偏心料斗颗粒速度和体积分数分布自相似特性

doi:10.13229/j.cnki.jdxbgxb.20240293

摘要/Abstract

摘要：

基于离散元法对颗粒流在重力驱动下通过偏心料斗出口的流动特性进行了数值模拟分析，分别使用偏心量 $e$ （料斗中心与出口中心的距离）和 $s$ （料斗左侧墙壁与料斗出口左端之间的距离）表征偏心料斗卸料过程，系统研究了出口偏心位置对出口处颗粒速度和体积分数分布的影响。结果表明，针对不同出口尺寸，采用偏心量 $e$ 表征卸料过程会导致不同的颗粒流动模式，而采用偏心量 $s$ 时，卸料过程中颗粒流动模式具有相似性。进一步基于偏心量 $s$ 的分析表明，颗粒速度和体积分数分布具有自相似特征，其归一化轮廓曲线可以用指数函数描述，指数参数决定曲线轮廓的变化趋势，具有明确的物理意义。结合出口偏心位置与质量流量，提出了矩形偏心料斗的颗粒流量预测公式，通过该公式发现，出口在料斗壁面（ $s = 0$ ）相对其他位置具有较高的卸料速度。在微观尺度下，研究料斗卸料过程中的颗粒动力学特征和物理规律，有助于优化料斗结构和颗粒流动，并精确预测卸料流量。

关键词: 农业工程, 颗粒速度分布, 体积分数分布, 颗粒流量预测, 离散元

Abstract:

Based on the discrete element method， the flow characteristics of granular matter through eccentric hopper outlet driven by gravity were numerically investigated. Two different eccentricities $e$ （distance between the center of the hopper and the center of the outlet） and $s$ （distance between the left wall of the hopper and the left end of the hopper outlet） were used to characterize the discharge process of the eccentric hopper， the influence of the eccentricities on the distribution of particle velocity and volume fraction at the orifice was systematically studied. The results show that for different outlet sizes， when the eccentricity $e$ is used to characterize the discharge process， the granular flow exhibits different flow patterns， while the discharge flow patterns are similar when the eccentricity variable $s$ is used. Further， according to the analysis of eccentricity $s$ ， the distribution of particle velocity and volume fraction have self-similar characteristics， their normalized contour curves can be well described by the exponential function， and the exponential parameter determines the trend of curve contour change， which has clear physical significance. Combining the profiles of particle velocity and volume fraction， a normalized formula for predicting flow rate of rectangular eccentric hopper is proposed. It is found that it has the maximum discharge rate when the outlet is located at the wall of the hopper （ $s = 0$ ）. At the microscopic scale， understanding the dynamic characteristics and physical laws of the particle discharging is helpful to optimize the structure of the hopper and particle flow， as well as accurately predict the discharge rate.

Key words: agricultural engineering, particle velocity distribution, volume fraction distribution, discharge rate prediction, discrete element method

中图分类号:

S126

范建华,张亮,王宏伟,张磊,于建群. 偏心料斗颗粒速度和体积分数分布自相似特性[J]. 吉林大学学报(工学版), 2025, 55(9): 2913-2925.

Jian-hua FAN,Liang ZHANG,Hong-wei WANG,Lei ZHANG,Jian-qun YU. Self⁃similar characteristics of particle velocity and volume fraction distribution in eccentric hopper[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(9): 2913-2925.

图/表 15

图1

表1

仿真相关参数"

类型	参数	数值
颗粒参数	颗粒数 $N$	3 000
	颗粒直径 $d$ /mm	3
	颗粒密度 $ρ p$ /（kg·m^-3）	2 500
	泊松比 $ν$	0.25
	剪切模量 $G$ /Pa	$1 × 108$
颗粒接触参数	颗粒-颗粒滑动摩擦因数 $μ p, p$	0.5
	颗粒-颗粒滚动摩擦因数 $μ r ? p, p$	0.01
	颗粒-颗粒碰撞恢复因数 $e p, p$	0.2
	颗粒-料斗壁面滑动摩擦因数 $μ p, w$	0.5
	颗粒-料斗壁面滚动摩擦因数 $μ r ? p, w$	0.01
	颗粒-料斗壁面碰撞恢复因数 $e p, w$	0.2
料斗几何参数	宽度 $L$ /mm	100
	出口尺寸 $D$ /mm	18， 30， 45， 60
	高度 $H$ /mm	300
	偏心量 $e$ /mm	0， 3， 27
	偏心量 $s$ /mm	0， 6， 12， 18， 24， 30

表1

图2

图3

图4

图5

表2

偏心量e的颗粒速度分布与体积分数分布拟合参数"

e/mm	$ε$	$m$	$n$
0	1.266	0.39	0.386
3	1.258	0.39	0.393
27	1.389	0.39	0.418

表2

图6

图7

图8

表3

偏心量s表征颗粒速度轮廓与体积分数轮廓的拟合参数"

s/mm	$α 1$	$α 2$	$β 1$	$β 2$	$a$	$b$
0	-0.311	-0.130	1.462	1	0.278	0.32
12	-0.056	-0.007	1.312	1	0.371	0.42
30	-0.024	0.002	1.269	1	0.383	0.41

表3

图9

图10

图11

图12

参考文献 34

[1]	Lu F, Zhang C, Wei F. Compressibility of granular fluids [J]. Physics of Fluids, 2022, 34(3): No. 033307.
[2]	Huang Y, Zhu C, Xiang X. Granular flow under microgravity: A preliminary review[J]. Microgravity Science and Technology, 2014, 26(2): 131-138.
[3]	Meng F, Pang M, Liu K. Constitutive relation and mechanical mechanism analysis in granular lubrication [J]. Industrial Lubrication and Tribology, 2020, 72(5): 621-628.
[4]	Campbell C S. Granular material flows—An overview[J]. Powder Technology, 2006, 162(3): 208-229.
[5]	Zheng N, Zhu H W, Huang D C, et al. The effects of physical factors on the granular hopper flow[J]. Scientia Sinica: Physica, Mechanica et Astronomica, 2020, 50(9): No.090005.
[6]	孟凡净, 刘焜. 密集剪切颗粒流中速度波动和自扩散特性的离散元模拟[J]. 物理学报, 2014, 36(13): 262-270.
	Meng Fan-jing, Liu Kun. Velocity fluctuation and self diffusion character in a dense granular sheared flow studied by discrete element method[J]. Acta Physica Sinica, 2014,63(13): 262-270.
[7]	胡国琦, 张训生, 鲍德松, 等. 二维颗粒流通道宽度效应的分子动力学模拟[J]. 物理学报, 2004, 53(12):4277-4281.
	Hu Guo-qi, Zhang Xun-sheng, Bao De-song, et al. The molecular dynamics simulation of the effect of channel width on two-dimensional granular flow[J]. Acta Physica Sinica, 2004, 53(12): 4277-4281.
[8]	Anand A, Curtis J S, Wassgren C R, et al. Predicting discharge dynamics from a rectangular hopper using the discrete element method (DEM)[J]. Chemical Engineering Science, 2008, 63(24): 5821-5830.
[9]	Beverloo W A, Leniger H A, Van de velde J. The flow of granular solids through orifices[J]. Chemical Engineering Science, 1961, 15: 260-269.
[10]	Ji S, Wang S, Peng Z. Influence of external pressure on granular flow in a cylindrical silo based on discrete element method[J]. Powder Technology, 2019, 356: 702-714.
[11]	Ma H, Zhao Y. Influence of external pressure on granular flow in a cylindrical silo based on discrete element method[J]. Chemical Engineering Science, 2017, 172: 636-651.
[12]	Wang S, Zhuravkov M, Ji S. Granular flow of cylinder-like particles in a cylindrical hopper under external pressure based on DEM simulations[J]. Soft Matter, 2020, 16(33): 7760-7777.
[13]	Wu S M, Zhu H P, Yu A B, et al. DEM simulation of granular flows on a heap[J]. AIP Conference Proceedings, 2009, 1145: 621-624.
[14]	Zhou G, Ng C. Numerical investigation of reverse segregation in debris flows by DEM[J]. Granular Matter, 2010, 12(5): 507-516.
[15]	Fan J, Luu L H, Philippe P, et al. Discharge rate characterization for submerged grains flowing through a hopper using DEM-LBM simulations[J]. Powder Technology, 2022, 404: No.117421.
[16]	Fan J, Luu L H, Noury G, et al. DEM-LBM numerical modeling of submerged cohesive granular discharges[J]. Granular Matter, 2020, 22(3): No.66.
[17]	原方,杜乾,徐志军,等. 基于卸料流态模拟与观测的储粮仓壁动态压力增大机理研究[J]. 农业工程学报, 2019, 35(5): 286-293.
	Yuan Fang, Du Qian, Xu Zhi-jun, et al. Mechanism of dynamic pressure increase of grain silo wall based on simulation of discharge flow states[J]. Transactions of the Chinese Society of Agricultural Engineering, 2019, 35(5): 286-293.
[18]	徐贵玲, 李梦慧, 卢平, 等. 烘培生物质与煤不同配比混合物的流动及下料特性[J]. 农业工程学报, 2018, 34(1): 186-192.
	Xu Gui-ling, Li Meng-hui, Lu Ping, et al. Flowability and discharge characteristics of mixtures with different ratio of torrefied biomass and pulverized coal[J]. Transactions of the Chinese Society of Agricultural Engineering, 2018, 34(1): 186-192.
[19]	刘克瑾, 姚辉江, 袁铮. 平底筒仓中心卸料流态演化过程及仓壁压力波动性[J]. 农业工程学报,2023,39(15):15-24.
	Liu Ke-jin, Yao Hui-jiang, Yuan Zheng. Evolution process of center discharge flow pattern and pressure fluctuation of silo wall in a flat-bottomed silo[J]. Transactions of the Chinese Society of Agricultural Engineering, 2023, 39(15): 15-24.
[20]	Gao Q, Chen Y, Zhao C. Self-similarity of density and velocity profiles in a 2D hopper flow of elliptical particles: discrete element simulation[J]. Powder Technology, 2022, 402: No.117338.
[21]	Wang Y, Jia F, Zhang J, et al. Model construction method of discharge rate of eccentric silo[J]. Powder Technology, 2022, 405: No.117555.
[22]	Li T, Zhang H, Liu M, et al. DEM study of granular discharge rate through a vertical pipe with a bend outlet in small absorber sphere system[J]. Nuclear Engineering and Design, 2017, 314: 1-10.
[23]	Hilton J E, Cleary P W. Granular flow during hopper discharge[J]. Phys Rev E Stat Nonlin Soft Matter Phys, 2011, 84(1): No.011307.
[24]	Tang Y, Chan D H, Zhu D Z. The modeling of free-fall arch formation in granular flow through an aperture[J]. Frontiers in Physics, 2022, 10: No.963495.
[25]	Zhang Z, Liu Y, Zheng B, et al. Discharge characteristics of binary particles in a rectangular hopper with inclined bottom[J]. Computational Particle Mechanics, 2021, 8(2): 315-324.
[26]	Cundall P, Strack O. A discrete numerical model for granular assemblies[J]. Géotechnique, 1979, 29(1): 47-65.
[27]	Di Renzo A, Paolo Di Maio F. An improved integral non-linear model for the contact of particles in distinct element simulations[J]. Chemical Engineering Science, 2005, 60(5): 1303-1312.
[28]	Daniels K E, Behringe R P. Hysteresis and competition between disorder and crystallization in sheared and vibrated granular flow[J]. Physical Review Letters, 2005, 94(16): No.168001.
[29]	Jing L, Yang G C, Kwok C Y, et al. Dynamics and scaling laws of underwater granular collapse with varying aspect ratios[J]. Physical Review E, 2018, 98(4): No.042901.
[30]	Yang G C, Jing L, Kwok C Y, et al. Pore-scale simulation of immersed granular collapse: implications to submarine landslides[J]. Journal of Geophysical Research: Earth Surface, 2020, 125(1): e2019JF005044.
[31]	Yang G C, Jing L, Kwok C Y, et al. Size effects in underwater granular collapses: Experiments and coupled lattice Boltzmann and discrete element method simulations[J]. Physical Review Fluids, 2021, 6(11): No.114302.
[32]	Zhou Y, Ruyer P, Aussillous P. Discharge flow of a bidisperse granular media from a silo: discrete particle simulations[J]. Physical Review E, 2015, 92(6): No.062204.
[33]	Janda A, Zuriguel I, Maza D. Flow rate of particles through apertures obtained from self-similar density and velocity profiles [J]. Physical Review Letters, 2012, 108(24): No.248001.
[34]	Blanco-Rodríguez R, Hidalgo R C, Pérez-Ángel G, et al. Critical numerical analysis of quasi-two-dimensional silo-hopper discharging[J]. Granular Matter, 2021, 23(4): 86-96.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed