STUDY ON MOTION OF MULTI-COMPONENT FERROMAGNETIC PARTICLES WITH MODIFIED MAGNETIZATION MODEL
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摘要: 铁磁性颗粒因具有铁磁性被广泛应用于化工环保、生化工程和能源等各个领域, 磁场具有的穿透性质, 对于采用铁磁性颗粒的系统, 可通过改变磁场控制系统内颗粒的运动状态. 文章基于传统的磁化模型, 采用相对参考系转换方法, 提出了适用范围更广的修正P-E磁化模型, 可以计算铁磁性颗粒在任意方向磁场作用下所受磁化力. 通过有限体积法(FVM)与离散单元法(DEM)耦合进行数值模拟, 验证了修正P-E磁化模型的精确性, 并模拟多组分颗粒在磁场中的运动, 对比了铁磁性颗粒与惰性颗粒在不同配比及不同磁场条件下的运动特性, 对颗粒分布、颗粒速度矢量和颗粒总能量变化3个方面进行分析. 结果表明: 在多组分颗粒系统中, 铁磁性颗粒依旧保持成链特性, 但成链速度与长度降低; 随着铁磁性颗粒占比提高, 铁磁性颗粒初始能量增大, 聚链数量与成链长度将有所增加, 约束惰性颗粒能力增强; 此外, 施加水平与竖直方向磁场时, 多组分颗粒系统达到稳定速度最快, 可以通过增大铁磁性颗粒占比有效提升稳定速度, 使系统更快趋于稳定; 而施加含有倾角的磁场时, 随着铁磁性颗粒占比升高, 铁磁性颗粒达到稳定状态需要的时间逐渐降低, 较难通过改变铁磁性颗粒占比缩短稳定所需时间.Abstract: Ferromagnetic particles are widely used in chemical environmental protection, biochemical engineering, energy and other fields because of their ferromagnetism. The penetrating nature of the magnetic field, for systems employing ferromagnetic particles, can be controlled by changing the magnetic field to control the motion of the particles within the system. In this paper, based on the traditional magnetization model, a modified P-E magnetization model with a wider range of applicability is proposed by using the relative reference system conversion method, which can calculate the magnetization force on ferromagnetic particles under the action of a magnetic field in any direction. Numerical simulations by coupling the finite volume method (FVM) with the discrete element method (DEM) to verify the accuracy of the modified P-E magnetization model and to simulate the motion of multicomponent particles in a magnetic field. The motion characteristics of ferromagnetic particles and inert particles in different ratios and magnetic fields were compared. The particle distribution, particle velocity vector and particle total energy were analyzed. The results show that in the multi-component particle system, the ferromagnetic particles still maintain the chain formation characteristics, but the chain formation speed and length decrease. The initial energy of ferromagnetic particles increases as the proportion of ferromagnetic particles grows, as does the number of polymer chains and the length of chain creation, and the ability to limit inert particles. Furthermore, when both horizontal and vertical magnetic fields are applied, the multi-component particle system achieves the fastest rate of stability. The rate of stabilization can be efficiently increased by increasing the number of ferromagnetic particles, causing the system to stabilize faster. When the magnetic field containing inclination Angle is applied, the time required for ferromagnetic particles to reach the stable state gradually decreases with the increase of the proportion of ferromagnetic particles, and it is difficult to shorten the stability time by changing the proportion of ferromagnetic particles.
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表 1 网格无关性检验表
Table 1. Grid independence test table
Minimum mesh size Number of grids Total kinetic energy/10−8J 1 R 6279 0.00583 2 R 1104 0.00346 3 R 248 0.00256 4 R 138 0.00228 5 R 95 0.00316 6 R 64 0.00472 
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表 2 模拟参数
Table 2. Analog parameters
Parameter Data particle diameter/m 0.0005 particle density/(kg·m−3) 1010 gas density/(kg·m−3) 1.293 magnetic field direction/(°) 0 magnetic permeability/(H·m−1) 8.3 magnetic induction intensity/T 0.02
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表 3 模拟工况表
Table 3. Simulated working condition table
Working condition Particle spacing C1/m 0.0005 C2/m 0.00075 C3/m 0.001
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表 4 模拟参数表
Table 4. Analog parameter table
Parameter Data particle diameter/m 0.001 particle density/(kg·m−3) 1010 diameter of inert particles/m 0.001 density of inert particles/(kg·m−3) 1010 fluid density/(kg·m−3) 1000 number of particles 300 magnetic permeability/(H·m−1) 8.3 magnetic permeability of inert particles/(H·m−1) 0 magnetic induction intensity/T 0.02 Young’s module/GPa 68.95 Poisson’s ratio 0.33 friction coefficient of particles 0.3 normal spring stiffness of particles/(N·m−1) 800 friction coefficient of particle-wall 0.3 normal spring stiffness of walls/(N·m−1) 800 damping coefficient 0.05
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表 5 模拟工况表
Table 5. Simulated working condition table
Working condition Magnetic field angle Number of ferromagnetic particles Number of
inert particlesFraction of ferromagnetic particles /% C1 0 100 200 33 C2 30 100 200 33 C3 60 100 200 33 C4 90 100 200 33 C5 0 150 150 50 C6 30 150 150 50 C7 60 150 150 50 C8 90 150 150 50 C9 0 200 100 66 C10 30 200 100 66 C11 60 200 100 66 C12 90 200 100 66
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