This study proposes a numerical model of dense random packing of mustard seeds within a cylindrical volume. The aim of the research is to simulate the process of spherical particle sedimentation under gravity using the Discrete Element Method (DEM). The model accounts for interparticle interactions, including contact forces, friction, rolling resistance, and restitution, which ensures a realistic representation of the physical behavior of granular media. To describe contact forces between seeds, a nonlinear Hertz–Mindlin model is applied, allowing for accurate consideration of the elastic properties of particle materials and their interactions under load. The simulation is conducted under conditions that resemble real industrial processes of pouring and compacting granular food materials. The numerical experiment models the gradual filling of mustard seeds into a confined vertical container. Upon completion of sedimentation and system stabilization, the packing density and main geometric parameters of the formed structure are recorded. The results show that the maximum average packing density reaches values in the range of 0.63–0.64, which aligns well with classical theoretical estimates for random dense sphere packing. The obtained results are practically significant for applications in the agro-industrial and food processing sectors, particularly in the design of hoppers, storage tanks, and processing units for granular agricultural products. The developed model can serve as a basis for further research into compaction, mixing, and classification processes in granular systems. Additionally, the simulation outcomes may be integrated into multiscale models involving continuum mechanics to develop more accurate digital twins of agricultural technologies. Furthermore, the presented modeling methodology enables the evaluation of the influence of container geometry, material properties, and external loading on the microstructure and packing density of granular media, making it promising for advanced engineering applications.

bulk materials, seeds, oilseed crops, mustard, random packing, physico-mechanical properties, modeling, discrete element method, compression, elasticity, Hertz–Mindlin model

Full Text:

PDF

1. Gao, F., Liu, Y., & Zhang, J. (2018). Numerical study of spherical particle packing in silos. Powder Science and Technology, 36(9), 891–902.

2. Horabik, J., & Molenda, M. (2016). Parameters and contact models for DEM simulations of agricultural granular materials: A review. Biosystems Engineering, 147, 206–225.

3. Huang, W., Duan, R., & Zhang, M. (2020). Discrete element modeling for cereal seeds: Theory and practice. International Agrophysics, 34(3), 201–218.

4. Koshy, T. B., Borzooei, S., & Molenda, M. (2019). DEM simulation of seed metering: A review. Agricultural Engineering International: CIGR Journal, 21(3), 78–91.

5. Li, H., Wang, X., & Ma, X. (2021). Measurement and analysis of physical and mechanical properties of rapeseed. Processes, 9, 1394. https://doi.org/10.3390/pr9071394

6. Ma, Z., Jia, M., Liu, J., & Xu, W. (2024). Microstructural characterization of DEM-based random packings of cubic particles: Influence of particle shape. Journal of Chemical Physics, 160, 164901. https://doi.org/10.1063/5.0172545

7. Makwana, K., Patel, A., & Singh, S. (2021). Discrete element method in modelling grain flow: Recent advances. Powder Technology, 393, 354–366.

8. Maraveas, C., Tsigkas, N., & Bartzanas, T. (2025). Agricultural processes simulation using discrete element method: A review. Computers and Electronics in Agriculture, 237, 110733. https://doi.org/10.1016/j.compag.2025.110733

9. Modi, V., Singh, S., & Pal, K. K. (2019). DEM modelling of grain–machine interaction. Transactions of the ASABE, 62(4), 999–1008.

10. Nyagah, E. K., Jusoh, M., & Bashir, A. (2020). Simulation of granular seed flow: DEM approach. Powder Technology, 377, 255–263.

11. Pournale, R., & Koh, T. J. (2019). Advances in DEM modeling of agricultural materials. Powder Technology, 349, 1–15.

12. Ropelewska, E., Jankowski, K. J., Zapotoczny, P., & Bogucka, B. (2018). Thermophysical and chemical properties of seeds of traditional and double low cultivars of white mustard. Zemdirbyste-Agriculture, 105(3), 257–264. https://doi.org/10.13080/z-a.2018.105.033

13. Sahu, S., Kumar, S., & Prasad, S. (2022). Modelling granular agro-materials by discrete element method. Journal of Biosystems Engineering, 47(2), 125–137.

14. Singh, A. P., Angelidakis, V., Pöschel, T., & Roy, S. (2024). Shear zones in granular mixtures of hard and soft particles with high and low friction. Soft Matter, 20(1), 192–204. https://doi.org/10.1039/d3sm01159a

15. Singh, V., Moses, S. C., Noor Alam, R., & Dsouza, P. (2023). Investigation of physical and frictional properties of mustard seed varieties to design inclined plate metering mechanism. International Journal of Environment and Climate Change, 13(11), 1392–1399.

16. Tian, Y., Zeng, Z., & Xing, Y. (2024). A review of discrete element method applications in soil–plant interactions: Challenges and opportunities. Agriculture, 14(9), 1486. https://doi.org/10.3390/agriculture14091486

17. Xie, Q., Liu, G., & Wang, L. (2018). DEM simulation of seed sowing processes. Journal of Agricultural Mechanization Research, 40, 140–148.

18. Zhang, T., Wang, F., & Tao, Y. (2022). Characterization of granular seed beds using DEM. Computational Materials Science, 210, 111232.

19. Zhao, H., Huang, Y., Liu, Z., Liu, W., & Zheng, Z. (2021). Applications of discrete element method in the research of agricultural machinery: A review. Agriculture, 11(5), 425. https://doi.org/10.3390/agriculture11050425

20. Zhao, Z., Wu, M., & Jiang, X. (2024). A review of contact models’ properties for discrete element simulation in agricultural engineering. Agriculture, 14(2), 238. https://doi.org/10.3390/agriculture14020238