Dynamics of the transition of mass flow to funnel flow in a silo

doi:10.11949/0438-1157.20220120

Abstract

Abstract:

The flow of fuel element spheres in the pebble-bed high temperature reactor (HTR) is a typical granular flow. A mixed flow including mass flow and funnel flow can be found during HTR operation. Particle scale dynamics and mesoscale dynamics control the flow states and their transitions. In this work, we focus on analyzing the effects of particle translation, rotation and other dynamic quantities in physical model of the silo flow. We firstly carried out the experimental measurement of the rheological process of the silo particle, and used the discrete element method based on the Hertz-Mindlin and RVD (relative velocity dependent) rolling friction contact model. The kinetic quantities of spherical particles in the rheological process of particles in a conical silo were studied. Further, based on the analysis of DEM calculation results, it is found that the silo presents a mixed flow state of transition from mass flow to funnel flow from top to bottom. In the different flow pattern regions of the silo mixed flow, the correlation between the translational speed and the rotational speed is opposite; the regions with larger relative tangential motion between particles are concentrated in the funnel flow region and the side wall region. Understanding the dynamics of particles during silo rheology can help optimize silo particle flow and reduce particle surface wear.

Key words: granular flow, discrete element modeling, silo, granular kinetics

摘要：

球床模块式高温气冷堆的堆芯是全陶瓷型包覆铀燃料制成的球形颗粒，与石墨颗粒混合堆积而成，堆芯颗粒流的流态取决于颗粒尺度的平移、旋转等动力学量，以及力链、涡旋等介尺度物理量。为了分析颗粒的平移、旋转等动力学量对颗粒流流态的影响。基于筒仓颗粒流的物理模型，首先开展了筒仓颗粒流流变过程的实验测量，并使用基于 Hertz-Mindlin和 RVD （relative velocity dependent）滚动摩擦接触模型的离散单元法（distinct element method， DEM），研究了锥形筒仓颗粒流流变过程中球形颗粒的动力学量。进一步，基于DEM计算结果进行分析，发现筒仓自上而下呈现出质量流向漏斗流过渡的混合流状态。在筒仓混合流的不同流型区域中，平移速度和旋转速度之间的相关性是相反的；颗粒间的相对切向运动较大的区域集中在漏斗流区域与边壁区域。了解筒仓流变过程中颗粒的动力学特征，有助于优化筒仓颗粒流动，并减少颗粒表面的磨损。

关键词: 颗粒流, 离散元模拟, 筒仓, 颗粒动力学

CLC Number:

TQ 028.8

Hui YANG, Hongze LI, Quan CHEN, Zexi ZHENG, Ran LI, Qicheng SUN. Dynamics of the transition of mass flow to funnel flow in a silo[J]. CIESC Journal, 2022, 73(6): 2722-2731.

杨晖, 李宏泽, 陈泉, 郑泽希, 李然, 孙其诚. 从质量流向漏斗流转变过程中的动力学分析[J]. 化工学报, 2022, 73(6): 2722-2731.

Figures/Tables 9

Fig.1 Multiple scales in the flow of fuel element spheres in the pebble-bed high temperature reactor (HTR)

Fig.2 The geometry of the silo with an initial packed bed and movement of single particles

Table 1 Physical parameters and their values of the simulations

位置	参数	符号/单位	数值
颗粒	密度	ρ_p/(kg/m³)	1400
	杨氏模量	E_p/Pa	2.84×10⁹
	泊松比	ν	0.35
边壁	密度	ρ_w/(kg/m³)	1180
	杨氏模量	E_p/Pa	4.76×10⁹
	泊松比	ν	0.40
颗粒-颗粒	静摩擦因数	μ_p-p	0.6
	滚动摩擦因数	μ_rp-p	4.20×10^-5
	恢复系数	e_p	0.87
颗粒-边壁	静摩擦因数	μ_p-w	0.6
	滚动摩擦因数	μ_rp-w	2.71×10^-6
	恢复系数	e_w	0.88

Fig.3 The silo flow pattern diagrams during the discharge process

Fig.4 MFI and the flow pattern transformation height during the discharge process

Fig.5 Spatial distribution of average translation velocity in 2—6 s

Fig.6 Spatial distribution of average rotation velocity in 2—6 s

Fig.7 Spatial correlation of relative tangential velocities caused by translational motion and rotational motion among particles in different flow pattern regions within 2—6 s

Fig.8 Spatial distribution of average particle rolling contribution rate in 2—6 s

References 32

1	Villagrán O M C, Benito J G, Uñac R O, et al. Towards a one parameter equation for a silo discharging model with inclined outlets[J]. Powder Technology, 2018, 336: 265-272.
2	Mathews J C, Wu W. Model tests of silo discharge in a geotechnical centrifuge[J]. Powder Technology, 2016, 293: 3-14.
3	卫思辰, 贾海兵, 范怡平, 等. 引入大颗粒助剂对径向移动床流动特性的影响[J]. 化工学报, 2016, 67(8): 3313-3320.
	Wei S C, Jia H B, Fan Y P, et al. Effect of introducing large additive particles on flow characteristics in radial flow moving bed[J]. CIESC Journal, 2016, 67(8): 3313-3320.
4	Tu P, Vimonsatit V, Li J. Silo quake response spectrum of iron ore train load out bin[J]. Advanced Powder Technology, 2018, 29(11): 2775-2784.
5	Chen Q, Li R, Xiu W Z, et al. Measurement of granular temperature and velocity profile of granular flow in silos[J]. Powder Technology, 2021, 392: 123-129.
6	Sielamowicz I, Błoñski S, Kowalewski T A. Digital particle image velocimetry (DPIV) technique in measurements of granular material flows, part 2 of 3-converging hoppers[J]. Chemical Engineering Science, 2006, 61(16): 5307-5317.
7	Wang Q, Chen Q, Li R, et al. Shape of free-fall arch in quasi-2D silo[J]. Particuology, 2021, 55: 62-69.
8	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): 248001.
9	Wang R, Li R, Wang S S, et al. End wall effect on particle motion in a chute flow[J]. Particuology, 2021, 54: 102-108.
10	Yang H, Zhu Y H, Li R, et al. Kinetic granular temperature and its measurement using speckle visibility spectroscopy[J]. Particuology, 2020, 48: 160-169.
11	Song J, Yang H, Li R, et al. Improved PTV measurement based on Voronoi matching used in hopper flow[J]. Powder Technology, 2019, 355: 172-182.
12	Gentzler M, Tardos G I. Measurement of velocity and density profiles in discharging conical hoppers by NMR imaging[J]. Chemical Engineering Science, 2009, 64(22): 4463-4469.
13	Guillard F, Marks B, Einav I. Dynamic X-ray radiography reveals particle size and shape orientation fields during granular flow[J]. Scientific Reports, 2017, 7(1):8155.
14	Zhu Y H, Yang H, Li R, et al. Wireless detector for translational and rotational motion of spherical-particle flow[J]. Powder Technology, 2020, 360: 882-889.
15	赵颖, 朱兴望, 曲世祥, 等. 球形燃料元件累积旋转角度和角速度问题研究[J]. 核技术, 2016, 39(3): 76-82.
	Zhao Y, Zhu X W, Qu S X, et al. Rotation angles and angular velocities study of pebble-shaped fuel element based on a detection system[J]. Nuclear Techniques, 2016, 39(3): 76-82.
16	Balevičius R, Kačianauskas R, Mróz Z, et al. Analysis and DEM simulation of granular material flow patterns in hopper models of different shapes[J]. Advanced Powder Technology, 2011, 22(2): 226-235.
17	刘义伦, 刘思琪, 赵先琼, 等. 偏心楔形喂料斗卸料过程中颗粒流动特性[J]. 化工学报, 2018, 69(4): 1469-1475.
	Liu Y L, Liu S Q, Zhao X Q, et al. Flow characteristics of granule discharged from eccentric wedge-shaped feed hopper[J]. CIESC Journal, 2018, 69(4): 1469-1475.
18	Weinhart T, Labra C, Luding S, et al. Influence of coarse-graining parameters on the analysis of DEM simulations of silo flow[J]. Powder Technology, 2016, 293: 138-148.
19	Feng Y, Yuan Z R. Discrete element method modeling of granular flow characteristics transition in mixed flow[J]. Computational Particle Mechanics, 2021, 8(1): 21-34.
20	Yu Y W, Saxén H. Discrete element method simulation of properties of a 3D conical hopper with mono-sized spheres[J]. Advanced Powder Technology, 2011, 22(3): 324-331.
21	Washino K, Chan E L, Miyazaki K, et al. Time step criteria in DEM simulation of wet particles in viscosity dominant systems[J]. Powder Technology, 2016, 302: 100-107.
22	刘凡一, 张舰, 李博, 等. 基于堆积试验的小麦离散元参数分析及标定[J]. 农业工程学报, 2016, 32(12): 247-253.
	Liu F Y, Zhang J, Li B, et al. Calibration of parameters of wheat required in discrete element method simulation based on repose angle of particle heap[J]. Transactions of the Chinese Society of Agricultural Engineering, 2016, 32(12): 247-253.
23	Höhner D, Wirtz S, Scherer V. Experimental and numerical investigation on the influence of particle shape and shape approximation on hopper discharge using the discrete element method[J]. Powder Technology, 2013, 235: 614-627.
24	Simsek E. Experimental investigation and numerical simulation by means of the discrete element method[D]. Germany: Bochum University, 2011.
25	Tripathi A, Kumar V, Agarwal A, et al. Quantitative DEM simulation of pellet and sinter particles using rolling friction estimated from image analysis[J]. Powder Technology, 2021, 380: 288-302.
26	Mindlin R D. Compliance of elastic bodies in contact[J]. Journal of Applied Mechanics, 1949, 16(3): 259-268.
27	Ai J, Chen J F, Rotter J M, et al. Assessment of rolling resistance models in discrete element simulations[J]. Powder Technology, 2011, 206(3): 269-282.
28	Jenike A W. Gravity Flow of Bulk Solids[M]. Utah: Utah State University Press, 1961: 322.
29	Esteves P J, de Macêdo M C S, Souza R M, et al. Effect of ball rotation speed on wear coefficient and particle behavior in micro-abrasive wear tests[J]. Wear, 2019, 426/427: 137-141.
30	Zhang S, Yang G H, Lin P, et al. Inclined granular flow in a narrow chute[J]. The European Physical Journal. E, Soft Matter, 2019, 42(4): 40.
31	Han Y L, Jia F G, Li G R, et al. Numerical analysis of flow pattern transition in a conical silo with ellipsoid particles[J]. Advanced Powder Technology, 2019, 30(9): 1870-1881.
32	Zhang Y X, Jia F G, Zeng Y, et al. DEM study in the critical height of flow mechanism transition in a conical silo[J]. Powder Technology, 2018, 331: 98-106.

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