(479h) The Transition from Steady Non-Oscillatory Flow to Oscillatory Flow of Granular Material through a Vertical Channel: A DEM Study

Granular materials are widely used in industries, and are handled in our daily life. The lack of suitable constitutive equations poses challenges to predict the flows of such materials. During the past two decades, the discrete element method (DEM) has become a powerful tool to study granular flow. In the present work, the DEM is used to examine granular flow through vertical channels. These are widely used in industries for storing granular materials and filling them into bins, hoppers, and bunkers. Many efforts were reported in the literature on experiments and modelling this problem, a clear insight is lacking. There are very few studies on the use of DEM for this problem. Here an extensive study is performed on such flows by varying the bulk solids fraction <Φ> ranging from the dense regime to the very dilute regime. Periodic boundary conditions are applied in the flow z and vorticity y directions. Hence the variation in the solids fraction, velocity, and stress fields occurs only in the cross-stream direction x for the case of steady, fully developed flow. There are shear layers near the walls and an undeformed plug in the centre for the profile of the vertical velocity u_z, as reported earlier in the literature. For dense flows, the variation of the solids fraction Φ is similar to that of u_z. One of the major findings is the appearance of a third zone between the shear layer and the plug in Φ profiles as the flow becomes more dilute (Fig. 1) (the data are shown for the width 2W/d_p = 60, where d_p is the particle diameter, and x = 0 corresponds to the left wall of the channel). No specific structure in the flow is found though the values of Φ attain the value corresponding to dense random packing (0.64) in the plug, irrespective of <Φ>. As <Φ> decreases, the material dilates more near the walls. The average of the coordination number of the grains near the walls (based on the neighbours within a critical radius of 2 d_p) is < 3 for low values of <Φ>. This suggests that the grains are not in continuous contact, and collisions may become dominant near the wall. Video imaging shows an oscillation of the flowing material in the cross-stream x direction for low values of <Φ>. A transition from a non-oscillatory steady, fully developed flow to an oscillatory flow is observed as <Φ> decreases below the critical limit <Φ>_cr (Fig. 2). There is a range for which the flow is oscillatory. The x-coordinate of the centre of mass x_com and the cross-stream velocity of the centre of mass u_{x_com} are periodic with constant amplitudes and frequencies; these are negligible for dense flows, but significant for loose flows. The amplitudes of x_com are comparable to the thickness of the shear layers. As <Φ> decreases irrespective of 2W, the amplitude of x_com increases and the corresponding frequency decreases. Because of reduction in <Φ>, the fraction of empty space increases, resulting in a transition to higher amplitudes. The reduction in frequency follows from the former as the material requires a longer time to reach the wall. The ratio of amplitudes of u_{x_com} to x_com is 2Π times the corresponding frequency of x_com, and the frequency of u_{x_com} is same as the frequency of x_com. The wall stresses and other kinematic properties near the walls are oscillatory. Oscillatory wall stresses have been measured in the past, but the solids fraction has not been measured simultaneously near the walls. The oscillation in x direction is a possible reason for the existence of the third intermediate zone in the variation of Φ with x. As <Φ> decreases more, a minimum value <Φ>_min exists below which the flow becomes accelerated and the second transition occurs from oscillatory flow to accelerated flow (Fig. 2). In non-oscillatory steady, fully developed flow, the material is sheared uniformly by both the walls. However, in the oscillatory regime, the effect of walls on the flows is not uniform over time period. In accelerated flow, the material is in free fall under gravity. To best of our knowledge, no such phenomena have been described in literature, except for the unsteady flow of the sand at the exit orifice on an hour-glass. In the latter case, interaction with the air may be responsible for the oscillations. Modelling the oscillations and comparison with the above findings will form a part of the future work. The images are attached in the link provided below

https://screenshot.net/oe5llt2