## 3 Results and Discussion
### Effect of the Media Loading Evaluated from PEPT Experiments
The overprediction of the velocity by DEM could possibly be further reduced if the effect of other commonly calibrated input parameters such as rolling friction or coefficient of restitution was considered; this, however, will considerably increase the number of simulations required for the  
Figure 13: Histogram of the velocity magnitude for the attritor mill and for three sub-domains of the mill: top region, middle region and bottom region. PEPT test case using the bead loading of 2.4 kg, the impeller clearance of 19 mm and the impeller speed of 300 rpm. calibration. It should also be stressed that the predictions of the simulations are expected to improve after the data are averaged for the entire simulation time because of the high number of particle velocities available. Based on the plots of Figure 14 the static friction coefficient of 0.50 was selected as the best value for the three regions and, therefore, used to generate the following results. The PEPT and the DEM results were further analysed, after an averaging procedure, by a qualitative visualisation of the velocity flow fields and by a quantitative comparison based on the extraction of the velocity magnitude along the height of the attr at different radial positions. The DEM data were time averaged over 5 s of simulation, by means of a coarse graining method (CG) using the Iota software described above, and projected on a vertical plane passing through the centre of the vessel. The PEPT data were azimuthally averaged as previously explained in Figure 3.  
Figure 14: Probability density functions (pdf) of the velocity magnitude calculated for the top, middle and bottom regions. Comparison between PEPT data and DEM simulations as function of the static friction coefficient for the impeller speed of **(a)** 300 rpm and **(b)** 600 rpm. From the qualitative comparison, the simulations captured well the main structures of the flow field which can be summarised in three elements: bed height, position of the regions at low and high velocity and extent of these regions. Indeed, as can be seen from Figure 15 the simulations predicted those three elements at both impeller speeds of 300 rpm and 600 rpm. The colour scale in both DEM- and PEPT- velocity maps indicate low velocity and high velocity with dark blue and red colour, respectively. However, the dark blue region at the top of the DEM-velocity map is an artefact that can lead to misinterpretation. The blue colour in this region does not correspond to beads moving at low velocity, but instead indicates the absence of beads in that region and consequently a velocity equal to zero. This arises from the coarse graining methodology, which requires a volume domain for the average of the simulation data. Taking this into account, Figure 15 demonstrates an excellent agreement between the two techniques, highlighting that the maximum bead velocity was close to 50% of the tip speed value. For example, at 300 rpm the maximum bead velocity was 0.6 m/s (nearly 55% of the tip speed), whereas at 600 rpm it was 1.1m/s (nearly 52% of the tip speed). These data highlight the limitations of using the tip speed as the only parameter to describe the complex velocity field of the granular material. It is further noted that the DEM model was able to reproduce the bed expansion and the shape of the upper part of the packed-bed which is formed due to the generation of a large vortex at the attritor centre as observed in other studies [9; 11]. Figure 15: Comparison of the velocity flow field for DEM simulations and PEPT data at the impeller speed of (**a**) 300 rpm and (**b**) 600 rpm. To quantify the agreement between the DEM predictions and the experimental measurements, the media velocity along the vessel height was extracted for two impeller speeds (300 rpm and 600 rpm) at different radial positions.