Hopper Flow Research Articles

Wet Granular Flow in Hoppers by Discrete Element Method

This paper presents a comparison numerical study of the dry and wet granular flows in a cylindrical hopper with flat bottom by means of the discrete element method. A cohesion model is used to examine the impact of moisture presence in hopper flow. It is found that with the increase of Bond number, the discharge rate decreases. The particle force structure inside the hopper is investigated to explain the reason of the lower discharge rate for the wet particle cases. Compared with the dry particle case, in the wet particle case there are more force chains in the transitional zone and near orifice, which causes the lower flowability of particles.

Granular flow during hopper discharge

Granular material freely discharging from a hopper under gravity is one of the oldest and most widely studied problems in granular flow. Despite the apparent simplicity of the system, expressions relating the discharge rate of the hopper to the properties of the individual grains are difficult to determine and typically empirical in nature. A mathematical model for discharge from a hopper is derived based on the dynamics of individual particles just within the outlet. In contrast to previous models, this analysis derives a flow rate from granular dynamics, rather than dimensional arguments. The model, therefore, uses no assumptions about the form of the stress distribution within the hopper, or the addition of empirical factors or fitting parameters. Our model gives a flow rate identical in form to a well-known empirical expression, showing that an experimentally determined constant used in this expression is purely geometry-dependent. Our analysis is also extended to derive an expression for the flow rate incorporating gas drag, which becomes dominant at small grain sizes, significantly reducing the outflow rate. The resulting expression shows excellent agreement with a range of computational simulations using a coupled discrete element and Navier-Stokes method. These simulations also show that the gas flow is much more complex than previously assumed in this region, and simplified assumptions used in prior hopper flow models do not hold.

Membrane theory treatment of eccentric flows in concentric hoppers

This paper presents an initial study of the effects of an accidental eccentric flow channel that sometimes develops in the conical hopper of a metal storage silo. A simple assumed pressure regime is adopted, based on studies of eccentric discharge in cylindrical silos, and the structural actions are analysed using shell membrane theory. The results are verified against a finite element analysis. A set of equations is derived which give the complete membrane stress state in the hopper under such an unsymmetrical pressure regime. Under symmetrical loading, silo hoppers are subject to biaxial tension, with failure normally governed by material rupture due to tensile meridional membrane stresses. It is found that the eccentric flow channel leads to dramatically increased meridional membrane stresses at the transition. Compressive membrane stresses are also found near the hopper outlet and at the sides of the flow channel near the transition. A reasonably close correlation is found between the derived membrane theory equations in a right circular conical hopper and linear elastic finite element predictions.

Discrete element method modeling of corn-shaped particle flow in rectangular hopper

Discrete element method (DEM) was developed to simulate the corn-shaped particles flow in the hopper. The corn-shaped particle was described by four overlapping spheres. Contact force and gravity force were considered when establishing the model. In addition, flowing characteristic of particles in the hopper was studied. The effect of friction coefficient on the wall pressure, voidage and velocity distribution was analyzed. The results show that the discharge rate decreases with the friction coefficient increasing; and the “over-pressure” phenomenon occurs in the discharging process for two different friction coefficients. The voidage also increases as the friction coefficient increasing. And the velocity distribution is more uniformity and is closer to the mass flow with the friction coefficient deceasing.

Flowability of lunar soil simulant JSC-1a

We have done a complete flowability characterization of the lunar soil simulant, JSC-1a, following closely the ASTM-6773 standard for the Shulze ring shear test. The measurements, which involve pre-shearing the material before each yield point, show JSC-1a to be cohesionless, with an angle of internal friction near 40°. We also measured yield loci after consolidating the material in a vibration table which show it to have significant cohesion (≈ 1 kPa) and an internal friction angle of about 60°. Hopper designs based on each type of flowability test differ significantly. These differences highlight the need to discern the condition of the lunar soil in the specific process where flowability is an issue. We close with a list—not necessarily comprehensive—of engineering rules of thumb that apply to powder flow in hoppers.

Constitutive model to predict flow of cohesive powders in bench scale hoppers

Abstract This communication empirically correlates flow in two systems; an instrumented rotating drum (GDR) and a set of bench scale hoppers. A flow index obtained from measurements in the GDR is directly correlated to the flow through hoppers, providing a predictive method for hopper design and a convenient experimental test for screening materials and determining their suitability for specific hopper systems. Simulations were performed to understand the dynamics of flow in hoppers by using the same flow parameters in hoppers and rotating cylinders. Simulations showed that as cohesion increased it becomes harder for the particles to flow through the hoppers, in good agreement with the experiments. The effect of hopper angle also yields similar findings to experiments for Avicel, K =60, where the powder does not flow through the 45° hopper but flows well in a 75° hopper. Simulations were also used to calculate the normal forces on the walls of the hopper and the wall pressure distributions in both hoppers. As depth increases, the wall pressure increases for all cases. Finally, the simulations also helped understand the different flow behaviors (funnel and mass flow) that take place in a hopper. The simulated dynamics of flow in the rotating drum and in the hopper correlate very closely to experiments, indicating that the model cohesion parameters are, as desirable, material-specific but independent of geometry.

Discrete element method modeling of non-spherical granular flow in rectangular hopper

Discrete element method (DEM) was developed to simulate the corn-shaped particles flow in the hopper. The corn-shaped particle was described by four overlapping spheres. Contact force and gravity force were considered when establishing the model. In addition, the velocity distribution and voidage variance of corn-shaped and spherical particles were investigated. The results show that the vertical velocity difference between centre and side wall and the horizontal velocity of corn-shaped particles are relatively larger than that of spherical particles. The mean voidage for corn-shaped particles is smaller than for spherical particles in any hopper. And the mean voidage values decrease with the increase of the ratio of width and length ( D/ L) and the ratio of height and width ( H/ D) for both corn-shaped and spherical particles. The local voidage profiles in hoppers with different D/ L were also studied. It demonstrates that the wall effect on the voidage of spherical particles is more remarkable than that of the corn-shaped particles. The voidage fluctuations of corn-shaped and spherical particles decrease obviously with increasing D/ L when the particles are far away from the wall. And when the particles are discharging, the wall effect on the spherical particles is more remarkable than the condition of packing naturally.

Characteristics of Powder Flow and Interstitial Air Pressure in Dual Structure Hopper Using Air Vibration

A dual structure hopper which consists of a cone hard container and a flexible container of soft material can avoid the blockage phenomenon of cohesive powder near the orifice using the periodic vibration by the air pressure which changes on the opening and shutting times of the solenoid-controlled valve. This study experimentally investigated the characteristics of powder flow structure and interstitial air pressure during the discharge of flyash powder of 22.4μm from an orifice of this hopper when the air pressure and the opening time were changed. Then, the discharge mass of powder, the interstitial air pressure and the flow pattern in powder bed were measured. It is found that the cavity is generated by the collapse of powder bed due to the air vibration, and that it has risen toward the top of powder bed inside the hopper. And, the continuous discharge of powder and the periodic interstitial air pressure by the change of flow structure of powder bed can be confirmed. In addition, we made a schematic diagram of powder flow in the dual structure hopper using air vibration, and discussed powder flow state inside the hopper.

Molecular dynamics simulation of complex particles in three dimensions and the study of friction due to nonconvexity

We investigate the macroscopic properties of frictionless nonconvex particles using molecular dynamics. The calculations are based on a simple and efficient method to simulate complex-shaped interacting bodies. The particle shape is represented by Minkowski operators. A multicontact time-continuous interaction between bodies is derived using simple concepts of computational geometry. Three-dimensional simulations of hopper flow show that the nonconvexity of the particles strongly affects the jamming on granular flow. Also the model allows the representation of complex bodies with rough surfaces as in friction studies and the reproduction of a wide range of friction and dilatancy angles as in true triaxial tests.

PIV Technique applied to granular flows in hoppers

In this work we report a technical method based on PIV, usually used in fluid dynamics, to measure velocity profiles of granular materials in silos and hoppers. The particles inside the hopper were filmed by a digital video camera. Finally, we measure the velocity profile of granular materials inside a quasi-two dimensional hopper and compare the data with some existing models.

Vibration induced flow in hoppers: continuum and DEM model approaches

A 2D and a 3D discrete element model (DEM) simulation of cohesive spherical particles are applied to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The model is closely compared with a continuum model based on arch stability. A significant aspect of this study is the scaling of the continuum system to a discrete system of 500 particles in 2D and 2500 particles in 3D. This illustrates how such models can complement each other. The continuum model can cope with a full-scale industrial system, but is complex with significant assumptions. The discrete approach is relatively simple at the particle level with minimal assumptions but computationally demanding. The DEM model supports the basic conclusions of the continuum model. The vibration source must be located at the appropriate height above the outlet on the hopper to optimise its flow enhancement. Too low and stable arches can form above. Too high and it might not break the stable arches in the material below. The passive/active nature of the material during vibration and flow is also illustrated. The DEM model also shows that low frequency high amplitude vibration can enable flow through small orifices.

Vibration induced flow in hoppers: DEM 2D polygon model

A two-dimensional discrete element model (DEM) simulation of cohesive polygonal particles has been developed to assess the benefit of point source vibration to induce flow in wedge-shaped hoppers. The particle–particle interaction model used is based on a multi-contact principle. The first part of the study investigated particle discharge under gravity without vibration to determine the critical orifice size ( B c) to just sustain flow as a function of particle shape. It is shown that polygonal-shaped particles need a larger orifice than circular particles. It is also shown that B c decreases as the number of particle vertices increases. Addition of circular particles promotes flow of polygons in a linear manner. The second part of the study showed that vibration could enhance flow, effectively reducing B c. The model demonstrated the importance of vibrator location (height), consistent with previous continuum model results, and vibration amplitude in enhancing flow.

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.

Response to perturbations for granular flow in a hopper

We experimentally investigate the response to perturbations of circular symmetry for dense granular flow inside a three-dimensional right-conical hopper. These experiments consist of particle tracking velocimetry for the flow at the outer boundary of the hopper. We are able to test commonly used constitutive relations and observe granular flow phenomena that we can model numerically. Unperturbed conical hopper flow has been described as a radial velocity field with no azimuthal component. Guided by numerical models based upon continuum descriptions, we find experimental evidence for secondary, azimuthal circulation in response to perturbation of the symmetry with respect to gravity by tilting. For small perturbations we can discriminate between constitutive relations, based upon the agreement between the numerical predictions they produce and our experimental results. We find that the secondary circulation can be suppressed as wall friction is varied, also in agreement with numerical predictions. For large tilt angles we observe the abrupt onset of circulation for parameters where circulation was previously suppressed. Finally, we observe that for large tilt angles the fluctuations in velocity grow, independent of the onset of circulation.

Modeling granular segregation in flow from quasi-three-dimensional, wedge-shaped hoppers

Granular materials may segregate upon processing and handling based on differences in particle properties such as size, density, or shape. In most instances, this segregation is problematic in that product quality is usually dependent on maintaining homogeneity of the blend. The present work investigates the causes and extent of segregation of granular materials during discharge from a hopper using the discrete element method. A quasi-three-dimensional, wedge-shaped hopper is modeled using two parallel periodic boundary conditions. The effects of various particle properties, such as diameter ratio, mean size, and mass fraction of each species, as well as hopper geometries, such as the height, width, outlet width, and wall angle, on the segregation results are examined. Additionally, the effects of friction coefficient and hopper fill methods are investigated. Results show that many factors affect the extent of segregation during hopper discharge, but some of the key factors include the particle diameter ratio, mass fraction, and ratio of hopper outlet to mean particle diameter as well as the hopper wall angle and wall roughness. Additionally, the method used to fill the hopper is shown to play a significant role in determining the segregation upon discharge. Visualization of the internal hopper flow patterns gives insight into the causes of segregation, which then aids in the proposal of various recommendations for reducing the extent of segregation during hopper discharge.

Dilatant shear bands in solidifying metals

Compacted granular materials expand in response to shear, and can exhibit different behaviour from that of the solids, liquids and gases of which they are composed. Application of the physics of granular materials has increased the understanding of avalanches, geological faults, flow in hoppers and silos, and soil mechanics. During the equiaxed solidification of metallic alloys, there exists a range of solid fractions where the microstructure consists of a geometrically crowded disordered assembly of crystals saturated with liquid. It is therefore natural to ask if such a microstructure deforms as a granular material and what relevance this might have to solidification processing. Here we show that partially solidified alloys can exhibit the characteristics of a cohesionless granular material, including Reynolds' dilatancy and strain localization in dilatant shear bands 7-18 mean crystals wide. We show that this behaviour is important in defect formation during high pressure die casting of Al and Mg alloys, a global industry that contributes over $7.3 billion to the USA's economy alone and is used in the manufacture of products that include mobile-phone covers and steering wheels. More broadly, these findings highlight the potential to apply the principles and modelling approaches developed in granular mechanics to the field of solidification processing, and also indicate the possible benefits that might be gained from exploring and exploiting further synergies between these fields.

フロンティア研究シリーズ ＭＲＩによる粒子流および粒子系混相流の内部流動計測

It is difficult to measure a particle motion inside a dense granular flow or a fluid-particle flow because of the existence of other particles. MRI is one of the non-invasive measurement techniques for such flows. MRI can measure the velocity distribution (tagging method and phase method), which is an outstanding advantage of the MRI measurement. This paper briefly explains the principle of the MRI measurement. Then MRI is applied to some dense granular flows or fluid-particle flows, such as rotating drums, vibrated granular beds, hopper flows and spouted beds.

A method for predicting hopper flow characteristics of pharmaceutical powders

This communication correlates two empirical methods; flow in a rotating drum with flow in bench scale hoppers. The flow characteristics of 13 cohesive granular materials were studied in the gravitational displacement Rheometer (GDR) and compared to flow in hoppers of varying angle and discharge diameter at fixed temperature and moisture conditions. The GDR proved to be an effective and convenient tool for examining flow properties of pharmaceutical materials, both pure and mixtures. A flow Index obtained from GDR measurements is directly correlated to the flow through hoppers, providing a predictive method for hopper design and a convenient experimental test for screening materials and determining their suitability for specific hopper systems. Analysis of industrial scale hoppers will be addressed in future communication.

Analysis and Interpretation of Hopper Flow Behaviour Using Electrical Capacitance Tomography

AbstractThis paper presents a critical analysis of the application of electrical capacitance tomography (ECT) to exploring the behaviour of solids flow during hopper discharge. Particulate media are employed in many areas such as the food industry, civil and chemical engineering etc. This is a report of work on the measurement of parameters that determine hopper flow for several different types of particulate systems, using a hopper of adjustable geometry equipped with ECT sensors. There is a comparison of different data analysis methods including: Bayesian/MCMC spatial modelling; reconstructed measurements analysis; raw data processing and theoretical descriptions. Measurement and interpretation protocols suited to detection of particular flow phenomena are assessed and recommended.

Numerical investigation of steady and unsteady state hopper flows

This paper presents a numerical study of the steady and unsteady state granular flows in a cylindrical hopper with flat bottom by means of the discrete element method (DEM). For both flows, the simulations were conducted under comparable conditions so that the similarity and difference between them can be examined. The distributions of the physical properties including velocity, force structure, stress and couple stress for the two hopper flows are investigated. The results suggest that the trends of these distributions for the two hopper flows are similar. In particular, for both cases, the distributions of the normal stresses are related to the normal force structures. Thus, corresponding to the large interaction forces between particles near the bottom corner and in the transitional zone, all the normal stresses are large near the bottom corner, and the radial and circumferential normal stresses are relatively large in the transitional zone. However, there are differences in the magnitudes of some physical properties for the unsteady and steady state flows. Compared with the steady state flow, the unsteady state flow has a narrower velocity distribution, and more particles experience large contact forces. Its radial and circumferential normal stresses in the plug flow and transitional zones are larger. With the decrease of the number of particles or with discharging time, the plug flow and transitional zones reduce, and the differences in the considered properties except wall shear stress and couple stress between the two flows decrease.