竖直振动管中颗粒毛细效应的离散元模拟
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摘要
将一根细管插入填充有颗粒的静止容器中并对管施加竖直振动,颗粒将在管内发生上升运动,并最终稳定在一定高度,这一现象与液体毛细效应类似,被称为颗粒毛细效应.为探究颗粒毛细效应过程中伴随的颗粒尺度动力学行为及机理,基于离散元方法建立颗粒运动模型,对颗粒毛细效应动力学过程和特性开展数值模拟研究.模拟再现了文献中实验得到的颗粒毛细效应全过程,给出了管内颗粒柱高度随时间的演变规律,结果表明,受到颗粒系统参数的影响,本模拟条件下颗粒毛细效应过程呈现单周期上升、倍周期上升和倍周期稳定三个阶段,在倍周期上升阶段颗粒柱上升速度逐渐减小,平缓过渡到稳定阶段.在此基础上,分析了管内颗粒速度场和填充率分布随时间的演变特性,揭示了颗粒毛细效应过程中由容器传输到管内的颗粒的占比分布.研究发现,管内不同高度位置颗粒的运动并不同步,随着管的振动,管内出现速度波,速度波的传播引起管内颗粒出现膨胀和压缩交替的情况,从而管内颗粒填充率随时间发生周期性波动;在上升阶段,越接近管壁由容器传输到管内的颗粒占比越大,在稳定阶段,管内上层颗粒的对流引起容器传输到管内的颗粒占比发生反转.
When a narrow tube inserted into a static container filled with particles is subjected to vertical vibration, the particles rise in the tube and finally stabilize at a certain height. As this phenomenon much resembles the capillary effect of liquid, it is termed as granular capillarity. To explore the particle-scale dynamical behaviors and their mechanisms associated with the process of granular capillarity, the motion of particles was modeled based on the discrete element method(DEM). Using this model, the dynamical processes and behaviors of particles in the granular capillarity were numerically investigated. The entire process of the granular capillarity obtained by experiments in literature was numerically reproduced and the evolution of the height of the granular column in the tube with time was shown. The results show that depending on the parameters of the granular system, the granular capillarity process under the simulation condition exhibits three phases characterized as periodic rising, period-doubling rising, and period-doubling steady-state in turn. During the period-doubling rising phase the velocity of capillary rise decreases gradually and a smooth transition to period-doubling steady-state phase is observed. On this basis, the evolutions of particle velocity filed as well as the particle packing fraction in the tube were analyzed. Furthermore, the distributions of the percentage of particles transported from the container into the tube in the granular capillarity process were revealed. It is found that the particle velocities at different heights are unsynchronized, as a result, velocity wave appears in the tube with the vibrational motion of the tube.The propagation of the velocity wave causes alternative expansion and compression of particles in the tube, giving rise to the periodical change of particle packing density. Moreover, higher percentage of particles transported from the container into the tube is observed in the region closer to the tube wall in the rising phase, while granular convection that occurs in the upper layers of the granular column leads to a reversing distribution of percentage of particles transported from the container into the tube in the steady-state phase.
When a narrow tube inserted into a static container filled with particles is subjected to vertical vibration, the particles rise in the tube and finally stabilize at a certain height. As this phenomenon much resembles the capillary effect of liquid, it is termed as granular capillarity. To explore the particle-scale dynamical behaviors and their mechanisms associated with the process of granular capillarity, the motion of particles was modeled based on the discrete element method(DEM). Using this model, the dynamical processes and behaviors of particles in the granular capillarity were numerically investigated. The entire process of the granular capillarity obtained by experiments in literature was numerically reproduced and the evolution of the height of the granular column in the tube with time was shown. The results show that depending on the parameters of the granular system, the granular capillarity process under the simulation condition exhibits three phases characterized as periodic rising, period-doubling rising, and period-doubling steady-state in turn. During the period-doubling rising phase the velocity of capillary rise decreases gradually and a smooth transition to period-doubling steady-state phase is observed. On this basis, the evolutions of particle velocity filed as well as the particle packing fraction in the tube were analyzed. Furthermore, the distributions of the percentage of particles transported from the container into the tube in the granular capillarity process were revealed. It is found that the particle velocities at different heights are unsynchronized, as a result, velocity wave appears in the tube with the vibrational motion of the tube.The propagation of the velocity wave causes alternative expansion and compression of particles in the tube, giving rise to the periodical change of particle packing density. Moreover, higher percentage of particles transported from the container into the tube is observed in the region closer to the tube wall in the rising phase, while granular convection that occurs in the upper layers of the granular column leads to a reversing distribution of percentage of particles transported from the container into the tube in the steady-state phase.
引文
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2 Yamada TM,Katsuragi H.Scaling of convective velocity in a vertically vibrated granular bed.Planetary and Space Science,2014,100:79-86
3 Liao CC,Hsiau SS.Transport properties and segregation phenomena in vibrating granular beds.KONA Powder and Particle Journal,2016,2016(33):109-126
4 Darias JR,S′anchez I,Guti′errez G,et al.Study of the accumulation of grains in a two dimensional vibrated U-tube without interstitial fluid.Advanced Powder Technology,2013,24(6):1095-1099
5 S′anchez I,D′?az AA,Guerrero B,et al.Improved model for the U-tube granular instability:Analytical solution and delayed coupling.Mechanics Research Communications,2015,67:1-7
6 Clement CP,Pacheco-Martinez HA,Swift MR,et al.Partition instability in water-immersed granular systems.Physical Review E,2009,80(1):011311
7 Liu CP,Wu P,Wang L.Particle climbing along a vibrating tube:Avibrating tube that acts as a pump for lifting granular materials from a silo.Soft Matter,2013,9(19):4762-4766
8 Liu CP,Zhang FW,Wu P,et al.Effect of hoisting tube shape on particle climbing.Powder Technology,2014,259:137-143
9张富翁,王立,刘传平等.竖直振动管中颗粒的上升运动.物理学报,2014,63(1):014501(Zhang Fuweng,Wang Li,Liu Chuanping,et al.The rising motion of grains in a vibrating pipe.Acta Physica Sinica,2014,63(1):014501(in Chinese))
10 Fan F,Liu J,Parteli EJR,et al.Origin of granular capillarity revealed by particle-based simulations.Physical Review Letters,2017,118(21):218001
11 Fan F,Parteli EJR,P¨oschel T.Vertical motion of particles in vibration-induced granular capillarity.EPJ Web of Conferences,2017,140:16008
12刘举,白鹏博,凡凤仙等.竖直振动下颗粒物质的行为模式研究进展.化工进展,2016,35(7):1956-1962(Liu Ju,Bai Pengbo,Fan Fengxian,et al.Research progress on behavior mode of granular matter under vertical vibration.Chemical Industry&Engineering Progress,2016,35(7):1956-1962(in Chinese))
13 Shukla P,Ansari IH,Van Der Meer D,et al.Nonlinear instability and convection in a vertically vibrated granular bed.Journal of Fluid Mechanics,2014,761:123-167
14 Zhang F,Wang L,Liu C,et al.Patterns of convective flow in a vertically vibrated granular bed.Physics Letters A,2014,378(18-19):1303-1308
15 Zhang K,Chen T,He L.Damping behaviors of granular particles in a vertically vibrated closed container.Powder Technology,2017,321:173-179
16 Liu Y,Zhao JH.Experimental study and analysis on the rising motion of grains in a vertically-vibrated pipe.Chinese Physics B,2015,24(3):034502
17 Xu Y,Musser J,Li T,et al.Particles climbing along a vertically vibrating tube:Numerical simulation using the discrete element method(DEM).Powder Technology,2017,320:304-312
18 Zhang F,Cronin K,Lin Y,et al.Effects of vibration parameters and pipe insertion depth on the motion of particles induced by vertical vibration.Powder Technology,2018,333:421-428
19谭援强,肖湘武,张江涛等.尼龙粉末在SLS预热温度下的离散元模型参数确定及其流动特性分析.力学学报,2019,51(1):56-63(Tan Yuanqiang,Xiao Xiangwu,Zhang Jiangtao,et al.Determination of discrete element model contact parameters of nylon powder at SLS preheating temperature and its flow characteristics.Chinese Journal of Theoretical and Applied Mechanics,2019,51(1):56-63(in Chinese))
20钱劲松,陈康为,张磊.粒料固有各向异性的离散元模拟与细观分析.力学学报,2018,50(5):1041-1050(Qian Jinsong,Chen Kangwei,Zhang Lei.Simulation and micro-mechanics analysis of inherent anisotropy of granular by distinct element method.Chinese Journal of Theoretical and Applied Mechanics,2018,50(5):1041-1050(in Chinese))
21熊迅,李天密,马棋棋等.石英玻璃圆环高速膨胀碎裂过程的离散元模拟.力学学报,2018,50(3):622-632(Xiong Xun,Li Tianmi,Ma Qiqi,et al.Discrete element simulations of the high velocity expansion and fragmentation of quartz glass rings.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):622-632(in Chinese))
22 Brilliantov NV,Spahn F,Hertzsch JM,et al.Model for collisions in granular gases.Physical Review E,1996,53(1):5382-5392
23 M¨uller P,P¨oschel T.Collision of viscoelastic spheres:Compact expressions for the coefficient of normal restitution.Physical Review E,2011,84(2):021302
24 Cundall PA,Strack OD.A discrete numerical model for granular assemblies.G′eotechnique,1979,29(1):47-65
25 Rycroft CH,Orpe AV,Arshad K.Physical test of a particle simulation model in a sheared granular system.Physical Review E,2009,80(3):031305
26 Parteli EJR,Schmidt J,Bl¨umel C,et al.Attractive particle interaction forces and packing density of fine glass powders.Scientific Reports,2014,4:6227
27 Ai J,Chen JF,Rotter JM,et al.Assessment of rolling resistance models in discrete element simulations.Powder Technology,2011,206(3):269-282
28 Sch¨afer J,Dippel S,Wolf DE.Force schemes in simulations of granular materials.Journal de Physique I France,1996,6(1):5-20
29赵永志,程易,郑津洋.三方程线性弹性-阻尼DEM模型及碰撞参数确定.计算力学学报,2009,26(2):239-244(Zhao Yongzhi,Cheng Yi,Zheng Jinyang.Three-equation linear spring-dashpot DEM model and the determination of contact parameters.Chinese Journal of Computational Mechanics,2009,26(2):239-244(in Chinese))
30 Ng TT,Zhou W,Ma G,et al.Damping and particle mass in DEMsimulations under gravity.Journal of Engineering Mechanics,2015,141(6):04014167
31 Kloss C,Goniva C,Hager A,et al.Models,algorithms and validation for opensource DEM and CFD-DEM.Progress in Computational Fluid Dynamics,2012,12(2-3):140-152
2 Yamada TM,Katsuragi H.Scaling of convective velocity in a vertically vibrated granular bed.Planetary and Space Science,2014,100:79-86
3 Liao CC,Hsiau SS.Transport properties and segregation phenomena in vibrating granular beds.KONA Powder and Particle Journal,2016,2016(33):109-126
4 Darias JR,S′anchez I,Guti′errez G,et al.Study of the accumulation of grains in a two dimensional vibrated U-tube without interstitial fluid.Advanced Powder Technology,2013,24(6):1095-1099
5 S′anchez I,D′?az AA,Guerrero B,et al.Improved model for the U-tube granular instability:Analytical solution and delayed coupling.Mechanics Research Communications,2015,67:1-7
6 Clement CP,Pacheco-Martinez HA,Swift MR,et al.Partition instability in water-immersed granular systems.Physical Review E,2009,80(1):011311
7 Liu CP,Wu P,Wang L.Particle climbing along a vibrating tube:Avibrating tube that acts as a pump for lifting granular materials from a silo.Soft Matter,2013,9(19):4762-4766
8 Liu CP,Zhang FW,Wu P,et al.Effect of hoisting tube shape on particle climbing.Powder Technology,2014,259:137-143
9张富翁,王立,刘传平等.竖直振动管中颗粒的上升运动.物理学报,2014,63(1):014501(Zhang Fuweng,Wang Li,Liu Chuanping,et al.The rising motion of grains in a vibrating pipe.Acta Physica Sinica,2014,63(1):014501(in Chinese))
10 Fan F,Liu J,Parteli EJR,et al.Origin of granular capillarity revealed by particle-based simulations.Physical Review Letters,2017,118(21):218001
11 Fan F,Parteli EJR,P¨oschel T.Vertical motion of particles in vibration-induced granular capillarity.EPJ Web of Conferences,2017,140:16008
12刘举,白鹏博,凡凤仙等.竖直振动下颗粒物质的行为模式研究进展.化工进展,2016,35(7):1956-1962(Liu Ju,Bai Pengbo,Fan Fengxian,et al.Research progress on behavior mode of granular matter under vertical vibration.Chemical Industry&Engineering Progress,2016,35(7):1956-1962(in Chinese))
13 Shukla P,Ansari IH,Van Der Meer D,et al.Nonlinear instability and convection in a vertically vibrated granular bed.Journal of Fluid Mechanics,2014,761:123-167
14 Zhang F,Wang L,Liu C,et al.Patterns of convective flow in a vertically vibrated granular bed.Physics Letters A,2014,378(18-19):1303-1308
15 Zhang K,Chen T,He L.Damping behaviors of granular particles in a vertically vibrated closed container.Powder Technology,2017,321:173-179
16 Liu Y,Zhao JH.Experimental study and analysis on the rising motion of grains in a vertically-vibrated pipe.Chinese Physics B,2015,24(3):034502
17 Xu Y,Musser J,Li T,et al.Particles climbing along a vertically vibrating tube:Numerical simulation using the discrete element method(DEM).Powder Technology,2017,320:304-312
18 Zhang F,Cronin K,Lin Y,et al.Effects of vibration parameters and pipe insertion depth on the motion of particles induced by vertical vibration.Powder Technology,2018,333:421-428
19谭援强,肖湘武,张江涛等.尼龙粉末在SLS预热温度下的离散元模型参数确定及其流动特性分析.力学学报,2019,51(1):56-63(Tan Yuanqiang,Xiao Xiangwu,Zhang Jiangtao,et al.Determination of discrete element model contact parameters of nylon powder at SLS preheating temperature and its flow characteristics.Chinese Journal of Theoretical and Applied Mechanics,2019,51(1):56-63(in Chinese))
20钱劲松,陈康为,张磊.粒料固有各向异性的离散元模拟与细观分析.力学学报,2018,50(5):1041-1050(Qian Jinsong,Chen Kangwei,Zhang Lei.Simulation and micro-mechanics analysis of inherent anisotropy of granular by distinct element method.Chinese Journal of Theoretical and Applied Mechanics,2018,50(5):1041-1050(in Chinese))
21熊迅,李天密,马棋棋等.石英玻璃圆环高速膨胀碎裂过程的离散元模拟.力学学报,2018,50(3):622-632(Xiong Xun,Li Tianmi,Ma Qiqi,et al.Discrete element simulations of the high velocity expansion and fragmentation of quartz glass rings.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):622-632(in Chinese))
22 Brilliantov NV,Spahn F,Hertzsch JM,et al.Model for collisions in granular gases.Physical Review E,1996,53(1):5382-5392
23 M¨uller P,P¨oschel T.Collision of viscoelastic spheres:Compact expressions for the coefficient of normal restitution.Physical Review E,2011,84(2):021302
24 Cundall PA,Strack OD.A discrete numerical model for granular assemblies.G′eotechnique,1979,29(1):47-65
25 Rycroft CH,Orpe AV,Arshad K.Physical test of a particle simulation model in a sheared granular system.Physical Review E,2009,80(3):031305
26 Parteli EJR,Schmidt J,Bl¨umel C,et al.Attractive particle interaction forces and packing density of fine glass powders.Scientific Reports,2014,4:6227
27 Ai J,Chen JF,Rotter JM,et al.Assessment of rolling resistance models in discrete element simulations.Powder Technology,2011,206(3):269-282
28 Sch¨afer J,Dippel S,Wolf DE.Force schemes in simulations of granular materials.Journal de Physique I France,1996,6(1):5-20
29赵永志,程易,郑津洋.三方程线性弹性-阻尼DEM模型及碰撞参数确定.计算力学学报,2009,26(2):239-244(Zhao Yongzhi,Cheng Yi,Zheng Jinyang.Three-equation linear spring-dashpot DEM model and the determination of contact parameters.Chinese Journal of Computational Mechanics,2009,26(2):239-244(in Chinese))
30 Ng TT,Zhou W,Ma G,et al.Damping and particle mass in DEMsimulations under gravity.Journal of Engineering Mechanics,2015,141(6):04014167
31 Kloss C,Goniva C,Hager A,et al.Models,algorithms and validation for opensource DEM and CFD-DEM.Progress in Computational Fluid Dynamics,2012,12(2-3):140-152