Hopper Opening Research Articles

A DEM Analysis of Flow Characteristics of Noncohesive Particles in Hopper

Flow characteristics of material in hoppers, silos, and bins are critical issues for operational stability as well as structural integrity of these units. In this work, flow of noncohesive particles in hopper is studied using the discrete element method (DEM) where each particle is tracked for its position, velocity, and acceleration. Material properties tend to alter during hopper flow due to compaction, expansion, and segregation. These features are difficult to model with a continuum approach. In the first part, material flow patterns are correlated with hopper angle and hopper opening, the two main design parameters. The typical shift from mass flow to funnel flow depending on the hopper angle was successfully simulated. In the second part, the discharge rate of material was quantitatively analyzed as function of hopper design parameters. Beverloo model 1 was tested on these simulated flow rates and it was shown that the simulated flow rates follow the model for this specific granular system. However, the DEM analysis was also able to demonstrate the failure of the traditional Beverloo model in the restricted flow regime. Simulated flow rates also follow the empirical correlations with hopper angle as stated in literature. DEM simulations were validated with experimental data for both material flow pattern and discharge rates.

Propriedade de fluxo e característica de escoabilidade de rações avícolas para dimensionamento de silos

O conhecimento das propriedades físicas e de fluxo dos produtos é de extrema importância no que se refere ao seu manuseio e processamento. Com a correta aplicação desses conhecimentos, é possível dimensionar de forma racional os sistemas de transporte e armazenagem utilizados, prevendo, assim, o tipo de fluxo ideal para cada operação. Este trabalho teve como objetivo determinar as propriedades físicas e de fluxo de três diferentes rações avícolas e avaliar suas influências nas características geométricas de tremonhas. Na obtenção dos dados, foi utilizado o aparelho de cisalhamento direto de translação (célula de cisalhamento de Jenike) e duas superfícies de parede: aço liso e rugoso. Para determinar o índice de fluxo (ff c) e o diâmetro mínimo do orifício de descarga (D), adotou-se a metodologia de Jenike enquanto que para o ângulo mínimo de inclinação da tremonha cônica, utilizou-se a metodologia de Enstad. Com base nos resultados obtidos, conclui-se que as Rações A e B foram classificadas como produtos coesivos enquanto que a Ração C apresentou os menores ângulos de inclinação da tremonha e maiores diâmetros de orifício de descarga.

Rapid granular flows on a rough incline: Phase diagram, gas transition, and effects of air drag

We report experiments on the overall phase diagram of granular flows on an incline with emphasis on high inclination angles where the mean layer velocity approaches the terminal velocity of a single particle free falling in air. The granular flow was characterized by measurements of the surface velocity, the average layer height, and the mean density of the layer as functions of the hopper opening, the plane inclination angle, and the downstream distance x of the flow. At high inclination angles the flow does not reach an x -invariant steady state over the length of the inclined plane. For low volume flow rates, a transition was detected between dense and very dilute (gas) flow regimes. We show using a vacuum flow channel that air did not qualitatively change the phase diagram and did not quantitatively modify mean flow velocities of the granular layer except for small changes in the very dilute gaslike phase.

Jamming patterns in a two-dimensional hopper

We report experimental studies of jamming phenomenon of monodisperse metal disks falling through a two-dimensional hopper when the hopper opening is larger than three times the size of the disks. For each jamming event, the configuration of the arch formed at the hopper opening is studied. The cumulative distribution functionsf d (X) for hoppers of opening sized are measured. (HereX is the horizontal component of the arch vector, which is defined as the displacement vector from the center of the first disk to the center of the last disk in the arch.) We found that the distribution off d (X) can be collasped into a master curveG(X) = f d (X)μ(d) that decays exponentially forX > 4. The scaling factorμ(d) is a decreasing function ofd and is approximately proportional to the jamming probability.

Flow property measurement of food powders and sensitivity of Jenike’s hopper design methodology to the measured values

The flow properties and powder physical properties were measured for 13 food powders. The flow properties were measured using shear cell techniques, and the powder physical properties measured were particle size, moisture, bulk and particle densities. The flowability of the food powders, as characterised by flow index, varied from easy flow to very cohesive. Particle size and moisture content do affect flowability, however there was no strong relationship for trying to relate the flowability of the food powders based solely on these physical properties. There was no relationship between measured powder physical properties and their wall friction characteristics. As a result, surface forces between the powder particles, and between particles and the wall surface play an important role in determining the flow nature of the powders, and this is an area requiring research. Jenike’s mathematical analysis to determine the minimum hopper angle and opening size for mass flow is the engineering standard practice for designing a hopper. Applying this analysis, using values of the measured food powder flow properties, shows that this can occasionally produce some unexpected values for the hopper opening size.

Jamming pattern in a two-dimensional hopper.

We perform granular flow experiments using metal disks falling through a two-dimensional hopper. When the opening of the hopper d is small, jamming occurs due to formation of an arch at the hopper opening. We study the statistical properties of the horizontal component X and the vertical component Y of the arch vector that is defined as the displacement vector from the center of the first disk to the center of the last disk in the arch. As d increases, the distribution function of X changes from a steplike function to a smooth function while that of Y remains symmetrical and peaked at Y=0. When the arch vectors are classified according to the number of disk n in the arch, the mean value <n> is found to increase with d. In addition, the horizontal component X(n) and the absolute value of the vertical component /Y(n)/ in each class have mean values increasing with n. Regarding the arch as a trajectory of a restricted random walker, we derive an expression for the probability density function a(n)(X) of forming an n-disk arch. The statistics (<n>,<X(n)>,</Y(n)/> and the fraction g(d)(n) of n-disk arches) of the arches generated by a(n)(X) agree with those found in the experiment.

Flow and jam of granular particles in a two-dimensional hopper

The jamming phenomenon of granular flow of mono-disperse disks in a two-dimensional hopper is studied experimentally. When the opening of the hopper d is small, jamming occurs due to formation of an arch at the hopper opening. The jamming probability as a function of the hopper opening width is measured which show a sharp decrease at some range of d. By observing the disk configurations of the arch in the jamming events, the jamming probability can be explained quantitatively using a restricted random walker model. The average horizontal and vertical spans of the jamming arch are calculated from the restricted random walk model which compares favorably with experiments.

DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge

While the discrete element method (DEM) is attracting increasing interest for the simulation of industrial granular flow, much of the previous DEM modelling has considered two-dimensional (2D) flows and used circular particles. The inclusion of particle shape into DEM models is very important and allows many flow features, particularly in hoppers, to be more accurately reproduced than was possible when using only circular particles. Elongated particles are shown here to produce flow rates up to 30% lower than for circular particles and give flow patterns that are quite different. The yielding of the particle microstructure resembles more the tearing of a continuum solid, with large-scale quasi-stable voids being formed and large groups of particles moving together. The flow becomes increasingly concentrated in a relatively narrow funnel above the hopper opening. This encourages the hope that DEM may be able to predict important problems such as bridging and rat-holing. Increasing the blockiness or angularity of the particles is also shown to increase resistance to flow and reduces the flow rates by up to 28%, but without having perceptible effect on the nature of the flow. We also describe our methodology for constructing and modelling geometrically complex industrial applications in three dimensions and present a series of industrially important three-dimensional (3D) case studies. The charge motion in a 5 m diameter ball mill and in a Hicom nutating mill, discharge from single- and four-port cylindrical hoppers, and particle size separation by a vibrating screen are demonstrated. For each case, plausible particle size distributions (PSDs) have been used. The results obtained indicate that DEM modelling is now sufficiently advanced that it can make useful contributions to process optimisation and equipment design. Finally the parallelisation of such a DEM code is described and benchmark performance results for a large-scale 2D hopper flow are presented.

FLOW PROPERTIES OF AFRICAN YAM BEAN (SPHENOSTYLIS STENOCARPA) AS AFFECTED BY ACCESSION AND MOISTURE CONTENT

Flow properties such as normal stress, shear stress, and initial shear stress, and hopper flow characteristics oftwo yam bean accessions (TSs 137 and TSs 138) were studied at four moisture content levels (4%, 8%, 12%, and 16 % wetbasis) to provide data for the design of handling and storage equipment. Two experimental designs were used: Randomizedcomplete block design (RCBD) with one observation per cell, and split plot in RCBD. The initial shear stress increased withmoisture content from 1.31 to 2.91 g/cm2 for TSs 137, while it increased from 1.58 to 3.09 g/cm2 for TSs 138. The hopper sidewall slope for the two accessions increased with moisture content from 60.21 to 64.06. The hopper opening size requiredincreased with moisture content and more than doubled at the highest value of moisture content studied, while the coefficientof mobility decreased with moisture content from 0.33 to 0.24. The accessions were found not to be statistically different interms of shear stress, coefficient of mobility, and side wall slope, but were statistically different in terms of normal stress, initialshear stress, and hopper opening dimensions. The methods of calculation of coefficient of mobility were observed not to bestatistically different, and the effect of normal loads and type of hopper opening was highly significant. There was also a highlysignificant effect of moisture content on all the flow properties (p < 0.05).

Finite Element Analysis of Bulk Solids Flow: Part 2, Application to a Parametric Study

Silos and bins are used in most process industries for the storage and handling of bulk solids. This paper deals with the application of a secant constitutive relationship for bulk solids in a transient finite element analysis of stresses, displacements and velocities during discharge of soybean from a silo. The object is to illustrate the use of the analysis procedure in a limited parametric study. The results in this paper are normal bin wall pressures, principal stresses in the stored material, soybean, and the spread of plasticity through the continuum. It is shown that the friction between wall and soybean and the hopper opening have a significant effect on normal wall pressures. It was found that in the hopper they increase considerably beyond the static ones in the first few seconds of flow, before decreasing as the level of the material falls. It was also found that the normal wall pressures in the vertical part of the bin increased very little during discharge.

Funnel Flow in Hoppers

Detailed observations of funnel flows of dry granular materials in wedge-shaped hoppers of different geometries are presented. The variations of the flow regime with changes in the height of material in the hopper/vertical bin configuration, the width of the vertical bin, the hopper angle and the hopper opening width were investigated and a number of specific flow regimes identified (mass flow and several forms of funnel flow). In the first part of the paper particular attention is paid to the conditions for transition from one flow regime to another; in particular it is shown that the existence of a funnel depends not only on the hopper angle but is also strongly dependent on the geometry of the hopper/bin system. In the second part of the paper the variations in the shape of the funnel near the exit opening are explored in detail.

E-90-P COMPARATIVE TEST OF HAMMER MILL PULVERIZER AND DRY PAN FOR CRUSHING STREATOR SHALE1

In the machines as described below the following points are discussed: (1) the grinding action, (2) energy consumption per ton ground, (3) capacity to produce fines six-mesh and under, (4) to determine the operating characteristics of the hammer mill. The conclusions given are: (1) The dry pan will not grind shale chunks larger than 15 inches maximum diameter, nor chert nodules of any size. The hammer mill grinds easily in one operation all chunks small enough to go through the 20 × 42-inch hopper opening and all chert nodules. (2) The energy consumption of the dry pan as compared to the hammer mill in kw. hrs. per ton of fines through six-mesh is approximately as 1.40 to 1.25. (3) The maximum capacity of the Frost %foot dry pan with 1/4-inch screen plate openings was known to be approximately 25 tons through six-mesh per hour. The maximum capacity of the 30 × 42-inch Williams hammer mill as reached in these tests with hand feeding was found to be 56 tons total feed and 42 tons through six-mesh per hour. This figure could have been greatly exceeded if the material could have been fed more rapidly. The dry pan tailings coarser than six-mesh compared to the hammer mill tailings of the same coarseness are as 40 to 25%. (4) The hammer mill is more efficient than the dry pan in practically all respects if properly set up and operated, but it is easily possible to secure less efficient results from the hammer mill, particularly if the feeding is not properly regulated.