DEM SIMULATION OF ORDERING OF CUBES WITH ROUNDED CORNERS BY ROTATION DRIVEN
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摘要: 宏观颗粒体系的有序堆积研究可以为热系统中微观粒子的自组装提供研究模型, 也有助于工业生产中提高颗粒材料的填充率. 实验发现圆筒中的圆角立方体颗粒受容器往复旋转剪切作用会实现有序堆积. 为探究旋转圆筒中立方体颗粒有序堆积过程的内部结构演化过程和动力学机理, 采用超二次曲面方程构造了圆角立方体颗粒, 基于离散元方法对旋转剪切作用下圆角立方体颗粒有序堆积过程开展数值模拟研究. 模拟复现了实验中立方体颗粒从随机堆积状态向有序致密堆积状态转变的过程, 给出了体积分数和有序度参数在容器不同运动条件下随旋转次数增加的变化规律. 结果表明, 立方体颗粒的体积分数和有序度表现为随着容器旋转次数增加而逐渐增大直至稳定的变化趋势. 体系的有序堆积过程由外层颗粒开始逐渐向内部颗粒扩展. 通过调控容器旋转角位移发现颗粒完成有序堆积过程所需的特征旋转次数与容器旋转角位移呈现反比例关系. 旋转角位移过低, 体系只会形成两种颗粒团簇共存的结构, 即某一面平行容器底面的颗粒团簇与面对角线平行重力方向的颗粒团簇共存. 研究也发现在亚重力环境下立方体颗粒同样可以通过容器的旋转实现有序堆积. 重力加速度的减少会抑制立方体颗粒从无序堆积向有序堆积的转变.Abstract: The study of the orderly packing of macroscopic particle can not only provide a research model for the self-assembly of microscopic particles in thermal systems but also help to imcrease the packing fraction of granular materials in industry. Experimental results showed that cubic particles with rounded corners subjected to alternating rotation of the cylinder would achieve orderly packing. In order to investigate the internal structure evolution and mechanism of the orderly packing process of cubic particles with rounded corners in rotational cylinders, the cubic particles with rounded corners are constructed by the superquadric surface equation. Numerical simulations are carried out to investigate the orderly packing process of cubic particles with rounded corners in the rotation cylinder based on discrete element method. The simulation reproduces the transition of cubic particles from the random packing state to the ordered dense packing state in the experiment, and gives the variation of packing fraction and cubatic order parameter with the increase of rotation number under different motion. The results show that the packing fraction and the cubatic order parameter to increase gradually with the increase of the number of rotation until a stable value. The orderly packing process of the system starts from the external particles to the inner particles gradually. By regulating the angular displacement of the cylinder, it is found that the characteristic number of alternating rotation for the particles to complete the orderly packing process is inversely proportional to the angular displacement of the cylinder. If the angular displacement is too low, the system will only form a structure with clusters of particles whose sides are parallel to the horizontal plane and clusters of particles whose diagonal of the face parallel to gravity. It is also found that cubic particles in a sub-gravity environment can also achieve orderly packing through the alternating rotation of the cylinder. The reduction of gravitational acceleration inhibits the transition from disordered to ordered packing of cubic particles.
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Key words:
- DEM /
- cubic particle /
- orderly packing /
- microgravity
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图 1 装置示意图以及边界旋转方式
Figure 1. Schematic diagram of simulation and boundary rotation mode
图 2 体积分数及有序度随旋转次数的变化
Figure 2. Packing fraction
$ \varPhi $ and cubatic order parameter$ {S}_{4} $ versus number of rotation
图 4
$ \gamma $ 一定, 不同峰值角速度$ {\omega }_{0} $ 下, 填充率$ \varPhi $ 和有序度参量$ {S}_{4} $ 的变化Figure 4. Volume fraction
$ \varPhi $ and cubatic order parameter$ {S}_{4} $ versus number of rotation N for$ \gamma $ =1.01 and different$ {\omega }_{0} $ 
图 5 角速度
$ {\omega }_{0} $ 一定, 不同$ \gamma $ 下, 填充率$ \varPhi $ 和有序度参量$ {S}_{4} $ 的变化Figure 5. Volume fraction
$ \varPhi $ and cubatic order parameter$ {S}_{4} $ versus number of rotation N for$ {\omega }_{0} $ =5.0 rad/s and different$ \gamma $ 
图 6 反转时间一定, 不同
$ \gamma $ 下, 填充率$ \varPhi $ 和有序度参量$ {S}_{4} $ 的变化Figure 6. Volume fraction
$ \varPhi $ and cubatic order parameter$ {S}_{4} $ versus number of rotation N for the constant inversion time and different$ \gamma $ 
图 7 特征旋转次数与旋转角位移的关系
Figure 7. Characteristics rotation number versus angular displacement
图 8 相同
$ \beta $ 值下, 填充率$\varPhi $ 和有序度参量$ {S}_{4} $ 的变化曲线.Figure 8. Volume fraction
$ \varPhi $ and cubatic order parameter$ {S}_{4} $ versus number of rotation N for the constant$ \beta $ 
图 9 不同重力加速度下, 填充率
$ \varPhi $ 和有序度参量$ {S}_{4} $ 的变化曲线(模拟参数: 边界$ \gamma =4.04 $ , 峰值角速度$ {\omega }_{0}=10.0\;\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s} $ )Figure 9. Volume fraction
$\varPhi $ and order parameter$ {S}_{4} $ versus number of rotation N for different acceleration of gravity ($ \gamma =4.04 $ ,$ {\omega }_{0}=10.0\;\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s} $ )表 1 转动驱动立方体颗粒有序堆积过程的主要计算参数
Table 1. DEM simulation parameters of ordering of cubes
Parameter Symbol Value density/(kg·m−3) $ \rho $ 928 Young's modulus/GPa $ E $ 2.5 Poisson's ratio $ \nu $ 0.2 damping coefficient (particle-particle) $ {C}_{t} $ 0.1 damping coefficient (particle-wall) $ {C}_{tw} $ 0.1 sliding friction coefficient (particle-particle) $ {\mu }_{t} $ 0.3 sliding friction coefficient (particle-wall) $ {\mu }_{tw} $ 0.8 rolling friction coefficient $ {\mu }_{r} $ 0.005 
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