椭球颗粒材料在水平转筒内混合特性的超二次曲面离散元分析

Mixing characteristics of ellipsoidal granular materials in horizontal rotating drum based on analysis by discrete element method

转筒中的颗粒流广泛存在于工业生产中,颗粒形状是影响颗粒流动的重要因素.本文基于超二次曲面方程描述球体和椭球颗粒的几何形态,采用离散元方法对水平转筒中颗粒物质的流动和混合特性进行数值分析,并与椭球混合过程的实验结果进行对比验证.在此基础之上,进一步研究了圆筒转速、颗粒填充分数和颗粒长宽比对混合率的影响规律.计算结果表明:颗粒材料的混合率随着转速的增加或填充分数的减小而增加.在相同转速和填充分数下,椭球颗粒的混合率高于球形颗粒.同时,长宽比为0.75和1.5时椭球颗粒具有最高的混合率.当长宽比小于0.75时,混合率随着长宽比的增加而增加;当长宽比大于1.5时,混合率随着长宽比的增加而减小.此外,椭球颗粒出现更明显的速度分层现象.颗粒长宽比改变颗粒间的接触模式和系统的密集度,增加了颗粒系统的平动而限制了转动,在一定程度上提高了外部能量向颗粒系统转化的效率.

Granular flow in the drum widely appears in the fields of industrial production, and discrete element method(DEM) proves to be a critical tool for studying the flow characteristics of granular materials.Considering simple contact and efficient calculations, the three-dimensional spheres are originally adopted by the DEM. Therefore, the DEM simulations mainly focus on spherical particles, while the dynamics of nonspherical particles in rotating drums is relatively rarely studied. It is reported that particle shape significantly affects the macroscopic and microscopic properties of the granular flow. Compared with spherical particles, nonspherical particles have low fluidity and great interlock. Meanwhile, it is questionable whether conclusions drawn from spherical particle systems can be transplanted to non-spherical particle systems. In this work,super-quadric equations based on continuous function representation are used to describe the spherical and ellipsoidal particles. Considering the complex contact detection between particles, the Newton iteration algorithm is used to solve the non-linear equations. Meanwhile, a non-linear contact model considering the equivalent radius of curvature at the local contact point is used to calculate the contact force between the super-quadric elements.To examine the validity of DEM model, we compare our simulated results with the previous experimental results for mixing process of ellipsoids, and this method is verified by good agreement between the simulated results and the experimental results. According to the aforementioned method, the influences of rotating speed,fill level, and aspect ratio on the mixing rate are discussed. The results show that the granular system reaches the cascading regime and the S-shaped surface of the granular bed is observed. In addition, Lacey mixing index is used to quantify the mixing of granular systems, and the mixing rate is obtained by fitting the Lacey mixing index. The mixing rate increases as the rotating speed increases. At the same rotating speed, the mixing rate of ellipsoids is faster than that of spheres. Meanwhile, the ellipsoidal particles have the fastest mixing rate when the aspect ratio is 0.75 or 1.50. When the aspect ratio is less than 0.75, the mixing ratio increases as the aspect ratio increases;when the aspect ratio is greater than 1.50, the mixing ratio decreases as the aspect ratio increases. Moreover, more pronounced velocity stratification is observed for ellipsoids. The translational kinetic energy of ellipsoidal particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. The aspect ratio of particles can adjust the contact mode between particles and cause the interlock. It means that the relative rotation between particles is limited and the efficiency of the external energy transferring to the non-spherical system may be improved.