypes of mills.

It was shown that the structure of the media flow pat-terns and density variations in the packed beds of thesemills can be very well explored using novel visualisationtechniques such as using isosurfaces of the key variablesarising from collecting stress and motion data on an Eule-rian grid co-moving with the agitators. Investigation offorce networks and particle trajectories provide additionalmethods for extracting information from densely packedcirculating beds. These three techniques are expected to


be powerful tools for understanding the internal dynamicsof media and rock motion on stirred and other high inten-sity mills.

Specific conclusions can be drawn about each of themills.

5.1. Tower mill

• The media in the tower mill swirls around the axis of thescrew at a reasonably high speed with the peak tangen-tial speed occurring at the outer edge of the screw anddeclining both towards the mill shell and towards theaxis of the screw. The screw is very effective at pushingmaterial vertically upwards in a central core leading toan axial recirculation as this material then flows downthrough an annular region adjacent to the mill shell.

• The energy absorption by the media (and therefore thegrinding of feed) is very uniform throughout the heightof this mill meaning that the full mill height is beingeffectively utilised. The energy absorption rate is lowerfor media that are closer to the axis of the mill, so theenergy absorption rate is not uniform with radii, but ispeaked near the edge of the screw. A more even radialdistribution of energy absorption might improve perfor-mance of this mill.

• Detailed analysis of the energy absorption isosurfacesreveals that this is high over a broad cylindrical volumeof the mill charge extending from nearly the base to rea-sonably close to the free surface. The fraction of parti-cles within the high energy absorption region, which isa measure of the grinding participation rate of the mediais quite high for this mill.

• The predicted power draw for the tower mill comparesfavourably with the current best semi-empirical model.

• The tower mill was found to be an effective mixer due tostrong convective axial transport of the media by thescrew agitator and strong diffusive radial mixing. Thisis positive for rapid distribution of feed material through-out the mill and should also assist in timely removal ofprogeny from the mill. Overall, the tower mill appearsto have excellent mixing and transport properties.

• Energy dissipation in the tower mill is predominantly dueto shear with the contribution from normal componentsof collisions a factor of five lower. Media–liner collisionsare more efficient at dissipating energy than media–media. This largely results from the fairly high wall slipvelocities observed against the outer mill chamber.

• The pressure distribution for the tower mill is fully axi-ally symmetric. The largest normal and shear stresses areexperienced along the edge of the screw’s top helical sur-face and at the ‘toe’.

• The predictions of wear for the tower mill found abra-sive wear to be the leading cause of damage to the cham-ber lining and agitator surface. The edge of the screwand the front corner of the ‘toe’ are expected to erodeover time.

• The main comparative drawback of this mill, comparedto the pin mill, is that it operates at a much lower rota-tional speed. The strong vertical transport characteris-tics of the screw will mean that the charge will notremain within the mill if the speed is too high.

• This mill appears to have many attractive attributes forthe range of rotation speeds that it functions effectivelyover.

5.2. Pin mill

• The flow in the pin mill is substantially circulatory innature when not near the base plate or the free surface.The tangential or swirl velocity is highest at the radius ofthe pins and declines with increasing and decreasingradius. There is no global transport of media in the axialdirection as there was for the tower mill. Near the baseof the mill, the flow is complex with particles beingpushed radially outward by the lowest pins of the loweroffset pin columns. The particles are also forced abovethese pins and then flow down under the lowest pinsof the following pin column (which were offset verticallyupwards by half a pin spacing). This oscillatory wavemotion of media at the base of the mill leads to strongstress and wear concentrations on the mill agitator andto reasonable density variations with the charge.

• The rate of energy absorption by the media increasesstrongly with depth. Energy absorption by the mediais poor in the upper half of this mill meaning that a rea-sonable fraction of the mill volume is under-utilised.Energy absorption close to the agitator shaft is alsopoor, further diminishing the volume available for effec-tive comminution.

• Analysis of the energy absorption isosurfaces reveals acomplex pattern of energy absorption with significantvertical and azimuthal variation. The high energyabsorption regions are concentrated in small regions infront of the pins and increase rapidly with depth. Theparticipation rate for media in this mill is quite low, withonly a very small fraction of particles contributing togrinding at any specific time.

• The average energy dissipated in collisions in the pinmill are very similar to that of the tower mill with theincrease in rotational speed substantially cancelled outby the use of smaller media. Whilst the statistical distri-bution of collision energies is similar, the spatial distri-bution of these collisions are radically different andthis leads to large differences in machine performance.

• The pin mill experiences substantially higher and unbal-anced pressures than the tower mill (about 2–3 timesgreater). This is strongest at the leading edge of the pins,along the shaft above the pins, and on the disc top sur-face. The vertical offsetting of the pins results in asym-metric loading of the agitator shaft with implicationsfor mill operation and mechanical damage.


• The pin mill has a higher power draw and greater levelsof energy absorption than the tower mill. This is pre-dominantly due to the higher agitator speed and moreviolent action of the pins with the media. Wear on thechamber lining and the agitator shaft are dominatedby abrasion. The most significant changes to the millover time will likely include flattening of the pins dueto impact with media and rounding of the edges of thepins. The top of the base plate and the shaft will alsobe eroded over time.

• Particle transport within the mill is very poor, particu-larly in the axial direction. The mixing is purely diffu-sive. In the radial mixing, the rate of mixing is aroundhalf that observed for the tower mill, but only 60% ofthe charge is mixed since the material beyond the endsof the pins is not perturbed. Particles within the packedbed are broadly isolated in fixed circular paths, co-rotat-ing substantially with the pins and with only gentle ran-dom walks in the axial direction.

• The poor mixing will restrict the ability of feed particlesto move to high breakage areas of the mill and willrestrict the ability of fine progeny to escape from highbreakage areas. This might reasonably be expected tolead to over-grinding of some feed and under-grindingof others depending on their locations within the mill,resulting in a broader size distribution than would occurif the transport was better.

• The poor vertical transport of particles means that thismill can operate at much higher speeds than the towermill with little risk of loosing grinding media from thesurface of the charge. So its comparative strong pointis that it can operate at much higher speeds and there-fore higher energy intensities, but much of this is usedless effectively. This machine appears to grind to finersizes by brute force.

• In normal operation, slurry is pumped into the bottomof the mill and exits through a pipe above the charge.Hence feed particles are exposed to high energy shearfollowed by low energy shear and discharge. As achiev-ing interaction with very fine particles requires intenseshear, in many cases the upper layers of the pin millcharge may not add significantly to the comminutionprocess.

Mixing in the tower mill has both convective and diffu-sive components, is very efficient, and achieves almost fullmixing of the particles in both the radial and axial direc-tions in only 30 screw revolutions. In contrast, the pin millmixing is purely diffusive in nature, is around 20 timesslower in the axial direction, more than twice as slow inthe radial direction with an asymptotic mixing limit ofonly 60% and is quite inefficient. This means that thetower mill is likely to be well mixed and that feed materialwill be rapidly circulated into strong grinding regions to becomminuted and then efficiently transported to the dis-charge location. This will limit over-grinding and make

good use of the full grinding volume. Conversely, onecould reasonably expect that the pin mill transport of feedmaterial to the optimal grinding region (which is a smalllocalised region near the bottom most pins) will be poor.Most of the feed material will be located in parts of themill with poor grinding characteristics which will limitthe comminution performance of this mill. Similarly, thepoor transport properties of the mill will make removalof product difficult and expose it to continuing comminu-tion, potentially wasting substantial energy in over-grind-ing the fine tail. These observations on mixing apply tothe media and will be broadly the same for both wetand dry systems. Our deductions here on the behaviourof the feed and product transport are predominantly fordry systems. For wet systems, the issues will remain butwill be modified by the extent and manner of water addi-tion and removal. Forcing large volumes of water througha mill with poor transport characteristics can improve thetransport, but its better to design mills with good trans-port properties to start with. From a transport perspective,the tower mill is very attractive. This should not be a sur-prise since screws, not vastly different to the one used in atower mill are used for screw feeders, screw mixers andscrew conveyors.

Acknowledgement

The DEM modelling work reported in this paper hasbeen partially funded by the Centre for Sustainable Re-source Processing.

References

Barker, G.C., 1994. Computer simulations of granular materials. In:Mehta, Anita (Ed.), Granular matter: An interdisciplinary approach.Springer Verlag, NY.

Barley, R.W., Conway-Baker, J., Pascoe, R.D., Kostuch, J., McLoughlin,B., Parker, D.J., 2004. Measurement of the motion of grinding mediain a vertically stirred mill using positron emission particle tracking(PEPT) Part II. Minerals Engineering 17, 1179–1187.

Campbell, C.S., 1990. Rapid Granular Flows. Annual Review of FluidMechanics 22, 57–92.

Cleary, P.W., 1998. Predicting charge motion, power draw, segregation,wear and particle breakage in ball mills using discrete elementmethods. Minerals Engineering 11, 1061–1080.

Cleary, P.W., 2001a. Modelling comminution devices using DEM.International Journal for Numerical and Analytical Methods inGeomechanics 25, 83–105.

Cleary, P.W., 2001b. Charge behaviour and power consumption in ballmills: sensitivity to mill operating conditions, liner geometry andcharge composition. International Journal of Mineral Processing 63,79–114.

Cleary, P.W., 2001c. Recent advances in DEM modelling of tumblingmills. Minerals Engineering 14, 1295–1319.

Cleary, P.W., 2004. Large scale industrial DEM modelling. EngineeringComputations 21, 169–204.

Cleary, P.W., Metcalfe, G., Liffman, K., 1998. How well do discreteelement granular flow models capture the essentials of the mixingprocess? Applied Mathematical Modelling 22, 995–1008.


Cleary, P.W., Morrison, R., Morrell, S., 2003. Comparison of DEM andexp. for a scale model SAG mill. International Journal of MineralProcessing 68, 129–165.

Conway-Baker, J., Barley, R.W., Williams, R.A., Jia, X., Kostuch, J.,McLoughlin, B., et al., 2002. Measurement of the motion of grindingmedia in a vertically stirred mill using positron emission particletracking (PEPT). Minerals Engineering 53–59.

Eskin, D., Zhupanska, O., Hamey, R., Moudgil, B., Scarlett, B., 2005.Microhydrodynamics of stirred media milling. Powder Technology156, 95–102.

Jankovic, A. 1999. Mathematical modelling of stirred mills. PhD Thesis,University of Queensland, unpublished.

Jankovic, A., 2003. Variables affecting the fine grinding of minerals usingstirred mills. Minerals Engineering 16, 337–345.

Morrison, R., Cleary, P.W., Valery, W., 2001. Comparing power andperformance trends from DEM and JK modelling. In: ProceedingsSAG 2001, IV, p. 284.

Sinnott, M.D., Cleary, P.W., Morrison, R.D., in press. Analysis of stirredmill performance using DEM simulation: Part 1 – media motion,energy consumption and collisional environment, Minerals Engineer-ing, doi:10.1016/j.mineng.2006.08.012.

Walton, O.R., 1994. Numerical simulation of inelastic frictional particle–particle interaction Chapter 25. In: Roco, M.C., (Ed.), Particulate two-phase flow. pp. 884–911.

Weller, K.R., Spencer, S.J., Gao, M.W., Liu, Y., 2000. Tracer studies andbreakage testing in pilot-scale stirred mills. Minerals Engineering 13,429–458.

http://dx.doi.org/10.1016/j.mineeng.2006.08.012

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Tower Mill Rotation Speed