Periodic instationarities of granular flows in conical hoppers
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ORIGINAL PAPER
Periodic instationarities of granular flows in conical hoppers Guilhem Mollon1 Received: 24 January 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Granular flows through converging sections such as conical hoppers have been reported to be submitted to instationarities, which in certain circumstances can appear to be organized and periodic. In this paper, we explore this phenomenon by conducting discrete element modelling simulations of a 3D gravity-driven hopper flow and varying a large number of parameters such as hopper geometry and granular sample properties. Dedicated postprocessing techniques are developed and used to investigate the spatial and temporal patterns of these instationarities and to bring some understanding on the physics of this spontaneous phenomenon. Numerical results show that a clear structure appears for these instationarities, under the form of rapidly propagating waves relating variations in velocity magnitude and coordination number. While very faint, periodic variations of the sample density are also detected. The parametric study reveals that the self-organization of these variations requires a narrow set of conditions in terms of hopper geometry and intergranular contact friction coefficient. Keywords Granular flow · Periodic variations · Hopper flow · DEM
1 Introduction Hopper flow is a common problem in physics of granular flows [1]. It consists in the gravity-driven flow of a granular assembly through a converging channel, and the classic hourglass problem is a good example of this class of situations. Besides its theoretical interest, this problem also has a large number of practical applications since converging flows are used in a wide variety of industries manipulating powders and grains [2–5]. It has therefore attracted a large attention from the scientific community, both from the practical and academic viewpoints. Theoretical [6–9], experimental [10–17] and numerical [18–22] studies have been reported using a number of different tools. The most common quantity of interest that is extracted from such studies is the hopper discharge rate, i.e. the amount of matter passing through the hopper outlet in a certain amount of time. Contemporary studies use the hopper flow configuration to investigate such complex topics as avalanching [23], self-structuration of the granular fabric triggered by the converging flow [24], shape-induced flow * Guilhem Mollon guilhem.mollon@insa‑lyon.fr 1
regimes [25], or phase change (i.e. jamming) of the granular sample [26]. Despite the simplicity of its geometry, the hopper flow gives rise to fairly complex behaviors, and one of the most mysterious is the spontaneous emergence of periodic flow instationarities. Such instationarities, sometimes called fluctuations, have been reported experimentally [11, 13, 14, 16] and numerically [18, 20, 22]. In particular, a numerical study accounting for realistic sand grains shapes but limited to 2D kinematics [20] showed that these periodic instationarities cou
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