三维漏斗中颗粒物质堵塞问题的数值实验研究

对于工程和实验中使用漏斗颗粒流而言,连续稳定的流量是必要的.当漏斗口较小时,很容易发生堵塞行为.堵塞现象对于交通流、疏散问题等也具有重要的意义.前人主要使用扰动的方法破坏漏斗中已有的堵塞,以便引起下一次堵塞,加快实验进程.本文利用自主开发的基于GPU(graphics processing unit)的密集颗粒流模拟程序,主要研究当三维漏斗开口打开后的第一次堵塞行为,不再引入扰动.详细讨论了漏斗开口尺寸、漏斗锥角等几何参数对坍塌规模的影响.发现对于坍塌规模的概率分布符合前人的研究结果,可以分为两部分:峰的左边呈幂函数上升形式,峰的右边呈指数衰减趋势.对于漏斗开口尺寸和漏斗锥角而言,均存在一个临界值使得堵塞不再发生.

Numerical experiment studies of clogging during the discharge of granular matter in a three-dimensional hopper

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.