## 2 Material and Methods
### Challenges of Comparing Simulations to Experiments  
One of the key factors in the use of CFD-DEM for predicting particle concentrations lies in the justification that the simulation method has been verified and calibrated correctly and that the simulation results can be extracted in a useable format [6]. When considering simulation extraction procedures; many challenges are faced such as: mesh alignment (comparison of one mesh definition to another), material loading (number of particles contained in a simulation), the particle size distribution and the particle shape. These challenges need to be addressed such that the resulting simulation data is reliable and the results it produces can be used for comparison. Mesh alignment was a problem faced in the final stages of data comparison, once the data had been extracted from a simulation the format was given as concentrations on nodes. The simulation mesh then needed to be overlaid onto the experimental data (in this case a pixel grid) for comparison of the results. \begin{table}
\begin{tabular}{l l} \hline \hline
**Description** & **Alumina Simulation** \\ \hline Domain & 3D—Quarter silo \\ Turbulence model & K-epsilon realisable standard wall functions \\ Coupling & Discrete Phase Model (DPM) with two-way turbulence \\ Material (particle density) & coupling enabled \\  & alumina (3900 kg/m\({}^{3}\)) \\  & Rosin-Rammler distribution \\  & D min = 5.2 um \\ PSD—fines & D mean = 72.8 um \\  & D max = 350 um \\  & n = 1.61 \\ Mass flow rate—fines & \(1.9\times 10^{-5}\) kg/s \\ PSD—coarse & Uniform distribution \\  & D = 350 um \\ Mass flow rate—coarse & \(1.9\times 10^{-02}\) kg/s \\ DPM—parcels & \(1\) particle per parcel \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. However, the mesh for the simulation depended on the meshing method used, whether it be tetrahedrons, hexahedrons or cubic. In this analysis the cut cell method was used as it provides a highly uniform mesh. Further, cut cells resembled a cubic grid and therefore allowed for better comparison to the pixels used in experimental data post processing while also offering more consistent node spacing. For this investigation a mesh cell size of 9 mm was used; this was found to give an independent mesh as outlined in work conducted by [PERSON] et al. [15] for the same domain and silo. In addition to the previous study, the traditional methods of CFD analysis needed be adjusted. Typically, the mesh was refined to the point where independence is reached i.e., further refinements indicate no improvement in the results observed. However, due to the limitation that each mesh cell must contain a fluid volume, stability issues could arise if the cell was completely occupied by a particle; the governing equations could not be solved. The mesh size was three times the maximum particle diameter to ensure there was always fluid volume in a cell even when particles were present. From the sensitivity analysis and subsequent simulations, a mesh cell size of 9 mm was found to be sufficient in order to maintain an independent mesh while achieving a stable simulation. The mesh parameters are outlined in Table 2 and for values not specified the software defaults were used. In addition to the challenges of mesh alignment it was important to understand how Fluent reports the concentrations calculated in the simulations. The dust concentration calculation is illustrated by assuming a cell (blue) of volume ONE meter cube as shown in Figure 11. The blue cell contains one particle which has a mass of 1 kg and, therefore, the cell concentration is 1 kg/m\({}^{3}\). The other cells are assumed to have a concentration of 0 kg/m\({}^{3}\). When the concentration is exported, Fluent converts the cell concentration to a node concentration which takes into account neighbouring cells.