## 5 Conclusions  
To clarify the effect of different vertical pressures on the pressure drop of soybean bulk, the DEM-CFD method was used to simulate the pressure drop characteristics of soybean packed beds under different compression states. The following conclusions were obtained by comparing the experimental and empirical equation results.  
1. The deformation of the soybean bulk increases with vertical pressure. After applying vertical pressure, a large transient deformation of the grain bulk occurs, and then the deformation change rate decreases. The total compression of soybean bulk occurred mainly within two hours after loading and stabilized after about four hours. The compressions under 50, 150, and 250 kPa pressures were 4.29 mm, 7.18 mm, and 8.98 mm, respectively.
2. The distribution of particle center coordinates close to the cylindrical wall generated by DEM is approximately circular. With the increase in vertical pressure, the internal particles move towards the pore area and the central coordinates become more scattered. The amplitude of radial porosity oscillation decreases with increasing vertical pressure. The compression process leads to an increase in the compactness of the packed bed and a more continuous particle distribution. The central porosity of the packed bed was 0.39, 0.36, and 0.35, respectively, in 50, 150, and 250 kPa com  
Figure 12: The contours of pressure drop under different vertical pressures at inlet velocity \(V_{0}\) = 0.6 m/s: (**a**) 0 kPa (**b**) 50 kPa (**c**) 150 kPa (**d**) 250 kPa.  
pression states. The porosity distribution simulated by DEM is consistent with the experimental results in the literature.
3. The radially mean dimensionless velocity is consistent with the trend of porosity oscillation distribution. The local maximum velocity increases with the vertical pressure. The mean velocities in the particle packed region were 0.75 m/s, 0.78 m/s, 0.81 m/s, and 0.86 m/s at vertical pressures of 0, 50, 150, and 250 kPa, respectively. The radially averaged dimensionless velocity distribution is not only determined by the porosity but also related to the pore channel connectivity.
4. The packed bed airflow path is more tortuous with the increase in vertical pressure, and the pressure drop of the soybean packed bed increases with the increase in inlet velocity and vertical pressure. Considering the variation in porosity and pore connectivity, the pressure drop results calculated by the DEM-CFD method and the Forchheimer equation were in close agreement with the experimental results.  
Conceptualization, W.L., G.C. and M.G.; methodology, W.L. and D.Z.; software, W.L.; validation, W.L. and C.L.; formal analysis, W.L. and M.G.; investigation, W.L. and C.L.; resources, G.C. and D.Z.; data curation, W.L. and M.G.; writing--original draft preparation, W.L.; writing review and editing, G.C. and D.Z.; supervision, G.C. and D.Z.; project administration, D.Z.; funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Grain Public Welfare Research Project of China, grant number 201513001-01; the Innovative Funds Plan of the Henan University of Technology, grant number 2020 ZKC0J5; and the Open Project of Henan Key Laboratory of Grain and oil storage facility & safety, grant number 2020 KF-A02.  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflict of interest.