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For a granular flow in hopper in engineering and experimental applications, it is necessary to guarantee the discharge continuously and steadily. The clogging will easily happen if the outlet size is small enough via formation of the arch above the outlet. The clogging phenomenon is also important for studying traffic or evacuation problems. In previous numerical and experimental study, to expedite the experiments or simulations, the perturbations, such as a jet of pressurized air or the vibration of the wall of the hopper, were induced to break the clogging and restart the flow. But these perturbations are hardly normalized and described in modeling the process. In this paper, we present a series of numerical experiments of clogging in the discharge of particles from a three-dimensional hopper through a circular opening. We employ our discrete element method simulation code for large scale dense granular flow based on the graphic processing unit to expedite this simulation. In contrast to pervious studies, here we study the first clogging after opening the outlet of hopper, thus the above perturbations are avoided. From simulating granular flow in hopper in a wide range of outlet size and cone angle, we obtain the size of distribution of avalanche, which is defined as the number of particles that fall through the opening from the outlet opening to the first clogging. The effects of the outlet size and cone angle of hopper on avalanche size are investigated and discussed. The results show that the previous conclusion of the distribution of possibility of avalanche size is also valid in this study. There is a peak in the distribution of possibility of avalanche size, and the distribution can be divided into two regions, which can be fitted with a power-law and an exponential function respectively. The exponential part can be explained by a possibility model which is suggested by Janda et al. From the fitting we find that it has a critical value for the outlet size above which no clogging will occur and the value in this work (4.75d) is slightly lower than in Zuriguel et al.'s experiment (4.94d). Moreover, there is also a critical value for the cone angle of hopper, which supports the inference in previous study and the value in this paper (77) is closed to the predicted one (75) in To et al.'s work.
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Keywords:
- GPU-based simulation /
- granular flow in a three-dimensional hopper /
- clogging /
- critical value
[1] Peng Y J, Zhang Z, Wang Y, et al. 2012 Acta Phys. Sin. 61 134501 (in Chinese)[彭亚晶, 张卓, 王勇, 等 2012 物理学报 61 134501]
[2] Xie X M, Jiang Y M, Wang H Y, et al. 2003 Acta Phys. Sin. 52 2194 (in Chinese)[谢晓明, 蒋亦民, 王焕友, 等 2003 物理学报 52 2194]
[3] Lu K Q, Hou M Y, Jiang Z H, et al. 2012 Acta Phys. Sin. 61 119103 (in Chinese)[陆坤权, 厚美瑛, 姜泽辉, 等 2012 物理学报 61 119103]
[4] Zuriguel I, Pugnaloni L A, Garcimartin A, Maza D 2003 Phys. Rev. E 68 3
[5] Thomas C C, Durian D J 2015 Phys. Rev. Lett. 114 17
[6] Lu K, Liu J 2004 Physics 33 10 (in Chinese)[陆坤权, 刘寄星 2004 物理 33 10]
[7] Zuriguel I, Parisi D R, Hidalgo R C, Lozano C, Janda A, Gago P A, Peralta J P, Ferrer L M, Pugnaloni L A, Clement E, Maza D, Pagonabarraga I, Garcimartin A 2014 Sci. Reports 4 7324
[8] To K, Lai P Y, Pak H K 2001 Phys. Rev. Lett. 86 1
[9] Masuda T, Nishinari K, Schadschneider A 2014 Phys. Rev. Lett. 112 13
[10] To K W 2005 Phys. Rev. E 71 6
[11] Janda A, Zuriguel I, Garcimartin A, Pugnaloni L A, Maza D 2008 EPL 84 4
[12] Kondic L 2014 Granular Matter 16 2
[13] Guariguata A, Pascall M A, Gilmer M W, Sum A K, Sloan E D, Koh C A, Wu D T 2012 Phys. Rev. E 86 6
[14] Lin Y J, Fang C 2016 J. Mech. 32 6
[15] Longjas A, Monterola C, Saloma C 2009 J. Statist. Mech. Theory and Experiment 2009 05006
[16] Kunte A, Doshi P, Orpe A V 2014 Phys. Rev. E 90 2
[17] Hong X, Kohne M, Weeks E R 2015 arXiv preprint
[18] Zuriguel I, Garcimartin A, Maza D 2005 Phys. Rev. E 71 5
[19] Mankoc C, Garcimartin A, Zuriguel I, Maza D 2009 Phys. Rev. E 80 1
[20] Zuriguel I 2014 Papers in Physics 6 060014
[21] Zuriguel I, Janda A, Garcimartin A, Lozano C, Arevalo R, Maza D 2011 Phys. Rev. Lett. 107 27
[22] Lozano C, Janda A, Garcimartin A, Maza D, Zuriguel I 2012 Phys. Rev. E 86 3
[23] Saraf S, Franklin S V 2011 Phys. Rev. E 83 3
[24] Tian Y, Qi J, Lai J, Zhou Q, Yang L 2013 Proceedings of the Awareness Science and Technology and Ubi-Media Computing Aizu-Wakamatsu, Japan, November 2-4, 2013 p547
[25] Tian Y, Zhang S, Lin P, Yang Q, Yang G, Yang L 2017 Comput. Chem. Engineer. 104 231
[26] Snoeijer J H, van Hecke M, Somfai E, van Saarloos W 2003 Phys. Rev. E 67 3
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[1] Peng Y J, Zhang Z, Wang Y, et al. 2012 Acta Phys. Sin. 61 134501 (in Chinese)[彭亚晶, 张卓, 王勇, 等 2012 物理学报 61 134501]
[2] Xie X M, Jiang Y M, Wang H Y, et al. 2003 Acta Phys. Sin. 52 2194 (in Chinese)[谢晓明, 蒋亦民, 王焕友, 等 2003 物理学报 52 2194]
[3] Lu K Q, Hou M Y, Jiang Z H, et al. 2012 Acta Phys. Sin. 61 119103 (in Chinese)[陆坤权, 厚美瑛, 姜泽辉, 等 2012 物理学报 61 119103]
[4] Zuriguel I, Pugnaloni L A, Garcimartin A, Maza D 2003 Phys. Rev. E 68 3
[5] Thomas C C, Durian D J 2015 Phys. Rev. Lett. 114 17
[6] Lu K, Liu J 2004 Physics 33 10 (in Chinese)[陆坤权, 刘寄星 2004 物理 33 10]
[7] Zuriguel I, Parisi D R, Hidalgo R C, Lozano C, Janda A, Gago P A, Peralta J P, Ferrer L M, Pugnaloni L A, Clement E, Maza D, Pagonabarraga I, Garcimartin A 2014 Sci. Reports 4 7324
[8] To K, Lai P Y, Pak H K 2001 Phys. Rev. Lett. 86 1
[9] Masuda T, Nishinari K, Schadschneider A 2014 Phys. Rev. Lett. 112 13
[10] To K W 2005 Phys. Rev. E 71 6
[11] Janda A, Zuriguel I, Garcimartin A, Pugnaloni L A, Maza D 2008 EPL 84 4
[12] Kondic L 2014 Granular Matter 16 2
[13] Guariguata A, Pascall M A, Gilmer M W, Sum A K, Sloan E D, Koh C A, Wu D T 2012 Phys. Rev. E 86 6
[14] Lin Y J, Fang C 2016 J. Mech. 32 6
[15] Longjas A, Monterola C, Saloma C 2009 J. Statist. Mech. Theory and Experiment 2009 05006
[16] Kunte A, Doshi P, Orpe A V 2014 Phys. Rev. E 90 2
[17] Hong X, Kohne M, Weeks E R 2015 arXiv preprint
[18] Zuriguel I, Garcimartin A, Maza D 2005 Phys. Rev. E 71 5
[19] Mankoc C, Garcimartin A, Zuriguel I, Maza D 2009 Phys. Rev. E 80 1
[20] Zuriguel I 2014 Papers in Physics 6 060014
[21] Zuriguel I, Janda A, Garcimartin A, Lozano C, Arevalo R, Maza D 2011 Phys. Rev. Lett. 107 27
[22] Lozano C, Janda A, Garcimartin A, Maza D, Zuriguel I 2012 Phys. Rev. E 86 3
[23] Saraf S, Franklin S V 2011 Phys. Rev. E 83 3
[24] Tian Y, Qi J, Lai J, Zhou Q, Yang L 2013 Proceedings of the Awareness Science and Technology and Ubi-Media Computing Aizu-Wakamatsu, Japan, November 2-4, 2013 p547
[25] Tian Y, Zhang S, Lin P, Yang Q, Yang G, Yang L 2017 Comput. Chem. Engineer. 104 231
[26] Snoeijer J H, van Hecke M, Somfai E, van Saarloos W 2003 Phys. Rev. E 67 3
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