**1. Introduction**

Supernormal particles, particles with irregular geometric shapes whose length is at least several times the diameter, cannot be simplified into a spherical-shape mathematical model. The flow of supernormal particles has the characteristics of anisotropy and involves complex forces, so conventional methods for non-spherical particles such as equivalent diameter, shape factor and specific surface area are not suitable for supernormal particle problems to be solved in the agricultural field [1–3]. Taking the problem of jujube branch picking as an example, since jujube pruning stubs have typical characteristics such as jujube thorns, crotches, sizeable stem-to-length ratio, and high degree of irregularity, the jujube branch picking process is commonly seen as a specific abnormal particle flow problem. Exploring advanced and accurate simulation methods is the key to solving the complex flow problem of agricultural supernormal particles [4–7].

Presently, research on spherical particles, non-spherical particles and slender particles is extensive in the agricultural field, with different algorithms of particle movement being widely applied in various types of research. A two-stage dust removal device for straw carbonization flue gas has been designed by Xin et al. [8] and simulated the separation efficiency of dust particles using the DPM model to test the relationship between the particle

**Citation:** Zhang, R.; Wang, G.; Wang, W.; Ren, D.; Gong, Y.; Yue, X.; Hou, J.; Yang, M. Numerical Simulation of the Picking Process of Supernormal Jujube Branches. *Agriculture* **2023**, *13*, 408. https://doi.org/10.3390/ agriculture13020408

Academic Editor: Massimo Cecchini

Received: 20 December 2022 Revised: 24 January 2023 Accepted: 25 January 2023 Published: 9 February 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

size and the separation efficiency of the cyclone separator. The separation of grains and short stalks under the action of airflow using the CFD-DEM coupling method has been simulated by Jiang et al. [9], which solved the problem of the indoor settlement of imperfect grains reasonably. The flow characteristics of straw-like slender particles in the flow field has been researched by Cai et al. [10], and a two-way coupling relationship between the slender particles and the flow field has been constructed. Since there are many crops with highly irregular geometric characteristics in the agricultural field, it is urgent to explore an appropriate method to cope with the flow characteristics of such supernormal particles.

There are plenty of calculation methods for particle flow, such as the finite element method based on Lagrange (Euler), the lattice-Boltzmann method and the immersed boundary method [11–13]. The finite element method based on Lagrange (Euler) involves thinking of particles as point sources and then using the Lagrangian method to calculate particle motion, solve fluid interaction with N-S equation, and employ phase interaction to describe the law of particle force and the interaction between particles and walls [14,15]. The lattice-Boltzmann method uses the Boltzmann equation of microscopic statistical mechanics to calculate, and it provides a simplified dynamic model for the microscopic particles in the system. The macroscopic physical quantities of particles (such as density, velocity, etc.) are obtained through mathematical statistical methods, which meet the macroscopic fluid dynamics equations, so this method boasts relatively prominent advantages in describing fluid effects [16,17]. The embedded boundary method proposed by Fadlun et al. uses linear velocity interpolation on the interface between the wall and the fluid to obtain the velocity of the calculated point on the interface and to calculate the interaction force between the fluid and the embedded boundary of the solid wall [18].

Research has shown that a new DEM numerical solution method based on the meshless Galerkin method is being studied by scholars [19–21]. The method uses the weight function and the kernel function to solve the mechanical properties of any point in the region to solve the particle motion problem eventually [22–24]. Instead of mesh generation, it only needs the node information. In addition, it has the advantages of high accuracy, fast convergence, and convenient post-processing. Finally, the meshless Galerkin method eliminates the influence of geometry on the flow to the largest extent; emphasizes the interaction between different particles, between particles and walls, and between particles and fluids; and provides a theoretical basis and mathematical method for solving supernormal particle flow problems.

In summary, the movement of supernormal particle flow is a widespread phenomenon in the agricultural multiphase flow field. However, the understanding of supernormal particle flow in related studies is neither systematic nor in depth, such as that of the mechanical picking of jujube branches, hairy vetch, and straw. The meshless Galerkin method was first used to simulate the motion of supernormal particles, whose numerical results could further reveal the influence of the main flow factors (particle size, particle number and particle force) on the jujube branch. Based on numerical analysis and experimental results, the relationship between sizes of jujube branches, the total feeding number, the rotation speed and shape of the gears and the picking rate of jujube branches were clarified. This research provides a necessary theoretical basis for solving the problem of supernormal particle flow in agricultural machinery engineering, which boasts extensive use prospects and important academic value in the mechanical picking of crop residues.
