基于随机弹道沉积方法的黏附性椭球颗粒疏松堆积极限的研究

doi:10.11949/0438-1157.20250309

化工学报 ›› 2025, Vol. 76 ›› Issue (11): 5533-5543.DOI: 10.11949/0438-1157.20250309

• 专栏：能源利用过程中的多相流与传热 • 上一篇下一篇

基于随机弹道沉积方法的黏附性椭球颗粒疏松堆积极限的研究

方筑¹(), 廖亚琴²(), 张乾², 张易阳³, 李水清¹()

^1.清华大学能源与动力工程系，北京 100084
^2.东方电气集团科学技术研究院有限公司，四川成都 611731
^3.清华大学核能与新能源技术研究院，北京 100084

收稿日期:2025-03-27 修回日期:2025-05-10 出版日期:2025-11-25 发布日期:2025-12-19
通讯作者: 廖亚琴,李水清
作者简介:方筑（1994—），男，博士， fangz17@tsinghua.org.cn
基金资助:
国家自然科学基金项目(52406187);国家自然科学基金项目(52322608);东方电气中央研究院企业委托项目;清华大学水木学者计划项目(2022SM021)

Study on adhesion loose packing limit of adhesive ellipsoids based on random ballistic deposition method

Zhu FANG¹(), Yaqin LIAO²(), Qian ZHANG², Yiyang ZHANG³, Shuiqing LI¹()

^1.Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China
^2.DEC Academy of Science and Technology Co. , Ltd. , Chengdu 611731, Sichuan, China
^3.Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China

Received:2025-03-27 Revised:2025-05-10 Online:2025-11-25 Published:2025-12-19
Contact: Yaqin LIAO, Shuiqing LI

摘要/Abstract

摘要：

采用基于碰撞-黏附-冻结假设的随机弹道沉积方法，研究了椭球颗粒的几何形状（长径比变化范围为0.003~60）对黏附疏松堆积结构的影响。统计结果表明，球形颗粒的堆积密度最大，为0.1469。随着颗粒形状偏离球形，堆积密度迅速降低。当长径比小于0.1或大于10时，堆积密度与长径比之间分别近似服从1和-2的幂律关系。局部配位数与颗粒形状无关，不仅服从高斯分布，而且统计平均值均为2.001，表明对于短程接触相互作用控制的非球形颗粒堆积系统，形成力学稳定结构的最小配位数仍为2。径向分布函数表明，扁平形椭球的局部堆积结构由短轴-长轴和长轴-长轴接触主导，长条形椭球的局部堆积结构由短轴-短轴和短轴-长轴接触主导。最后，类比经典球形颗粒的填充理论，构建了堆积密度与长径比之间的预测关联式。

关键词: 计算机模拟, 粒子, 沉积物, 颗粒过程, 随机堆积, 非球形

Abstract:

The effect of the geometric shape of ellipsoids (covering a wide aspect ratio range from 0.003 to 60) on the structure of adhesive loose packings is investigated by the random ballistic deposition method with the hit-stick-freeze assumption. Statistical results show that the packing density of spherical particles is the largest, which is 0.1469. As the particle shape deviates from spherical shape, the packing density decreases rapidly. When the aspect ratio is below 0.1 and above 10, the packing density is approximately correlated with the aspect ratio in 1 and -2 power-law relations. The local coordination number is independent of the particle shape, which not only follows the Gaussian normal distribution, but also has a common average value of 2.001. This result indicates that for packing systems of non-spherical particles controlled by short-range interparticle contact interactions, 2 is the lowest coordination number for forming a mechanically stable structure. The radial distribution function shows that the local packing structure is dominated by local minor-to-major and major-to-major contact for oblate ellipsoids, and by local minor-to-minor and minor-to-major contact for prolate ellipsoids. Finally, analogous to the classical filling theory of spherical particles, a predicting correlation between the packing density and the aspect ratio is established.

Key words: computer simulation, particle, deposition, particulate processes, random packing, non-spherical

中图分类号:

TQ 021.9

方筑, 廖亚琴, 张乾, 张易阳, 李水清. 基于随机弹道沉积方法的黏附性椭球颗粒疏松堆积极限的研究[J]. 化工学报, 2025, 76(11): 5533-5543.

Zhu FANG, Yaqin LIAO, Qian ZHANG, Yiyang ZHANG, Shuiqing LI. Study on adhesion loose packing limit of adhesive ellipsoids based on random ballistic deposition method[J]. CIESC Journal, 2025, 76(11): 5533-5543.

图/表 7

图1 不同长径比的椭球颗粒

Fig.1 Ellipsoidal particles with different aspect ratios

图2 球形颗粒疏松堆积结构（颗粒数目分别为3万、20万、50万、100万和160万）

Fig.2 Packing structures of spherical particles (with particle number of 30000, 200000, 500000, 1000000 and 1600000)

图3 球形颗粒堆积密度沿高度方向的变化

Fig.3 Packing fraction as a function of height for spherical particles

图4 堆积密度与长径比的关系

Fig.4 Relationship between packing fraction and aspect ratio

图5 局部配位数的统计分布

Fig.5 Statistical distribution of local coordination number

表1 不同长径比颗粒配位数分布函数的拟合参数

Table 1 Fitting coefficients of the distribution function of coordination number of differently shaped particles

λ	A	Z_m	σ_z	R²	RMSE
0.005	0.455	1.840	0.925	0.9991	0.0067
0.1	0.465	1.863	0.897	0.9990	0.0057
0.2	0.479	1.889	0.862	0.9992	0.0050
0.3	0.492	1.909	0.834	0.9994	0.0043
0.5	0.513	1.934	0.794	0.9998	0.0037
0.7	0.526	1.945	0.772	0.9998	0.0032
1	0.531	1.949	0.763	0.9999	0.0030
1.4	0.525	1.945	0.773	0.9998	0.0031
2	0.507	1.930	0.807	0.9997	0.0032
3	0.476	1.894	0.873	0.9997	0.0031
5	0.436	1.810	0.992	0.9997	0.0035
10	0.399	1.604	1.197	0.9997	0.0028
20	0.389	1.311	1.415	0.9998	0.0019
60	0.411	0.772	1.720	0.9999	0.0009

图6 不同形状颗粒的径向分布函数

Fig.6 Radial distribution function of differently shaped particles

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基于随机弹道沉积方法的黏附性椭球颗粒疏松堆积极限的研究

Study on adhesion loose packing limit of adhesive ellipsoids based on random ballistic deposition method

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