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

Abstract

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

CLC Number:

S126

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.

Figures/Tables 15

Fig.1

Table 1

Parameters in the simulations"

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

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Table 2

Fitting parameters of particle velocity distribution and volume fraction distribution of eccentric variable e"

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

Table 2

Fig.6

Fig.7

Fig.8

Table 3

Fitting parameters of particle velocity distribution and volume fraction distribution of eccentric variable s"

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

Table 3

Fig.9

Fig.10

Fig.11

Fig.12

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Self⁃similar characteristics of particle velocity and volume fraction distribution in eccentric hopper

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