Rapid Gravity Flow of a Granular Medium

Abstract

Rapid gravity flows of granular materials are a widely present type of rapid shear flows occurring in a large number of natural phenomena and engineering processes. However, to date, the parameters of rapid gravity flows have been hard to adequately describe because of experimental and analytical difficulties [1]. The investigation of rapid shear flows is within the scope of the mechanics of granular media. Rapid shear flows are often referred to as inertial flows since their properties are determined mainly by the inertia and mutual collisions of particles.Currently, there are quite a lot of mathematical models of rapid shear flows. They can be divided into two groups: (1) models formulated in terms of continuum theories, which are based on different forms of the relationship between the stress tensor and the strain rate and (2) models based on microstructural analysis, which evaluates stresses as functions of the momentum transfer by collisions of particles.Savage [2] proposed a mathematical model of the rapid gravity flow of particulate solids down a rough chute. This model is based on the Goodman-Cowin model, founded on the basic principles of continuum mechanics [3]. A serious drawback of these models [2, 3] is that they ignored the dependence of the properties of the flow on the boundary conditions at the flow surface.Later, taking into account the obvious disadvantages of the model formulated in terms of continuum theories, a number of researchers [4-7] developed rapid gravity flow models based on microstructural analysis. These researchers determined the stress tensor by analyzing the momentum transfer in interparticle interaction and solved a set of equations of conservation of energy and momentum of particles in their fluctuations and displacement. However, the assumptions made in these models led to errors, whose significance was shown by Hutter and Scheiwiller [1]. Hutter and Scheiwiller, using the Jenkins-Savage model [5], performed numerical simulation of the flow of a granular material down an inclined chute. They also established that the above models [4][5][6][7] require the adequate formulation of boundary conditions, which are difficult to define.Ackermann and Shen [6] carried out a geometric analysis of the microstructure of the shear flow and concluded that gravity flows are characterized by significant transverse mass transfer (quasi-diffusion) of particles. This should necessarily be taken into account in adequate simulation of flows. Moreover, in most of the available works devoted to analytically studying the fast shear gravity flows of granular media, it was assumed that the conditions of interaction of particles in a bed of a granular material are independent of the solid-phase concentration. This assumption significantly reduces the worth of these models. This was convincingly confirmed by Campbell and Brennen [8], who performed computer simulation of rapid shear flows of cohesionless inelastic rough particles and concluded that the effective friction coefficient (the ratio of the shea...

Interrelation of structural and kinematic characteristics during free-surface gravity flows of granular materials

“…The adequacy of Eq. (11) was checked by means of comparison of modeling results with experimental data obtained by the X-ray photography method [35]. As it shown in Fig.…”