Frictional–collisional equations of motion for participate flows and their application to chutes

Abstract

Measurements of the relation between mass hold-up and flow rate have been made for glass beads in fully developed flow down an inclined chute, over the whole range of inclinations for which such flows are possible. Velocity profiles in the flowing material have also been measured. For a given inclination it is found that two different flow regimes may exist for each value of the flow rate in a certain interval. One is an ‘energetic’ flow, and is produced when the particles are dropped into the chute from a height, while the other is relatively quiescent and occurs when entry to the chute is regulated by a gate. At some values of the inclination jumps in the flow pattern occur between these branches, and it is even possible for both branches to coexist in the same chute, separated by a shock. A theoretical treatment of chute flow has been based on a rheological model of the material which takes into account both collisional and fractional mechanisms for generating stress. Its predictions include most aspects of the observed behaviour, but quantitative comparison of theory and experiment is difficult because of the uncertain values of some parameters appearing in the theory.

A visco‐elasto‐plastic model for granular materials under simple shear conditions

“…The model hereafter illustrated can be interpreted as the extension to unsteady conditions of the model discussed in Berzi et al [39] and Vescovi et al [40]. The parallel scheme was already proposed by some authors [34,35,36,37,38], but the novelty of the approach introduced by Berzi et al [39] and Vescovi et al [40] concerns the role of critical state [41,42,43,44,28]: this is here interpreted as the limit for granular stationary flows, under simple shear conditions, when the granular temperature nullifies.…”

“…In contrast, the theoretical constitutive model hereafter presented, as in Johnson and Jackson [34,35], Savage [36], Louge [37], Lee and Huang [38], Berzi et al [39] and Vescovi et al [40], assumes a parallel scheme according to which the stress tensor is evaluated as the sum of two contributions: one "ratedependent" and another "rate-independent". The model hereafter illustrated can be interpreted as the extension to unsteady conditions of the model discussed in Berzi et al [39] and Vescovi et al [40].…”

Virtual Characterization of Dense Granular Flow through a Vertically Rotating Feeding Experiment

“…The continuum model of Latz and Schmidt [4] is employed, which combines the properties of the granular gas kinetic theory, a well-verified theory on dilute granular systems [5] and critical state plasticity, a framework widely employed for soil mechanics applications [6]. This leads to the splitting of the stresses into a rate-dependent and a rate-independent term, a common approach also used [6][7][8][9][10].…”

“…This leads to the splitting of the stresses into a rate-dependent and a rate-independent term, a common approach also used [6][7][8][9][10]. One main difference between those models and the model of Latz and Schmidt lies in the singularity of the radial distribution function at contact between the model: The rate-independent term diverges in the model of Latz and Schmidt, ensuring numerical stability in the dense regime, whereas it does not diverge in [9,10].…”

Mathematical Model of Solid Flow Behavior in a Real Dimension Blast Furnace

“…Therefore, the surface stress τs in Eq. (3) may be considered to consist of two parts: [38][39][40][41][42] . (4) where, as it is introduced by Zhang et al, 8) τrd is the ratedependent part of the surface stress and τri is the rateindependent part.…”