## 4 Results and Discussion
### Pressure Drop
#### 4.4.2 Numerical Simulation of Pressure Drop
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Symbol** & & & **Value** & \\ \hline  & & **0 kPa** & **50 kPa** & **150 kPa** & **250 kPa** \\ \hline Average number of & - & 34 & 33 & 32 & 30 \\ path points & - & 34 & 33 & 32 & 30 \\ Tortuosity & \(\tau\) & 1.25 & 1.32 & 1.43 & 1.47 \\ Porosity & \(\epsilon\) & 0.428 & 0.391 & 0.362 & 0.353 \\ Inner surface & \(S_{p}\), m\({}^{2}\) & & & 0.275 & \\ Solid volume & \(V_{p}\), m\({}^{3}\) & & & 0.00033 & \\ Specific surface & \(S_{0}\), m\({}^{2}\) & & & 824.73 & \\ pore shape factor & \(C_{kz}\) & & & 5 & \\ Forchheimer & A & 17,740,438.61 & 27,852,990.67 & 41,729,700.98 & 47,576,815.47 \\ coefficient & & & & & \\ Forchheimer & B & 191.24 & 246.34 & 320.98 & 329.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of PathFinder code calculations. difference of 15% at 150 kPa. The DEM-CFD method and Forchheimer equation coefficients calculated by the PathFinder code take into account not only the decrease in porosity of the packed bed under the difference in vertical pressure but also the increase in the tortuosity of the pore path, which means the calculations were more accurate. The Ergun equation can only consider the effect of porosity variation on pressure drop, and the results have a greater difference. The contours of pressure drop under different vertical pressures are shown in Figure 12. The inlet velocity \(V_{0}\) = 0.6 m/s was chosen for the study. The distribution of static pressure  
Figure 11: Comparison results of soybean pressure drop at different vertical pressures: (**a**) 0 kPa (**b**) 50 kPa (**c**) 150 kPa (**d**) 250 kPa. Figure 10: Airflow path distribution under different vertical pressure: (**a**) 0 kPa (**b**) 50 kPa (**c**) 150 kPa (**d**) 250 kPa. values at different vertical pressures was similar, and the static pressure decreases gradually. The static pressure decreased gradually and showed a clear layered phenomenon along the outlet direction, and the static pressure distribution was constant at the inlet and outlet regions. The static pressure at the inlet and the pressure drop through the soybean packed bed increase with the vertical pressure, which was consistent with the pressure drop test and empirical equation calculation. The test and simulation results can be extrapolated at a larger scale. However, it is worth mentioning that the DEM-CFD method requires high computer computing power and requires reasonable simplification of operations. The pressure drop is relevant for the bed characteristics, which increase with the compression of the bed. As to an actual on-farm silo, the static pressure distribution is uneven under compaction by the self-weight of grain [47; 48]. The temperature and moisture distributions will be quite different in a larger packed bed. Summarizing the velocity distribution and pressure drop under vertical pressure, the DEM-CFD method is suitable to describe the airflow characteristics precisely. The vertical pressure reduces the porosity of the packed bed, reducing the voids occupied by air, resulting in a larger particle contact area and increased thermal conductivity. The temperature and moisture change in the soybean packed bed accelerated under vertical pressure. The temperature and moisture distributions should be considered in further investigations using the DEM-CFD method.