Kinematics of the mass flow of granular material through a plane hopper

Abstract

A kinematically admissible velocity field for the mass flow of a granular material in a plane converging hopper is presented in this Paper. The proposed solution is based on assumptions suggested by the flow pattern observed during experimental work. In particular, the rupture surfaces observed during flow are incorporated into the solution. The material filling the hopper is treated as plastic, though different flow rules are specified for difference areas of the material. Stresses are not considered because the static counterpart of the kinematic solution does not contribute to the approach adopted. The main aim of the work is to provide a realistic mathematical model for understanding the velocity fields observed in experiments, rather than a complete solution based on simplifying assumptions. A criterion is suggested which may govern the transition from mass to core flow as the head of material in the hopper is reduced. Un champ de vitesse cinématiquement admissible in-situ pour l'écoulement d'une masse de materiau granulaire à travers d'une trémie convergente, est présentée dans cette étude. La solution proposée est basée sur des hypothises inspirées par l'observation experimental d'écoulement d'enchantillons. En particulier, les surfaces de rupture observées pendant l'écoulement son incorporées dans la solution. Le matériau qui remplit le trémie est supposé plastique, bien que des règles différentes d'écoulement sont déterminées pour différentes niveaux du matériau. Les contraintes ne son pas considérées parce que la contre-partie statique de la solution cinématique ne contribue pas à l'approche adoptée. Le but principal de l'étude est plus de fournir un modèle mathématique réaliste pour comprendre les champs de vitesse observés experimentalement, plutôt qu'une solution complète basée sur la simplification des hypothises. Un critère est suggéré, qui pourrait gouverner la transition de l'écoulement de la masse au noyau alors que dans le trémie la charge du materiau est réduite.

Investigations of Shear Localization during Granular Silo Flow with Non-Local Hypoplastic Constitutive Model

“…They do not reach the walls. The shape of shear zones in a model hopper with smooth walls and very rough walls are almost identical as in experiments by Drescher et al [1] and Michalowski [2] (Fig.4). For smooth walls in a model bin, the interior shear zones occur only close to the bottom-wall region due to insignificant deformation.…”

“…It was recognized that shear zones occur always during silo flow along walls and in the interior of initially dense granular solids [1], [2], [3]. Their thickness depends on the initial density, mean grain diameter, wall roughness, silo size, grain roughness and emptying velocity [3].…”

“…The FE results of forces were compared with corresponding silo model tests performed by Tejchman [3]. In turn, the results of the distribution of void ratio were compared with silo model tests by Drescher et al [1] and Michalowski [2].…”

Application of ECT to solid concentration measurements during granular flow in a rectangular model silo

“…14C and D) and in the interior of the initially dense material with smooth walls (in the form of curvilinear zones above the outlet, Fig. 14B) similarly as in the experiments (Drescher et al, 1978;Nedderman and Laohakul, 1980;Michalowski, 1984;Tejchman and Gudehus, 2000) and in the FE-calculations (Tejchman and Gudehus, 2000;Wojcik and Tejchman, 2009).…”

Comparative analysis of empirical descriptions of eccentric flow in silo model by the linear and nonlinear regressions

“…Optical techniques are commonly used in the analysis of velocity profiles near the transparent silo walls. The X-ray technique was frequently applied to obtain information from deeper flow layers [36,37]. Also, other non-invasive measurement techniques were applied to register granular flow, density and velocity fields in flowing zones, among others spy-holes, radio transmitters, positron emission [38], magnetic resonance imaging, radioactive tracers, and ultrasonic speckle velocimetry.…”