## 3 Simulation Setup
### Accumulation Bed and Particle-to-Particle Contact Point Treatment  
Following the creation of a homogeneous mesh covering the complete fluid domain, it became evident that a gradient strategy was necessary. Near the contact points, the pores are very narrow, and the curvature is large, creating voids near the contact points. As a result, direct meshing is insufficient around the contact points and may negatively affect the accuracy of the calculations. Thus, the mesh must be improved to ensure accurate calculation results. The performance around the contact points can be enhanced by using a uniform mesh, although this exponentially increases the computational requirements.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Unit** & **Value** \\ \hline Cylinder radius & \(D\) & mm & 26.64/33.6/37.5 \\ Particle radius & \(d_{p}\) & mm & 6 \\ Cylinder-to-particle size ratio & \(D/d_{p}\) & & 4.44/5.6/6.25 \\ Particle density & \(\rho_{\rm p}\) & kg/m\({}^{3}\) & 1257 \\ Shear modulus & \(G\) & Pa & \(2.71\times 10^{8}\) \\ Young’s modulus & \(E\) & Pa & \(7.588\times 10^{8}\) \\ Poisson’s ratio & \(\
u\) & & 0.4 \\ Restitution coefficient & \(e_{\rm pp}\) & & 0.627 \\ Static friction coefficient & \(\mu_{\rm st}\) & & 0.2 \\ Rolling friction coefficient & \(\mu_{\rm r}\) & & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Particle parameters used in the DEM simulation.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Symbol** & **Value** \\ \hline \multirow{3}{*}{Soybean} & \(\rho_{\rm s}\), kg/m\({}^{3}\) & 1257 \\ \cline{2-3}  & \(k_{\rm s}\), \(W\)/(m\(\cdot\)K) & 0.136 \\ \cline{2-3}  & \(c_{\rm s}\), J/(kg\(\cdot\)K) & \(c_{\rm s}=2000+35.5(\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{ \rm{ \rm{ \rm{ }}}}}}}}}}}}}})\)\(/1+\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{ \rm{\rm{\rm{\rm{\rm{\rm{\rm{{\rm{\rm{{\rm{{ }}}}}}}}}}}}}}}}}}}}}\)\) \\ \hline \multirow{3}{*}{Air}} & \(\rho_{\rm f}\), kg/m\({}^{3}\) & \(\rho_{\rm f}=8.666\times 10^{-6}{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{{\rm{\rm{\rm{\rm{ \rm{\rm{\rm{\rm{\rm{\rm{{\rm{\rm{{ }}}}}}}}}}}}}}}}}}}}\)\(/1+\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{ \rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{\rm{{\rm{\rm{\rm{During the random accumulation of particles in the bed, contact occurs between individual particles and also between particles and the surrounding walls. Despite the packed structure of the accumulation bed, it is challenging to generate high-quality meshes in the vicinity of contact points. This difficulty is largely due to the narrow pores and significant curvature near these contact points, which often cause the mesh elements to become highly inclined or even generate negative volumes. Such issues can adversely affect the simulations and compromise the accuracy of the results. Consequently, various strategies have been developed to mitigate the effects of contact points, including the models proposed by [PERSON] (2014); [PERSON] (2016), and [PERSON] et al. (2017). To minimize the presence of \"bridge models\", which refer to the fine and curved calculation meshes that surround contact points, cylindrical contact points can be substituted in those regions. In this study, the \"gap model\" was used to examine the porosity and flow characteristics in consideration of particle-particle and particle-wall interactions, as illustrated in Figure 3.  
Figure 3: Schematic diagram of the gap model and grid division of \(D/d_{p}=4.44\).  
Figure 2: Graphical representation of a coaxial cylindrical surface.