Gravity Flow Of Granular Materials Research Articles

Dense granular flow through a flat-bottomed silo: Comparison of the DEM and continuum models with experiments

The gravity flow of granular materials through a flat-bottomed rectangular silo is examined using experiments, the discrete element method (DEM), and continuum models. The flow is bounded by four flat frictional side walls, and the mass flow rate is controlled by an exit slot. The velocity and wall stresses are measured simultaneously in a steady fully developed zone which occurs far from the upper free surface and the exit slot, and they are compared with predictions of the DEM and the continuum models. The scaled velocities measured adjacent to the front face are in excellent agreement with the DEM. The centreline velocity is predicted to within 5%–30% by the DEM for larger widths. The normal and shear stresses measured at the mid-plane of one of the walls agree to within 5%–20% for the DEM. The DEM results are less sensitive to the spring stiffness kn, but are more sensitive to the interparticle coefficient of friction μp. There are larger discrepancies in the predictions of the continuum models when the effect of the front and rear walls are not included. The approximate inclusion of the latter improves the prediction of the shear stress and the slip velocity.

Mechanism and kinetics of separation of impurity particles with different densities in a rapid gravity flow of granular material

Mechanism and kinetics of separation of impurity particles with different densities in a rapid gravity flow of granular material

Mechanisms and Kinetics of Separation of Impurities of Large and Small Particles in Gravity Flow of Granular Material

Mechanisms and Kinetics of Separation of Impurities of Large and Small Particles in Gravity Flow of Granular Material

Structural Inhomogeneity and Effects of Separation by Size and Density in Gravity Flow of Granular Materials

Structural Inhomogeneity and Effects of Separation by Size and Density in Gravity Flow of Granular Materials

Transversal mass transfer and shear stress formation during rapid gravity flow of a granular medium

The micro structural models for shear stress generation during rapid gravity flow of granular materials on a rough chute are discussed. The mechanism of the shear stress formation, taking into account the tangential impulse formed under transversal mass transfer of particles, is suggested. The analogy between granular media during rapid shear deformation and dense gases is used to develop the suggested mechanism on the basis of kinetic theory. The total shear stress is determined as the sum of the stress components induced by collisions, transversal mass transfer and contact interactions of uniform cohesionless inelastic spherical particles. The mathematical models describing the components of shear kinetic stresses are developed as the functions of particle properties, structural and kinematical gravity flow characteristics. The equations of impulse and energy conservation in the course of rapid gravity flow of uniform cohesionless particles are formulated. A variant of the formulation of boundary conditions at the flow bottom is proposed for mathematical modeling of the dynamics of rapid gravity flows of granular materials on a rough chute. The variant assumes the displacement of the area with the most intense shear rate inside the flow and into its layers adjacent to the rough chute surface.

Effect of horizontal vibrations on mass flow rate and segregation during hopper discharge: discrete element method approach

Vibration is often utilized as a means of initiating and/or controlling flow from hopper in industries dealing with powder/granular materials such as packing, conveying, etc. The effect of horizontal vibration on gravity flow of granular material from conical hopper is modeled using the discrete element method. Material considered in this study includes glass beads of diameter ranging between 0.7 mm and 2.0 mm. The flow dynamics and segregation of material are analyzed for different mixtures characterized based on mass percentage of smaller particles (fines) and multi-component mixtures (binary and ternary) at different vibration parameters. The study includes the influence of vibration frequency, acceleration amplitude, fines percentage, diameter ratio and mixture components on segregation and mass flow rate during vibratory hopper discharge. The extent of segregation is calculated by means of mass fraction of fines inside hopper for different operating conditions. The numerical results indicate that the increase in vibration acceleration at a fixed frequency results into increased mass flow rate and there exists acceleration amplitude beyond which segregation is predominant. Mixture components play significant role in segregation behaviour and binary mixture suffers more segregation as compared to ternary mixture. The spatial distribution of the velocity profile indicates that different mixtures behave differently at a particular vibration conditions. The phenomena like sieving or percolation are also observed based on the analysis of top view simulation snap shots.

Forced flow of granular media: Breakdown of the Beverloo scaling

The Beverloo scaling for the gravity flow of granular materials through orifices has two distinct universal features. On the one hand, the flow rate is independent of the height of the granular column. On the other hand, less well-known yet more striking, the flow rate is fairly insensitive to the material properties of the grains (density, Young's modulus, friction coefficient, etc.). We show that both universal features are lost if work is done on the system at a high rate. In contrast to viscous fluids, the flow rate increases during discharge if a constant pressure is applied to the free surface of a granular column. Moreover, the flow rate becomes sensitive to the material properties. Nevertheless, a new universal feature emerges: the dissipated power scaled by the mean pressure and the flow rate follows a master curve for forced and unforced conditions and for all material properties studied. We show that this feature can be explained if the granular flow in the silo is assumed to be a quasistatic shear flow under the -rheology.

Detection of tracer particles in tomography images for analysis of gravitational flow in silo

Abstract This paper presents a method for the investigations of the gravity flow of granular materials based on the analysis of CT images. The system of X-ray tomography allows to visualize the distribution of bulk material inside the silo model. The images of the distribution of the concentration of the material, both in the form of 3D tomography images and 2D radiographic images, allow to track the behaviour of the material during the silo discharging process. Application of image processing and analysis provides an in-depth tool for investigation of the flow. The proposed, in the paper, methodology of the tracer particles allow to track the particles position changes during the gravitational flow in silo. The determination of tracer particles position is based on the vision information stored in volumetric computed tomography images and two-dimensional radiography.

Modeling coal discharge in mechanized steep and thick coal mining

The physical and analytical modeling of coal discharge in thick coal mining by sublevel caving involves the method when coal is discharged under gravity on the powered support units and is proportioned-fed to a face conveyor placed between the support units. Based on the physical modeling, the authors put forward a mathematical model to study the gravity flow of granular material in three dimensional formulation using discrete elements.

Measurement of granular flow in a vertical column using pulse induction (PI)

Gravity flow of granular materials in vertical columns can generate pressure and density fluctuations which are difficult to quantify. Examination of prior research led us to propose a new measurement technique based on the principle of pulse induction (PI) for metal detection. An experimental device using 8 mm diameter spherical particles flowing through a polyvinylchloride (PVC) pipe of 75 mm diameter and 1000 mm height was developed to demonstrate the feasibility of PI. Ten PI coils were used to quantify tracer movement through the column with time. Average and instantaneous velocities were determined for five diameters of outlet orifices: 68.0, 62.5, 54.5, 44.0 and 36.5 mm. Flow rate was calculated and modelled. When compared to prior research, PI proved to be a reliable method for flow measurement in opaque ducts.

Segregation kinetics in the rapid gravity flow of granular materials

An experimental analytical method for determining the kinetic segregation coefficient in the rapid gravity flow of a granular material down a rough incline is proposed. It is found that it is possible to predict the velocity of transverse displacement of individual large and small particles in the rapid gravity flow using a single kinetic segregation coefficient for different particle sizes and structural and kinematic characteristics of the flow. A previously proposed equation of segregation kinetics is refined, and its predictive power is analyzed.

Some exact velocity profiles for granular flow in converging hoppers

Gravity flow of granular materials through hoppers occurs in many industrial processes. For an ideal cohesionless granular material, which satisfies the Coulomb-Mohr yield condition, the number of known analytical solutions is limited. However, for the special case of the angle of internal friction δ equal to ninety degrees, there exist exact parametric solutions for the governing coupled ordinary differential equations for both two-dimensional wedges and three-dimensional cones, both of which involve two arbitrary constants of integration. These solutions are the only known analytical solutions of this generality. Here, we utilize the double-shearing theory of granular materials to determine the velocity field corresponding to these exact parametric solutions for the two problems of gravity flow through converging wedge and conical hoppers. An independent numerical solution for other angles of internal friction is shown to coincide with the analytical solution.

The limiting ideal theory for shear-index cohesionless granular materials

AbstractTo model cohesionless granular flow using continuum theory, the usual approach is to assume the cohesionless Coulomb-Mohr yield condition. However, this yield condition assumes that the angle of internal friction is constant, when according to experimental evidence for most powders the angle of internal friction is not constant along the yield locus, but decreases for decreasing normal stress component σ from a maximum value of π/2. For this reason, we consider here the more general yield function which applies for shear-index granular materials, where the angle of internal friction varies with σ. In this case, failure due to frictional slip between particles occurs when the shear and normal components of stress τ and σ satisfy the so-called Warren Spring equation (|τ|/c)n = 1 − (σ/t), where c, t and n are positive constants which are referred to as the cohesion, tensile strength and shear-index respectively, and experimental evidence indicates for many materials that the value of the shear-index n lies between 1 and 2. For many materials, the cohesion is close to zero and therefore the notion of a cohesionless shear-index granular material arises. For such materials, a continuum theory applying for shear-index cohesionless granular materials is physically plausible as a limiting ideal theory, and any analytical solutions might provide important benchmarks for numerical schemes. Here, we examine the cohesionless shearindex theory for the problem of gravity flow of granular materials through two-dimensional wedge-shaped hoppers, and we attempt to determine analytical solutions. Although some analytical solutions are found, these do not correspond to the actual hopper problem, but may serve as benchmarks for purely numerical schemes. The special analytical solutions obtained are illustrated graphically, assuming only a symmetrical stress distribution.

Gravity flow of granular materials in contracting cylinders and tapered tubes

This paper presents two applications of the double-shearing theory for flow of granular materials under gravitational forces for axially symmetric flow. In the first the material is contained in a vertical circular cylinder which compresses the material by contracting radially. Exact solutions for the stress and velocity fields are derived, under the boundary conditions that the cylinder wall is either `perfectly rough' or subject to Coulomb friction. In the second problem the material flows under gravity through a tube with circular cross-section of radius that decreases slowly with depth. For this problem an approximate solution is derived that is accurate to first order in the slope of the tube wall relative to the vertical. It is also shown that an alternative theory, in which it is postulated that the principal axes of the stress and rate-of-strain tensors are coincident, leads to the prediction of unacceptable singularities in the flow field in the interior of the material.

Filling a silo: density profiles and friction induced segregation

This paper provides a review on the flow of free-flowing coarse particles inside silos. Basic principles and elementary mechanisms involved in gravity flow of granular materials are discussed. The main focus is put on flow patterns, stress distribution, velocity profiles, mass flowrate, Residence Time Distribution (RTD) and segregation inside the silo. A summary of empirical correlations as well as a synthesis of more physical and mechanistic models related to these aspects are presented. Computational and numerical methods used to describe the granular flow of particles will be discussed in a separate paper.

Some aspects of flow in granular materials in hoppers

The main part of the paper is devoted to the description of the localized deformation zones in plane (slow) flow of granular materials from hoppers. Specifically, two types of zones are discussed i...

Fully developed flow of coarse granular materials through a vertical channel

Some recent studies have proposed a simple manner of combining the frictional contributions to the stress with the kinetic theory based models for granular flow. In this paper, kinetic and frictional-kinetic models are used to study the gravity flow of granular materials through a vertical channel. The results show that as the mean density v increases, the velocity profile predicted by the kinetic model shows a region of plug flow near the centre, and a shear layer adjacent to the wall. At high densities (v≈0.64), the thickness of the shear layer is a few particle diameters. The centerline velocity and the mass flow rate exhibit maxima as v increases. The maxima are due to the opposing effects of the weight of the material and the shear viscosity. For the parameter values used here, the grain temperature profile exhibits a maximum near the wall and, correspondingly, the density profile exhibits a minimum. Predictions of the frictional-kinetic model are qualitatively similar, except that (i) the profiles are discontinuous at the interface between the plug and the shear layer, and (ii) at high densities, the thickness of the shear layer is much less than in the kinetic case. When mean densities are matched with measured values, velocity profiles (scaled by the centerline velocities) predicted by both models are found to be in fair agreement with the experimental data. In contrast, the absolute centerline velocities are higher than the reported values by a factor of 10–50. This discrepancy cannot be attributed to air-drag, as calculations show that the latter has a negligible effect on the velocity profiles. When either the mass flow rates or the centerline velocities are matched with the experimental data, the kinetic profiles fit the data fairly well. This is a puzzling result, as at high densities, many of the assumptions of the kinetic model are unlikely to hold. Though the frictional-kinetic model is expected to be more realistic, the shear layer is much thinner than that observed. Both models underestimate the shear stresses at the channel walls by a factor of 1.5–3, and overestimate the normal stresses by a similar factor.

Flow of granular materials down a vertical pipe

The gravity flow of granular materials down a vertical pipe is studied using a continuum model [Goodman and Cowin, J. Fluid Mech. 45, 321–339 (1971), Goodman and Cowin, Arch. Rational Mech. Anal. 44, 249–266 (1972), Rajagopal and Massoudi, DOE/PETC/TR-90/3 (1990)]. The equations are developed for both the case of slip and no-slip at the boundary. The resulting boundary value problem is solved numerically. The effect of material parameters (compressibility, volume distribution, and viscous effects) on the volume fraction and velocity in the pipe are studied.

On equivalent friction for the accelerated gravity flow of granular materials in chutes

An equivalent friction model for the accelerated gravity flow of granular materials through chutes is discussed. Previous models were limited to chutes of rectangular cross-section. In this paper, the application of the model to chutes of circular cross-section is examined and it is shown that, under shallow bed conditions, the model may be approximated by a function linear in bed depth, similar to that applicable to chutes of rectangular cross-section. A closed-form solution of the flow equations, involving Coulomb and velocity-dependent drag forces for straight inclined chutes of rectangular cross-section, is presented. The extension of the solution to chutes of circular cross-section is discussed.

The effect of pipe length on the gravity flow of granular materials in vertical standpipes

In an earlier publication [1], a theory of motion of particulate materials in hopperfed vertical standpipes was developed. It was used to predict the performance of a pipe in response to changes in the restriction imposed by a valve at its lower end, and to changes in the back-pressure of gas below this valve. The theoretical predictions were compared with experimental observations on a laboratory standpipe of fixed length. The present paper supplements this by presenting experimental data on the influence of standpipe length on performance, and comparing these with predictions of the theory. It is found that most of the qualitative features observed are also predicted, and that quantitative agreement between theory and observations is also encouragingly good.