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本文采用数值方法分析了一维垂直振动床内颗粒动能/温度、能量耗散以及体积分数的分布规律. 离散元模拟结果表明: 当床底做低频、小振幅振动时，床层内颗粒整体随床底上下运动，沿床高方向颗粒动能逐渐增加；对于高频振动，床层内的颗粒做无规则的运动，沿床高方向颗粒动能逐渐降低.在不同振动频率（高频、低频）下体积分数、能量耗散也表现出不同的分布规律. 将离散元模拟结果与动力学理论计算值对比，当系统做高频振动时，两模型所得结果基本吻合；而对于低频、小振幅振动，所得结果存在较大差异. 由于低频、小振幅振动时床内颗粒并非做无规则运动，动力学理论的适用性需进一步完善.By using numerical simulation, the kinetic energy/temperature, the energy dissipation and the volume fraction in a 1D vertical vibrational bed are studied. Discrete element simulation shows that the granular bed moves up and down as an ensemble and the kinetic energy of the particles increases along the bed height when the bed bottom vibrates at a low-frequency and low-amplitude. For high-frequency vibrations, the particles in the bed move randomly and their kinetic energy decreases along the bed height. The energy dissipation and the volume fraction of the particles are also influenced by the vibrations frequency obviously, and they show different distributions at the high and low frequencies. In addition, we have compared the result of the discrete element simulation with that of the hydrodynamic simulation. When the bed bottom vibrates at high frequency, the two simulation methods can get the similar results. However, for the low-frequency and low-amplitude vibrations, the computed results are opposite to each other. Since the particles in the bed do not move and collide randomly, the application of the hydrodynamic simulation to the bed with low-frequency and low-amplitude vibrations should be investigated and discussed further.
[1] Jaeger H M, Nagel S R 1996 Rev. Mod. Phys. 68 1259
[2] Hu G Q, Tu H E, Hou M Y 2009 Acta Phys. Sin. 58 341 (in Chinese) [胡国琦, 徐洪恩, 厚美瑛 2009 58 341]
[3] Peng Z, Jiang Y M, Liu R, Hou M Y 2013 Acta Phys. Sin. 62 024502 (in Chinese) [彭政, 蒋亦民, 刘锐, 厚美瑛 2013 62 024502]
[4] Chen Y P, Pierre E, Hou M Y 2012 Chin. Phys. Lett. 29 074501
[5] Ehrichs E E, Jaeger H M, Karczmar G S, Knight J B, Kuperman V Y, Nagel S R 1995 Nature 267 1632
[6] Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[7] Duran J, Rajchenbach J, Clement E 1993 Phys. Rev. Lett. 70 2431
[8] Melo F, Umbanhowar P B, Swinney H L 1994 Phys. Rev. Lett. 72 172
[9] Fraige F Y, Langston P A, Matchett A J, Dodds J 2008 Particuology 6 455
[10] Zhou G D, Sun Q C 2013 Powder Technol. 239 115
[11] Li R, Xiao M, Li Z H, Zhang D M 2012 Chin. Phys. Lett. 29 128103
[12] Cai Q D, Chen S Y, Sheng X W 2011 Chin. Phys. B 20 024502
[13] Jenkins J T, Richman M W 1985 Phys. Fluids 28 3485
[14] Dufty J W, Brey J J 2003 Phys. Rev. E 68 030302
[15] Giardiná C, Livi R, Politi A, Vassalli M 2000 Phys. Rev. Lett. 84 2144
[16] Dhar A, Saito K 2008 Phys. Rev. E 78 061136
[17] Ítalo’Ivo L D P, Rosas A, Lindenberg K 2009 Phys. Rev. E 79 061307
[18] Mindlin R D, Deresezewicz H 1953 J. Appl. Mech. 20 327
[19] Wildman R D, Huntley J M 2003 Phys. Fluids 15 3090
[20] Viswanathan H, Wildman R D, Huntley J M, Martin T W 2006 Phys. Fluids 18 113302
[21] Carnahan N F, Starling K E 1969 J. Chem. Phys. 51 635
[22] Richman M W 1993 Mech. Mater. 16 211
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[1] Jaeger H M, Nagel S R 1996 Rev. Mod. Phys. 68 1259
[2] Hu G Q, Tu H E, Hou M Y 2009 Acta Phys. Sin. 58 341 (in Chinese) [胡国琦, 徐洪恩, 厚美瑛 2009 58 341]
[3] Peng Z, Jiang Y M, Liu R, Hou M Y 2013 Acta Phys. Sin. 62 024502 (in Chinese) [彭政, 蒋亦民, 刘锐, 厚美瑛 2013 62 024502]
[4] Chen Y P, Pierre E, Hou M Y 2012 Chin. Phys. Lett. 29 074501
[5] Ehrichs E E, Jaeger H M, Karczmar G S, Knight J B, Kuperman V Y, Nagel S R 1995 Nature 267 1632
[6] Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[7] Duran J, Rajchenbach J, Clement E 1993 Phys. Rev. Lett. 70 2431
[8] Melo F, Umbanhowar P B, Swinney H L 1994 Phys. Rev. Lett. 72 172
[9] Fraige F Y, Langston P A, Matchett A J, Dodds J 2008 Particuology 6 455
[10] Zhou G D, Sun Q C 2013 Powder Technol. 239 115
[11] Li R, Xiao M, Li Z H, Zhang D M 2012 Chin. Phys. Lett. 29 128103
[12] Cai Q D, Chen S Y, Sheng X W 2011 Chin. Phys. B 20 024502
[13] Jenkins J T, Richman M W 1985 Phys. Fluids 28 3485
[14] Dufty J W, Brey J J 2003 Phys. Rev. E 68 030302
[15] Giardiná C, Livi R, Politi A, Vassalli M 2000 Phys. Rev. Lett. 84 2144
[16] Dhar A, Saito K 2008 Phys. Rev. E 78 061136
[17] Ítalo’Ivo L D P, Rosas A, Lindenberg K 2009 Phys. Rev. E 79 061307
[18] Mindlin R D, Deresezewicz H 1953 J. Appl. Mech. 20 327
[19] Wildman R D, Huntley J M 2003 Phys. Fluids 15 3090
[20] Viswanathan H, Wildman R D, Huntley J M, Martin T W 2006 Phys. Fluids 18 113302
[21] Carnahan N F, Starling K E 1969 J. Chem. Phys. 51 635
[22] Richman M W 1993 Mech. Mater. 16 211
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