基于连续数值模拟的筒仓卸载过程中颗粒物压强及其速度场分析
|
摘要
应用基于局部本构理论的连续数值模拟方法,研究出口在底部和侧面的颗粒物在类三维矩形容器内的卸载现象.重点是容器厚度W和出口高度D对颗粒物压强与速度的影响.受力分析和数值模拟结果均表明,距离出口较近区域的颗粒物压强与W及D呈现如下相关性:当D/W足够小时,压强只与D相关;当D/W足够大时,压强只与W相关.且出口在底部和侧面时均有上述结果.模拟结果还显示,当出口在底部时,对于模拟中所有D/W值,出口中心处法向速度只和D相关;当出口在侧面时,颗粒物出口中心处法向速度则与压强变化规律一致.由此可见,出口处的压强并不控制颗粒物的出口法向速度.另外,与出口在侧面相比,出口在底部时,造成流量相关性规律改变的D/W临界值较大,一般实际情况无法满足,因此出口中心处法向速度只与D相关,始终满足Beverloo定律.
Granular medium is ubiquitous in nature, and is an important issue in many infrastructural construction projects. In particular, the gravity discharge of fine particles from a silo constitutes an important problem of research, because of its many industrial applications. However, the physical mechanism of this system remains unclear. In this work, we study the discharge of silo from the bottom or lateral orifice, by performing pseudothree-dimensional(3D) continuum simulations based on the local constitutive theory. The simulation is twodimensional(2D), in order to study the 3D silo, we add the lateral frictional force in the averaged momentum equation. For a rectangular silo with an orifice of height D and the silo thickness W, we study the influence of the orifice size(W and D) on the granular pressure and velocity. The force analysis and simulation results reveal that for the relation between the granular pressure and the orifice size, there exist two regimes: when D/W is small enough, the pressure near the orifice varies only with D; when D/W is large enough,the pressure varies only with W. These scaling laws are the same for both bottom and lateral orifice. Somewhat surprisingly, the simulation results also show that when the orifice is at the bottom, the scaling law of the vertical velocity is different from that of the pressure; when it is on the lateral side, the scaling law of the horizontal velocity is consistent with that of the pressure. This observation contradicts a hypothesis that the flow rate of discharge is controlled by the granular pressure near the orifice, and validates the recent experimental results reported in the literature. Furthermore, the relationship between the vertical velocity and the orifice size reveals that when the orifice is at the bottom, the critical value of D/W for the transition of regime is much larger than the lateral orifice case, the flow rate will depend only on W when D/W>>50.This condition is hardly satisfied in practice, so the new scaling law has not yet been observed for the bottom orifice case in the literature. Furthermore, this work demonstrates that the stagnant zone has an important effect on the discharge of silo, especially for the lateral orifice case. Since a non-local constitutive law can well describe the quasi-static flow, it will be interesting to modify the local constitutive model into a non-local constitutive model, and to compare the results from the two models.
Granular medium is ubiquitous in nature, and is an important issue in many infrastructural construction projects. In particular, the gravity discharge of fine particles from a silo constitutes an important problem of research, because of its many industrial applications. However, the physical mechanism of this system remains unclear. In this work, we study the discharge of silo from the bottom or lateral orifice, by performing pseudothree-dimensional(3D) continuum simulations based on the local constitutive theory. The simulation is twodimensional(2D), in order to study the 3D silo, we add the lateral frictional force in the averaged momentum equation. For a rectangular silo with an orifice of height D and the silo thickness W, we study the influence of the orifice size(W and D) on the granular pressure and velocity. The force analysis and simulation results reveal that for the relation between the granular pressure and the orifice size, there exist two regimes: when D/W is small enough, the pressure near the orifice varies only with D; when D/W is large enough,the pressure varies only with W. These scaling laws are the same for both bottom and lateral orifice. Somewhat surprisingly, the simulation results also show that when the orifice is at the bottom, the scaling law of the vertical velocity is different from that of the pressure; when it is on the lateral side, the scaling law of the horizontal velocity is consistent with that of the pressure. This observation contradicts a hypothesis that the flow rate of discharge is controlled by the granular pressure near the orifice, and validates the recent experimental results reported in the literature. Furthermore, the relationship between the vertical velocity and the orifice size reveals that when the orifice is at the bottom, the critical value of D/W for the transition of regime is much larger than the lateral orifice case, the flow rate will depend only on W when D/W>>50.This condition is hardly satisfied in practice, so the new scaling law has not yet been observed for the bottom orifice case in the literature. Furthermore, this work demonstrates that the stagnant zone has an important effect on the discharge of silo, especially for the lateral orifice case. Since a non-local constitutive law can well describe the quasi-static flow, it will be interesting to modify the local constitutive model into a non-local constitutive model, and to compare the results from the two models.
引文
[1]Andreotti B, Forterre Y, Pouliquen O 2013 Granular Media:Between Fluid and Solid(Cambridge:Cambridge University Press)p1
[2]Lu K Q, Liu J X 2004 Physics 33 629(in Chinese)[陆坤权,刘寄星2004物理33 629]
[3]Radjai F, Dubois F 2011 Discrete-element Modeling of Granular Materials(London:Wiley-Iste)p425
[4]Midi G D R 2004 Eur. Phys. J. E 14 341
[5]Jop P, Forterre Y, Pouliquen O 2006 Nature 441 727
[6]Lagree P Y, Staron L, Popinet S 2011 J. Fluid Mech. 686 378
[7]Staron L, Lagree P Y, Popinet S 2012 Phys. Fluids 24 103301
[8]Staron L, Lagree P Y, Popinet S 2014 Eur. Phys. J. E 37 1
[9]Andreotti B, Forterre Y, Pouliquen O 2013 Granular Media:Between Fluid and Solid(Cambridge:Cambridge University Press)pp239-246
[10]Andreotti B, Forterre Y, Pouliquen O 2013 Granular Media:Between Fluid and Solid(Cambridge:Cambridge University Press)pp87-91
[11]Sperl M 2006 Granular Matter 8 59
[12]Perge C, Aguirre M A, Gago P A, Pugnaloni L A, Le Tourneau D, Géminard J C 2012 Phys. Rev. E 85 021303
[13]Aguirre M A, Grande J G, Calvo A, Pugnaloni L A,Géminard J C 2011 Phys. Rev. E 83 061305
[14]Beverloo W A, Leniger H A, De Velde J V 1961 J. Chem.Eng. Sci. 15 260
[15]Sheldon H G, Durian D J 2010 Granular Matter 12 579
[16]Thomas C C, Durian D J 2015 Phys. Rev. Lett. 114 178001
[17]Zhang Y, Wei Y F, Peng Z, Jiang Y M, Duan W S, Hou M Y2011 Acta Phys. Sin. 65 084502(in Chinese)[张昱,韦艳芳,彭政,蒋亦民,段文山,厚美瑛2011物理学报65 084502]
[18]Zhou Y, Lagree P Y, Popinet S, Aussillous P, Ruyer P 2017J. Fluid Mech. 829 459
[19]Lagree P Y 2007 Math. Mech. 87 486
[20]Jop P, Forterre Y, Pouliquen O 2005 J. Fluid Mech. 541 167
[21]Popinet S 2009 J. Comput. Phys. 228 5838
[22]Janda A, Zuriguel I, Maza D 2012 Phys. Rev. Lett. 108248001
[23]Benyamine M, Djermane M, Dalloz-Dubrujeaud B, Aussillous P 2014 Phys. Rev. E 90 032201
[24]Kamrin K, Koval G 2012 Phys. Rev. Lett. 108 178301
[2]Lu K Q, Liu J X 2004 Physics 33 629(in Chinese)[陆坤权,刘寄星2004物理33 629]
[3]Radjai F, Dubois F 2011 Discrete-element Modeling of Granular Materials(London:Wiley-Iste)p425
[4]Midi G D R 2004 Eur. Phys. J. E 14 341
[5]Jop P, Forterre Y, Pouliquen O 2006 Nature 441 727
[6]Lagree P Y, Staron L, Popinet S 2011 J. Fluid Mech. 686 378
[7]Staron L, Lagree P Y, Popinet S 2012 Phys. Fluids 24 103301
[8]Staron L, Lagree P Y, Popinet S 2014 Eur. Phys. J. E 37 1
[9]Andreotti B, Forterre Y, Pouliquen O 2013 Granular Media:Between Fluid and Solid(Cambridge:Cambridge University Press)pp239-246
[10]Andreotti B, Forterre Y, Pouliquen O 2013 Granular Media:Between Fluid and Solid(Cambridge:Cambridge University Press)pp87-91
[11]Sperl M 2006 Granular Matter 8 59
[12]Perge C, Aguirre M A, Gago P A, Pugnaloni L A, Le Tourneau D, Géminard J C 2012 Phys. Rev. E 85 021303
[13]Aguirre M A, Grande J G, Calvo A, Pugnaloni L A,Géminard J C 2011 Phys. Rev. E 83 061305
[14]Beverloo W A, Leniger H A, De Velde J V 1961 J. Chem.Eng. Sci. 15 260
[15]Sheldon H G, Durian D J 2010 Granular Matter 12 579
[16]Thomas C C, Durian D J 2015 Phys. Rev. Lett. 114 178001
[17]Zhang Y, Wei Y F, Peng Z, Jiang Y M, Duan W S, Hou M Y2011 Acta Phys. Sin. 65 084502(in Chinese)[张昱,韦艳芳,彭政,蒋亦民,段文山,厚美瑛2011物理学报65 084502]
[18]Zhou Y, Lagree P Y, Popinet S, Aussillous P, Ruyer P 2017J. Fluid Mech. 829 459
[19]Lagree P Y 2007 Math. Mech. 87 486
[20]Jop P, Forterre Y, Pouliquen O 2005 J. Fluid Mech. 541 167
[21]Popinet S 2009 J. Comput. Phys. 228 5838
[22]Janda A, Zuriguel I, Maza D 2012 Phys. Rev. Lett. 108248001
[23]Benyamine M, Djermane M, Dalloz-Dubrujeaud B, Aussillous P 2014 Phys. Rev. E 90 032201
[24]Kamrin K, Koval G 2012 Phys. Rev. Lett. 108 178301