不同形状混合器中二元颗粒的分聚与混合研究
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摘要
采用实验、模拟及理论的分析方法,研究了在圆形混合器、椭圆形混合器、正方形混合器中,不同转速和填充率条件下,容器形状对二元颗粒体系分聚与混合的影响.实验中通过改变转速与填充率,可获得不同的颗粒分聚与混合图样,对示踪颗粒运动轨迹的分析发现,在圆形混合器中,随着混合器转速的增大,颗粒在径向的随机性减少;在正方形混合器中,随着混合器转速的增大,颗粒在径向的随机性增大.模拟结果发现颗粒流动分为两个区域,在表面的快速流动和在整体的旋转运动.通过理论分析发现颗粒分聚在圆形混合器中最明显,在正方形混合器中最弱,椭圆形混合器介于二者之间.
The effects of filling conditions and angular speeds of circle, ellipse and square mixers on segregation and mixing are studied adopting theoretical, experimental and simulation approaches. Different segregation and mixing patterns of granular material can be obtained by changing the angular speed or filling conditions in experiments. From the analysis of trajectory of tracer particles, we find that particles' motion randomness in radial direction decreases with the angular speeds augment, and contrast results occur in rectangular mixer. The simulation results show that the flow consists of two distinct regions: a flowing layer with nearly unidirectional flow and a bed below it undergoing solidbody rotation. Through theoretical analysis, we find the segregation phenomenon is most apparent in circle mixer, then in the ellipse mixer, and the weakest is in rectangular mixer.
The effects of filling conditions and angular speeds of circle, ellipse and square mixers on segregation and mixing are studied adopting theoretical, experimental and simulation approaches. Different segregation and mixing patterns of granular material can be obtained by changing the angular speed or filling conditions in experiments. From the analysis of trajectory of tracer particles, we find that particles' motion randomness in radial direction decreases with the angular speeds augment, and contrast results occur in rectangular mixer. The simulation results show that the flow consists of two distinct regions: a flowing layer with nearly unidirectional flow and a bed below it undergoing solidbody rotation. Through theoretical analysis, we find the segregation phenomenon is most apparent in circle mixer, then in the ellipse mixer, and the weakest is in rectangular mixer.
引文
1Shi Q,Sun G,Hou M,et al.Density-driven segregation in vertically vibrated binary granular mixtures.Phys.Rev.E,2007,75:061302
2Shi QF,Sun G,Hou MY,et al.Segregation in vertically vibrated binary granular mixtures with same size.Chinese Physics Letters,2006,23(11):3080
3Shi Q,Yan X,Hou M,et al.Experimental study of segregation patterns in binary granular mixtures under vertical vibration.Chinese Science Bulletin,2003,48(7):627-629
4Liu R,Li YC,Hou MY,et al.Waals-like phase separation instability of a driven granular gas in three dimensions.Phys.Rev.E,2007,75:079705
5Liu R,Li YC,Hou MY.Phase separation in a three dimensional granular gas system.Acta Physica Sinica,2008,67(8):4660
6Liu R,Li YC,Hou MY.Oscillatory phenomena of compartmentalized bi-disperse granular gases.Phys.Rev.E,2009,79:052301
7孙其诚,厚美瑛,金峰.颗粒物质物理与力学.北京:科学出版社,2011(Sun Qicheng,Hou Meiying,Jin Feng.Particulate Matter of Physics and Mechanics.Beijing:Science Press,2011(in Chinese))
8梁宣文,李粮生,侯兆国等.垂直振动作用下二元混合颗粒分层的动态循环反转.物理学报,2008,57(4):2300-2305(Liang Xuanwen,Li Liangsheng,Hou Zhaoguo,et al.Cycle of segregation patterns in vertically vibrated binary granular mixtures.Acta Phys Sin,2008,57(4):2300-2305(in Chinese))
9姜泽辉,陆坤权,厚美瑛等.振动颗粒混合物中的三明治式分离.物理学报,2003,52(9):2244-2248(Jiang Zehui,Lu Kunquan,Hou Meiying,et al.Sandwich-like segregation in vertically vibrated binary granular mixtures.Acta Phys Sin,2003,52(9):2244-2248(in Chinese))
10赵永志,江茂强,郑津洋.巴西果效应分离过程的计算颗粒力学模拟研究.物理学报,2009,58:1812(Zhao Yongzhi,Jiang Maoqiang,Zheng Jinyang.Discrete element simulation of the segregation in Brazil nut problem.Acta Phys Sin,2009,58:1812(in Chinese))
11史庆藩,阎学群,厚美瑛等.振动混合颗粒形成的反巴西果分层及其相图的实验观测.科学通报,2003,48(4):328-330
12厚美瑛.空间环境颗粒物质运动行为的研究.物理,2008,37(10):729-732(Hou Meiying.Granular behavior inmicrogravity.Physics,2008,37(10):729-732(in Chinese))
13Nityanand N,Manley B,Henein H.An analysis of radial segregation for different sized spherical solids in rotary cylinders.Trans,1986,B17:247
14Kwapinska M,Saage G,Tsotsas E.Mixing of particles in rotary drums a comparison of discrete element simulations with experimental results and penetration models for thermal processes.Powder Technology,2006,161(1):69-78
15赵永志,张宪旗,刘延雷等.滚筒内非等粒径二元颗粒体系增混合机理研究.物理学报,2009,58(12):321-328(Zhao Yongzhi,Zhang Xianqi,Liu Yanlei,et al.Augmenting the mixing of size-type binary granular systems in a rotating horizontal drum.Acta physica sinica,2009,58(12):321-328(in Chinese))
16Pereira GG,Tran N,Cleary PW.Segregation of combined size and density varying binary granular mixtures in a slowly rotating tumbler.Granular Matter,2014,16:5
17Ingram A,Seville JPK,Parker DJ,et al.Axial and radial dispersion in rolling mode rotating drums.Powder Technology,2005,158:76-91
18Mc Carthy JJ,Khakhar DV,Ottino JM.Computational studies of granular mixing.Powder Technol,2000,109:72-82
19Ottino JM,Khakhar DV.Mixing and segregation of granular materials.Annu.Rev.Fluid Mech,2000,32:55-91
20Khakhar DV,Mc Carthy JJ,Shinbrot T,et al.Transverse flowand and mixing of granular materials in rotating cylinders.Phys.Fluids,1997,9:31-43
21Lun CKK,Savage SB,Jeffrey DJ,et al.Kinetic theories for granular flow:inelastic particles in Couette flow and slightly inelastic particles in a general flow field.J.Fluid Mech,1984,140:223-256
22Gonzalez S,Windows-Yule CRK,Luding S,et al.Shaping Segregation:Convexity vs.Concavity.http://arxiv preprint arxiv,2014:1410.6286
23Ottino JM.The Kinematics of Mixing:Stretching.Chaos,and Transport Cambridge University Press.Cambridge,1990
24Henein H,Brimacombe JK,Watkinson AP.Experimental studies of transverse bed motion in rotary kilns.Metall.Trans.,1983,14B:191-205
25Hill KM,Jain NT,Ottino JM.Modes of granular segregation in a noncircular rotating cylinder.Phys.Rev.E,2001,64:011302
26Meier SW,Cisar SE,Lueptow RM,et al.Capturing patterns and symmetries in chaotic granular flow.Phys.Rev.E,2006,74:031310
27王瑞芳,李占勇,窦如彪等.水平转筒内大豆颗粒随机运动与混合特性模拟.农业机械学报,2013,44(6):93-99(Wang Ruifang,Li Zhanyong,Dou Ruibiao,et al.Simulation on random motion and mixing characteristic for soybean in rotary drum.Transactions of the Chinese Society for Agricultural Machinery,2013,44(6):93-99(in Chinese))
28Prasad DVN,Khakhar DV.Granular flow in rotating cylinders with noncircular cross sections.Phys.Rev.E,2008,77:041301
29Khakhar DV,Mc Carthy JJ,Gilchrist JF,et al.Chaotic mixing of granular materials in two-dimensional tumbling mixers.Chaos,1999,9:1
30Ottino JM,Khakhar DV.Mixing and segregation of granular materials.Annu.Rev.Fluid Mech.,2000,32:55-91
2Shi QF,Sun G,Hou MY,et al.Segregation in vertically vibrated binary granular mixtures with same size.Chinese Physics Letters,2006,23(11):3080
3Shi Q,Yan X,Hou M,et al.Experimental study of segregation patterns in binary granular mixtures under vertical vibration.Chinese Science Bulletin,2003,48(7):627-629
4Liu R,Li YC,Hou MY,et al.Waals-like phase separation instability of a driven granular gas in three dimensions.Phys.Rev.E,2007,75:079705
5Liu R,Li YC,Hou MY.Phase separation in a three dimensional granular gas system.Acta Physica Sinica,2008,67(8):4660
6Liu R,Li YC,Hou MY.Oscillatory phenomena of compartmentalized bi-disperse granular gases.Phys.Rev.E,2009,79:052301
7孙其诚,厚美瑛,金峰.颗粒物质物理与力学.北京:科学出版社,2011(Sun Qicheng,Hou Meiying,Jin Feng.Particulate Matter of Physics and Mechanics.Beijing:Science Press,2011(in Chinese))
8梁宣文,李粮生,侯兆国等.垂直振动作用下二元混合颗粒分层的动态循环反转.物理学报,2008,57(4):2300-2305(Liang Xuanwen,Li Liangsheng,Hou Zhaoguo,et al.Cycle of segregation patterns in vertically vibrated binary granular mixtures.Acta Phys Sin,2008,57(4):2300-2305(in Chinese))
9姜泽辉,陆坤权,厚美瑛等.振动颗粒混合物中的三明治式分离.物理学报,2003,52(9):2244-2248(Jiang Zehui,Lu Kunquan,Hou Meiying,et al.Sandwich-like segregation in vertically vibrated binary granular mixtures.Acta Phys Sin,2003,52(9):2244-2248(in Chinese))
10赵永志,江茂强,郑津洋.巴西果效应分离过程的计算颗粒力学模拟研究.物理学报,2009,58:1812(Zhao Yongzhi,Jiang Maoqiang,Zheng Jinyang.Discrete element simulation of the segregation in Brazil nut problem.Acta Phys Sin,2009,58:1812(in Chinese))
11史庆藩,阎学群,厚美瑛等.振动混合颗粒形成的反巴西果分层及其相图的实验观测.科学通报,2003,48(4):328-330
12厚美瑛.空间环境颗粒物质运动行为的研究.物理,2008,37(10):729-732(Hou Meiying.Granular behavior inmicrogravity.Physics,2008,37(10):729-732(in Chinese))
13Nityanand N,Manley B,Henein H.An analysis of radial segregation for different sized spherical solids in rotary cylinders.Trans,1986,B17:247
14Kwapinska M,Saage G,Tsotsas E.Mixing of particles in rotary drums a comparison of discrete element simulations with experimental results and penetration models for thermal processes.Powder Technology,2006,161(1):69-78
15赵永志,张宪旗,刘延雷等.滚筒内非等粒径二元颗粒体系增混合机理研究.物理学报,2009,58(12):321-328(Zhao Yongzhi,Zhang Xianqi,Liu Yanlei,et al.Augmenting the mixing of size-type binary granular systems in a rotating horizontal drum.Acta physica sinica,2009,58(12):321-328(in Chinese))
16Pereira GG,Tran N,Cleary PW.Segregation of combined size and density varying binary granular mixtures in a slowly rotating tumbler.Granular Matter,2014,16:5
17Ingram A,Seville JPK,Parker DJ,et al.Axial and radial dispersion in rolling mode rotating drums.Powder Technology,2005,158:76-91
18Mc Carthy JJ,Khakhar DV,Ottino JM.Computational studies of granular mixing.Powder Technol,2000,109:72-82
19Ottino JM,Khakhar DV.Mixing and segregation of granular materials.Annu.Rev.Fluid Mech,2000,32:55-91
20Khakhar DV,Mc Carthy JJ,Shinbrot T,et al.Transverse flowand and mixing of granular materials in rotating cylinders.Phys.Fluids,1997,9:31-43
21Lun CKK,Savage SB,Jeffrey DJ,et al.Kinetic theories for granular flow:inelastic particles in Couette flow and slightly inelastic particles in a general flow field.J.Fluid Mech,1984,140:223-256
22Gonzalez S,Windows-Yule CRK,Luding S,et al.Shaping Segregation:Convexity vs.Concavity.http://arxiv preprint arxiv,2014:1410.6286
23Ottino JM.The Kinematics of Mixing:Stretching.Chaos,and Transport Cambridge University Press.Cambridge,1990
24Henein H,Brimacombe JK,Watkinson AP.Experimental studies of transverse bed motion in rotary kilns.Metall.Trans.,1983,14B:191-205
25Hill KM,Jain NT,Ottino JM.Modes of granular segregation in a noncircular rotating cylinder.Phys.Rev.E,2001,64:011302
26Meier SW,Cisar SE,Lueptow RM,et al.Capturing patterns and symmetries in chaotic granular flow.Phys.Rev.E,2006,74:031310
27王瑞芳,李占勇,窦如彪等.水平转筒内大豆颗粒随机运动与混合特性模拟.农业机械学报,2013,44(6):93-99(Wang Ruifang,Li Zhanyong,Dou Ruibiao,et al.Simulation on random motion and mixing characteristic for soybean in rotary drum.Transactions of the Chinese Society for Agricultural Machinery,2013,44(6):93-99(in Chinese))
28Prasad DVN,Khakhar DV.Granular flow in rotating cylinders with noncircular cross sections.Phys.Rev.E,2008,77:041301
29Khakhar DV,Mc Carthy JJ,Gilchrist JF,et al.Chaotic mixing of granular materials in two-dimensional tumbling mixers.Chaos,1999,9:1
30Ottino JM,Khakhar DV.Mixing and segregation of granular materials.Annu.Rev.Fluid Mech.,2000,32:55-91