转鼓内圆柱形颗粒混合的超二次曲面离散单元法模拟

doi:10.16085/j.issn.1000-6613.2022-1373

化工进展 ›› 2023, Vol. 42 ›› Issue (5): 2252-2261.DOI: 10.16085/j.issn.1000-6613.2022-1373

转鼓内圆柱形颗粒混合的超二次曲面离散单元法模拟

卢兴福¹^,²(), 戴波¹^,², 杨世亮³()

^1.中冶长天国际工程有限责任公司，湖南长沙 410205
^2.国家烧结球团装备系统工程技术研究中心，湖南长沙 410205
^3.昆明理工大学省部共建复杂有色金属资源清洁利用国家重点实验室，云南昆明 650031

收稿日期:2022-07-21 修回日期:2022-11-14 出版日期:2023-05-10 发布日期:2023-06-02
通讯作者: 杨世亮
作者简介:卢兴福（1986—），男，高级工程师，研究方向为烧结球团相关技术装备开发。E-mail：13357213891@126.com。
基金资助:
云南省基础研究计划(202201AW070008);中冶长天科研开发基础研究基金(2020JCYC10)

Super-quadric discrete element method investigation of mixing behaviors of cylindrical particles in a rotating drum

LU Xingfu¹^,²(), DAI Bo¹^,², YANG Shiliang³()

^1.Zhongye Changtian International Engineering Co. , Ltd. , Changsha 410205, Hunan, China
^2.National Engineering Research Center of Sintering and Pelletizing Equipment System, Changsha 410205, Hunan, China
^3.State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming 650031, Yunnan, China

Received:2022-07-21 Revised:2022-11-14 Online:2023-05-10 Published:2023-06-02
Contact: YANG Shiliang

摘要/Abstract

摘要：

在离散单元法（DEM）框架下基于超二次曲面模型描述非球形颗粒，探讨了不同颗粒纵横比（AR）和转鼓转速对圆柱形颗粒混合性能及扩散特性的影响。结果表明：增大AR使得圆柱形颗粒的互锁和堆积效应增强，抬升高度更高，具有更陡的床面倾角。转鼓内混合存在三种机制：颗粒内循环导致的宏观对流混合、主动-被动区相对运动导致的介观剪切混合、颗粒扩散导致的微观扩散混合。在给定的研究参数范围内，AR为2时，圆柱形颗粒的时均混合指数最高；AR为4时，圆柱形颗粒的时均混合指数最低。转鼓转速是影响圆柱形颗粒混合速率的首要因素。增大转速加剧颗粒运动并缓慢增大颗粒的轴向时均扩散系数。主动区内的圆柱形颗粒和水平方向的夹角集中在0°~30°，转鼓内圆柱形颗粒倾向于和转鼓轴线方向垂直。基于超二次曲面方法的圆柱形颗粒计算耗时高于球形颗粒，增大AR进一步增加计算耗时。

关键词: 混合, 数值模拟, 扩散, 非球形颗粒

Abstract:

The cylindrical particles were characterized by a super-quadric model under the discrete element method (DEM) framework and the effects of aspect ratio (AR) and rotating speed on the mixing and diffusion characteristics of cylindrical particles in a rotating drum were studied. The results showed that enlarging AR increased the inter-locking and packing effects, leading to a higher elevation height and steeper inclination angle of free surface. Three mixing mechanisms were illuminated in the rotating drum: ①macro-scale convection mixing induced by particle internal circulation; ②meso-scale shear mixing induced by active-passive layers relative motion; ③micro-scale diffusion mixing induced by particle diffusion. Under the given operating parameters, cylindrical particles with the AR of 2 had the largest time-averaged mixing index while cylindrical particles with the AR of 4 had the smallest time-averaged mixing index. The primary factor influencing the mixing rate was rotating speed. Increasing the rotating speed enhanced the kinematic of cylindrical particles, and slightly increased the axial diffusion coefficients. The axis of cylindrical particles in the active layer tended to have the orientation in the range of 0°—30° while cylindrical particles in the drum preferred to be perpendicular to the drum axis. Computational costs for the cylindrical particles using the super-quadric model were higher than that for the spherical particles and increasing the AR increased computational costs.

Key words: mixing, numerical simulation, diffusion, non-spherical particles

中图分类号:

TQ051

卢兴福, 戴波, 杨世亮. 转鼓内圆柱形颗粒混合的超二次曲面离散单元法模拟[J]. 化工进展, 2023, 42(5): 2252-2261.

LU Xingfu, DAI Bo, YANG Shiliang. Super-quadric discrete element method investigation of mixing behaviors of cylindrical particles in a rotating drum[J]. Chemical Industry and Engineering Progress, 2023, 42(5): 2252-2261.

图/表 13

表1 验证算例中的非球形颗粒属性

参数	数值
短轴长（2a=2b）/mm	8.0
长轴长（2c）/mm	5.3
密度/kg·m^-3	1245
杨氏模量/Pa	5×10⁷
泊松比	0.35
恢复系数	0.85
滑动滑动系数	0.5

图1 转鼓内非球形颗粒运动与实验[17]对比

图2 几何模型及初始设置

表2 算例中的非颗粒属性

AR	a/mm	b/mm	c/mm	n₁	n₂	颗粒数
1	1.748	1.748	1.748	10	2	10000
2	1.387	1.387	2.775	10	2	10000
3	1.212	1.212	3.636	10	2	10000
4	1.101	1.101	4.405	10	2	10000

图3 不同AR下转鼓内圆柱形颗粒流态（Ω=20r/min，t=120s）

图4 不同运行及颗粒参数（Ω, AR）对不同区域内颗粒质量分数的影响

图5 转鼓内非球颗粒的混合过程（Ω=20r/min，AR=2）

图6 不同转速下非球形颗粒混合指数曲线演变

表3 不同运行及颗粒参数下转鼓内非球形颗粒的时均混合系数

参数	Ω=5r/min	Ω=10r/min	Ω=20r/min
AR=1	0.90772	0.90967	0.90746
AR=2	0.92288	0.92089	0.91077
AR=3	0.9164	0.91445	0.91076
AR=4	0.90098	0.90093	0.89281

图7 不同区域内颗粒扩散系数演变（Ω=20r/min，AR=2）

图8 不同运行及颗粒参数（Ω，AR）对时均轴向颗粒扩散系数的影响

图9 转鼓内颗粒取向的概率直方分布（AR=4，Ω=20r/min）

表4 球形颗粒与具有不同AR的圆柱形颗粒的计算耗时

类型	计算耗时/h
AR=1	115
AR=2	142.6
AR=3	160.1
AR=4	182.1
球形颗粒	85

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转鼓内圆柱形颗粒混合的超二次曲面离散单元法模拟

Super-quadric discrete element method investigation of mixing behaviors of cylindrical particles in a rotating drum

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