张昌松¹，高晓阳¹，陈飞昌¹，陶 俊²

（1. 陕西科技大学 机电工程学院，陕西 西安 710021；2. 西安近代化学研究所, 陕西 西安 710065）

DOI：10.13732/j.issn.1008-5548.2023.02.011

收稿日期：2022-08-13，修回日期：2022-09-14,在线出版时间：2023-01-04 10:48。

基金项目：西安近代化学研究所开放合作创新基金项目，编号：SYJJ200304。

第一作者简介：张昌松(1976—)，男，副教授，博士，硕士生导师，研究方向为离散元法、有限元仿真、材料成型技术。E-mail：zhangcs@sust.edu.cn。

摘要：以高能立式搅拌器模型为基础，建立微米级粉体机械活化过程的多尺度仿真模型，通过流体力学-离散元法(computational fluid dynamics-discrete element method，CFD-DEM)耦合模拟磨球运动规律，分析球磨稳定时不同磨球碰撞相对速度的概率占比，并通过稠密离散相模型对微米级粉体运动分布区域进行分析，基于以上仿真结果建立粉体应力概率分析模型。结果表明：粉体应力概率与磨球碰撞相对速度的切向、法向分量比值存在直接联系，拟合出二者关系曲线为指数型函数曲线，其中判定系数R²为0.93，数值接近于1，拟合曲线的预测效果较为理想，为分析粉体的塑性变形及破碎率提供数值基础。

关键词：高能球磨；流体力学-离散元法；应力概率；多尺度建模

Abstract：The multi-scale simulation model of the mechanical activation process of micron-sized powder was developed based on the high energy vertical agitator model, CFD-DEM coupling was used to model the motion of the ball.When ball grinding was steady, the probability ratio of various ball collision relative velocities was examined.The motion distribution area of micron powder was examined in accordance with the dense discrete phase model, and the powder stressing probability analysis model was developed based on the findings of the simulations mentioned above.The results show that the outcomes of the simulation demonstratea clear correlation between the stress probability of powder and the ratio of the tangential and normal components of the relative velocity of grinding ball contact.The fitting curve of the relation between them is exponential function curve.The determination coefficient R² is 0.93, which is close to 1, the prediction effect of fitting curve is ideal.The curve offers a numerical foundation for evaluating the powder plastic deformation and crushing rate.

Keywords：high energy ball mill；computational fluid dynamics-discrete element method；stress probability；multiscale modeling

参考文献(References)：

[1]SIPPEL T R, SON S F, GROVEN L J.Altering reactivity of aluminum with selective inclusion of polytetrafluoroethylene through mechanical activation[J].Propellants, Explosives, Pyrotechnics, 2013, 38(2): 286-295.

[2]ADAMENKO N A, KAZUROV A V, SAVIN D V, et al.Study of structure formation in aluminum filled polytetrafluoroethylene after explosive compression[J].Inorganic Materials: Applied Research, 2022, 13(1): 68-74.

[3]OKHLOPKOVA A A, SLEPTSOVA S A, PARNIKOVA A G, et al.Triboengineering and physicomechanical properties of nanocomposites based on PTFE and aluminum oxide[J].Journal of Friction and Wear, 2008, 29(6): 466-469.

[4]DING T, GUO W C, CAO W, et al.Experimental study of reaction properties of aluminum/polytetrafluoroethylene powder under laser ablation[J].AIP Advances, 2021, 11(8): 085010.

[5]陶俊, 王晓峰, 韩仲熙, 等.铝粉/聚四氟乙烯机械活化含能材料的制备及其微观性能研究[J].材料导报, 2018, 32(6): 894-898.

[6]UHLMANN E, EULITZ A, DETHLEFS A.Discrete element modelling of drag finishing[J].Procedia CIRP, 2015, 31: 369-374.

[7]CHANG Q, DI S B, XU J, et al.Direct numerical simulation of turbulent liquid-solid flow in a small-scale stirred tank[J].Chemical Engineering Journal, 2021, 420: 127562.

[8]李旭, 刘彦, 安丰江, 等.行星式球磨颗粒流场分布与形貌变化规律[J].兵工学报, 2022, 43(4): 876-891.

[9]BEINERT S, FRAGNIERE G, SCHILDE C, et al.Multiscale simulation of fine grinding and dispersing processes: stressing probability, stressing energy and resultant breakage rate[J].Advanced Powder Technology, 2018, 29(3): 573-583.

[10]BEINERT S, KWADE A, SCHILDE C.Strategies for multi-scale simulation of fine grinding and dispersing processes: drag coefficient and fracture of fractal aggregates[J].Advanced Powder Technology, 2018, 29(3): 707-718.

[11]BEINERT S, FRAGNIERE G, SCHILDE C, et al.Analysis and modelling of bead contacts in wet-operating stirred media and planetary ball mills with CFD-DEM simulations[J].Chemical Engineering Science, 2015, 134: 648-662.

[12]TSUJI Y, TANAKA T, ISHIDA T.Lagrangian numerical simulation of plug flow of cohesionless particles in a horizontal pipe[J].Powder Technology, 1992, 71(3): 239-250.

[13]吴亮.含固体颗粒的两相流界面变化的数值研究[D].天津: 天津大学, 2018.

[14]WANG Z K, TENG Y J, LIU M B.A semi-resolved CFD-DEM approach for particulate flows with kernel based approximation and hilbert curve based searching strategy[J].Journal of Computational Physics, 2019, 384: 151-169.

[15]BHARADWAJ R, KETTERHAGEN W R, HANCOCK B C.Discrete element simulation study of a freeman powder rheometer[J].Chemical Engineering Science, 2010, 65(21): 5747-5756.

[16]SUN Z N, ZHU J.A four-quadrant flow regime map for two-phase liquid-solids and gas-solids fluidization systems[J].Powder Technology, 2021, 394: 424-438.

[17]KIM S, WOO S C.Analysis of ball movement for research of grinding mechanism of a stirred ball mill with 3D discrete element method[J].Korean Journal of Chemical Engineering, 2008, 25(3): 585-592.

[18]WANG Z, TENG Y, LIU M.A semi-resolved CFD-DEM approach for particulate flows with kernel based approximation and hilbert curve based searching strategy[J].Journal of Computational Physics, 2019, 384: 151-169.