Hopper Discharge Research Articles

Effect of lognormal particle size distributions of non-spherical particles on hopper discharge characteristics

This study focusses on the hopper discharge characteristics of lognormal particle size distributions (PSDs) of non-spherical particles (namely, ellipsoids, cylinders and cuboids). Discrete element method is employed to understand the coupled effects of sphericity and lognormal PSD width. The results reveal that: (i) the ellipsoids have the most similar discharge behaviors with the spheres, but the differences increase as the PSD width increases; (ii) the packing density in the hopper increases as PSD width increases and particle sphericity decreases; (iii) regardless of sphericity, the discharge rate decreases and the jamming probability increases as the PSD width increases; (iv) for the same PSD width, the jamming probability is the greatest for cuboids and least for the ellipsoids; and (v) the lower-sphericity cylinder and cuboid have some residual particles left in the hopper upon complete discharge, and the number of residues is greater and increases with PSD width for the latter. The results provide new insights regarding the behavior of wide PSDs of non-spherical particles in the hopper, highlighting the non-negligible impact of the coupled effect of PSD and particle non-sphericity.

Study on the influence of different carrier gases on the fluidization properties of glass bead and FCC powders

The powder flow was influenced by carrier gas in the unit operation, such as pneumatic conveying and hopper discharge, in the pressurized entrained flow gasification technology. Carrier gases play a vital role in fluidization/ defluidization of powders. In this paper, we investigate the fluidization/ defluidization of absorbent Fluid Catalytic Cracking (FCC) and non-absorbent glass bead with two different carrier gases, N2 and CO2. The flowability of aerated powders with different carrier gases were obtained in the fixed bed region whose superficial gas velocity was lower than minimum fluidization gas velocity and fluidization region. The powder flowability was characterized by basic flow energy, flowability rate index and aeration energy with the help of FT4 powder Rheometer. The influence of different carrier gases on fluidization/ defluidization of powder bed was further discussed. Transition line of A/C powders with different carrier gases was revealed. Effect of gas type and interparticle force were calculated, compared with the flowability of aerated powder bed. In addition, combined with bed stress analysis, different bed fluidization mechanism with different gas velocities were revealed. Our findings might help people understand the influence of carrier gases on the fluidization/ defluidization of powders in the relative chemical unit operations.

Modeling segregation of polydisperse granular materials in hopper discharge

Size segregation of polydisperse materials during hopper discharge is problematic in various industrial situations. However, due to the complexity of hopper discharge flow kinematics and limited prediction techniques for polydisperse segregation, accurate modeling of polydisperse segregation during hopper discharge has been challenging. We extend the application of a general predictive continuum model that captures the effects of segregation, diffusion, and advection to polydisperse hopper flow. Model predictions of segregation within the hopper and the average particle diameter during discharge match experimentally validated discrete element method simulations and experiments.

Discrete element method study on hopper discharge behaviors of binary mixtures of nonspherical particles

AbstractThis study is aimed at unveiling the influence of binary mixtures of nonspherical particles on hopper discharge behavior, which remains poorly understood. The discrete element method (DEM) is employed to simulate seven particle types with aspect ratios between 0 and 2 (namely, a sphere, two ellipsoids, two cylinders, and two cuboids) with the same volume. Seven monodisperse systems and twelve binary‐shape mixtures are assessed. For the monodisperse systems, particle shape is the dominant factor dictating discharge rate, compared to other factors like aspect ratio, preferential orientation, and packing. Regarding the binary‐shape mixtures, the discharge rates are similar for all twelve mixtures, reflecting a surprising lack of shape effects, which in turn means the negligible impact of solid volume fraction, aspect ratio, and segregation extent. Moreover, collision force is generally negatively correlated with discharge rate.

Flow characteristics of nonspherical granular materials simulated with multi-superquadric elements

The superquadric equation is typically used to mathematically describe nonspherical particles and construct particle shapes with different surface sharpness and aspect ratios. However, nonspherical elements constructed using the superquadric equation are strictly convex, limiting their engineering application. In this study, a multi-superquadric model based on a superquadric equation is developed. The model combines several superquadric elements that can be used to construct concave and convex particle shapes. Four tests are performed to examine the applicability of the multi-superquadric approach. The first involves a comparison of theoretical results for a single spherocylinder impacting a flat wall. The second involves the formation of a nonspherical granular bed. The third investigates the effects of the particle shape on the hopper discharge and angle of repose. The final test evaluates the mixing behaviors of granular materials within a horizontally rotating drum. These tests demonstrate the applicability of the multi-superquadric approach to nonspherical granular systems. Furthermore, the effects of particle shape on the packing density, discharge rate, angle of repose, and Lacey mixing index are discussed. Results indicate that concave particles have a lower packing density, flow rate, and mixing rate and higher angles of repose than convex particles. Interlocking of elements becomes more pronounced for concave particles and results in local cluster structures, thereby enhancing the stability of granular systems and limiting sliding or rotation between nonspherical particles.

Effect of grain moisture content on physical, mechanical, and bulk dynamic behaviour of maize

Variations in the moisture content (MC) of grains strongly influence machine performance analysis during crop harvesting and post-harvest grain handling operations. For experimental or numerical methods such as discrete element method (DEM) technique to include the effect of MC on physical and mechanical properties, comprehensive study was conducted to investigate the effect of maize MC on single kernel properties and bulk grain dynamic responses, which have relevance for DEM crop model calibration. Individual kernel properties of shape, size, coefficient of restitution, and stiffness, and bulk material responses of bulk density, angle of repose, direct shear test (angle of internal friction, apparent cohesion), hopper flowability, and grain-machine interaction (GMI) impact plate forces responses were measured on maize samples at 11%, 16%, and 26% MC levels. At individual particle responses of coefficient of restitution and stiffness, maize kernels at MC of 26% had significantly the lowest values compared to the values at the other MC (11% and 16%). Increasing maize MC reduced the hopper discharge flowability by 20% and GMI impact plate forces by 25%. Significant effects of MC on the material behaviours should be considered for calibration of DEM maize models.

Hopper discharge of cohesive powders using pulsated airflow

AbstractAn aerated hopper with pulsated aeration was designed to study the effect of square‐wave pulsated airflow on the discharge characteristics of cohesive and non‐cohesive powders. Experiments were carried out with pulsation frequencies between 0 (continuous) and 50 Hz. Two flow patterns were observed at different aeration rates and pulsation frequencies: intermittent and smooth. For non‐cohesive powders, pulsated aeration has a worsening effect on discharge flow. For cohesive powders, results revealed that pulsated aeration can reduce the minimum aeration necessary to allow continuous discharge. And the maximum discharge rate that can be attained applying pulsated aeration is higher than that of continuous aeration and it is significantly more uniform. The aggregates size of the powder was estimated and used to understand the stabilizing mechanism of pulsated aeration on the aggregative discharge. The model value of the minimum aeration rate and the discharge rate were obtained and compared with the experimental values.

Scaled-up rice grain modelling for DEM calibration and the validation of hopper flow

Industrial-scale simulation of the interaction between rice grains and equipment using the discrete element method (DEM) is limited due to the high computing power requirement. Volume-based scaled-up modelling of DEM rice particle and calibration of DEM input parameters were investigated as an alternative approach towards realising industry scale simulation-based design support of rice grains flow behaviour. Calibration of DEM input parameters using scaled-up DEM particles is challenging because distortions in the DEM material properties due to unavoidable disparities between the true and DEM particle sizes. A DEM calibration methodology that applies virtual design of experiment (DOE) using scaled-up DEM rice particle model was applied to predict bulk angle of repose (AOR) of unshelled rice grains. Rice DEM particle shape was scaled-up by three times its original prolate spheroid particle shape and then approximated using seven-clumped DEM spheres matching the scaled-up spheroid rice particle. Using DEM parameter values of the rice model calibrated to match AOR at a relative error (RE) of 0.39%, the DEM model predicted hopper discharge rates from experiment and using the analytical solution of Beverloo et al analytical solution at relative errors (REs) of 0.66% and 0.03%, respectively. Hopper unloading time predicted by DEM had a RE of 0.93% when compared with experiment. A 60% saving in CPU time was achieved relative to the unscaled DEM rice particle model with good agreement to the rice flow test. This showed that the techniques of volume-based particle scaling and DOE calibration are effective methods for industry-scale simulation of small grains.

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.

Gas-assisted discharge flow of granular media from silos

We studied experimentally the discharge of a vertical silo filled by spherical glass beads and assisted by injection of air from the top at a constant flow rate, a situation which has practical interest for nuclear safety or air-assisted discharge of hoppers. The measured parameters are the mass flow rate and the pressure along the silo, while the controlled parameters are the size of particles and the flow rate of air. Increasing the air flow rate induces an increase in the granular media flow rate. Using a two-phase continuum model with a frictional rheology to describe particle-particle interactions, we reveal the role played by the air pressure gradient at the orifice. Based on this observation we propose a simple analytical model which predicts the mass flow rate of a granular media discharged from a silo with injection of gas. This model takes into account the coupling with the gas flow as well as the silo geometry, position and size of the orifice.

Characterization of microcrystalline cellulose spheres and prediction of hopper flow based on a μ(I)-rheology model

The objective of this study was to characterize the rheology of a pharmaceutical material in the context of the µ(I)-rheology model and to use this model to predict powder flow in a manufacturing operation that is relevant to pharmaceutical manufacturing. The rheology of microcrystalline cellulose spheres was therefore characterized in terms of the μ(I)-rheology model using a modified Malvern Kinexus rheometer. As an example of an important problem in pharmaceutical manufacturing, the flow of these particles from a hopper was studied experimentally and numerically using a continuum Navier-Stokes solver based on the Volume-Of-Fluid (VOF) interface-capturing numerical method. The work shows that the rheology of this typical pharmaceutical material can be measured using a modified annular shear rheometer and that the results can be interpreted in terms of the μ(I)-rheology model. It is demonstrated that both the simulation results and the experimental data show a constant hopper discharge rate. It is noted that the model can suffer from ill-posedness and it is shown how an increasingly fine grid resolution can result in predictions that are not entirely physically realistic. This shortcoming of the numerical framework implies that caution is required when making a one-to-one comparison with experimental data.

Effects of elongated particles rotation on discharge flow of mixed granular systems

Previous study has reported that adding elongated particles to cohesive granular matters can significantly improve their flowability. In this study, the mechanism of how the elongated particles work to this system was experimentally investigated. The experimental system included a quasi-two-dimensional visualization hopper and a high speed camera to record the flow behavior of the mixed granular systems consisting of glass beads and elongated particles during hopper discharge. Experiments revealed that the discharge rate first increased and then decreased as the mass fraction of elongated particles increased. It was observed that during the discharge flow, the elongated particles rotated and caused local secondary flow of the glass beads. This resulted in a significant increase in flowing layer thickness. Consequently, the effect of elongated particles rotation on discharge flow was discussed. Finally, the estimation of rotational torque of elongated particles was proposed to quantitatively describe the increase of discharge rate.

Hopper discharge of elongated particles of varying aspect ratio: Experiments and DEM simulations

Steady flow of particulate or granular materials and bulk solids through a hopper plays a critical role in many industrial and process engineering applications. The present work investigates hopper discharge of non-spherical particles, specifically cylindrical particles, from a rectangular hopper. The behavior of steel cylindrical particles with varying aspect ratio (both varying diameter with constant length and varying length with constant diameter) was explored experimentally and via DEM simulations. In addition, the effects of fill height, particle friction, hopper orifice width and hopper cone angle on hopper discharge rate of non-spherical particles were studied via DEM simulations and compared with previously published experimental correlations, experimental results of spherical particles. The results indicate that DEM simulations are fully capable of reproducing trends that are established experimentally. The results with particles of high aspect ratio indicate a different trend than that previously observed with rounded particles. As the fill height increases, the mass discharge rate increases and then asymptotes; further increases in fill height cause a decrease in the mass discharge rate. Further, the effect of particle friction showed a significant influence on the hopper discharge behavior. In addition, a decrease in the hopper angle from 90 degree to critical angle 55 degree decreases the mass discharge rate flow and further decrease in hopper angle increases the discharge rate rapidly.

Study of the discharge behavior of Rosin-Rammler particle-size distributions from hopper by discrete element method: A systematic analysis of mass flow rate, segregation and velocity profiles

In the present work, the discrete element method (DEM) is used to investigate the behaviour of Rosin-Rammler (R-R) particle size distribution (PSD) during hopper discharge. The study attempts to identify mass flow rate (MFR) and segregation as a function of spread parameter (PSD width) and location parameter, which includes detailed analysis of bulk density, segregation and velocity profile of particles. The applicability of the widely used Beverloo correlation for prediction of MFR for studied R-R PSDs is also investigated. The results show that, (1) MFR increases as PSD width (at fixed location parameter) increases, whereas MFR decreases with increase in location parameter at fixed PSD width; (2) the studied R-R PSDs exhibit a monotonic trend of flow bulk density and MFR with respect to PSD width and location parameter; (3) the effect of PSD width on overall segregation is found to be more than the location parameter; (4) the velocity profiles for considered R-R PSDs vary along the height of hopper, but remain uniform in shape and follow a pure parabolic increase from the hopper wall; (5) DEM flow rate prediction shows a good agreement with the Beverloo correlation by applying the concept of flow bulk density.

Standardized Friction Experiment for Parameter Determination of Discrete Element Method and Its Validation Using Angle of Repose and Hopper Discharge

The discrete element method (DEM) is the most common computational approach to simulate the dynamic behavior of powder. The material properties used in DEM simulation strongly affect its results. Among these material properties, it is difficult to measure the exact values of friction coefficients, including static and rolling friction coefficients, because they differ according to environmental conditions and other material properties such as particle size, particle shape, and roughness of vessel walls. In this study, four standardized experiments are performed to measure the static and rolling friction coefficients between particles and a vessel. The accuracy of the measured friction coefficients is confirmed using the repose angle and the discharge velocity of a hopper. DEM simulation is performed using the measured friction coefficients, and the results show excellent agreement with experimental results.

A fast detection algorithm based on the envelope function of dilated polyhedron

The dilated polyhedron is generated by the Minkowski Sum with a basic polyhedron and a dilated sphere. It has characteristics of both polyhedron and sphere and can be employed for the discrete element simulation of complex shaped particles. The weighted summation of the sphere function and the second-order dilated function of polyhedron is adopted as the envelope function of the dilated polyhedron. The contact detection problem of dilated polyhedrons is translated into an optimization problem between two envelope functions, which improves the detection efficiency of dilated polyhedrons. The contact center between these two envelope functions can be obtained through the optimization problem which can be solved by the Lagrange multiplier method. Based on the contact center, the nearest points on each basic polyhedron can be detected quickly, and therefore the contact normal and overlap between these two particles can be solved accordingly. With the above method, an improvement in the contact detection of dilated polyhedra is achieved by avoiding the complexity that caused by the calculation of each geometric feature in early methods. This article develops a non-spherical DEM based on the dilated polyhedron with the fast contact detection algorithm and the nonlinear contact force model. The single-particle falling process is simulated to analyze the effect of the smoothness parameter to the result. The analysis illustrates that the smoothness parameter has small effect at the range of 0.0001–0.1. Besides, the smaller the smoothness parameter is the closer the results, which shows that the method of this article has good stability. The discharge process of multiple particles in the rectangle hopper with different particle shapes is simulated, while the residual particle fraction during hopper discharge is adopted to validate with existing experimental and numerical results. The reliability of the fast detection algorithm and the nonlinear contact model proposed in this paper is verified by the validation.

Modeling granular material segregation using a combined finite element method and advection–diffusion–segregation equation model

A two-dimensional, transient, multi-scale modeling approach is presented for predicting the magnitude and rate of percolation segregation for binary mixtures of granular material in a rotating drum and conical hopper. The model utilizes finite element method simulations to determine the bulk-level granular velocity field, which is then combined with particle-level diffusion and segregation correlations using the advection-diffusion-segregation equation. The utility of this modeling approach is demonstrated by predicting segregation patterns in a rotating drum and during the discharge of conical hoppers with different geometries. The model exhibits good quantitative accuracy in predicting DEM and experimental segregation data reported in the literature for cohesionless granular materials. Moreover, since the numerical approach does not directly model individual particles, it is expected to scale well to systems of industrial scale.

Particle upscaling: Calibration and validation of the discrete element method

The discrete element method (DEM) is a numerical tool often used by engineers and researchers to design, analyse and improve bulk materials handling systems. However, the accuracy of any DEM model depends on the input values assigned to the parameters as determined through a calibration process. Together with this, limitations in computing power to model full scale systems are still limiting the use of DEM by industry. For this reason the particle size is often scaled up although the influence that it might have on the results has not been studied in great detail. In this study the calibration process made use of a large rotating drum to measure the dynamic angle of repose experimentally. The equivalent DEM model made use of particles scaled by a factor of up to 9. A small range of particle-particle coefficients of friction which accurately predicted the angle of repose could be identified for all scaling factors up to 4 (drum/particle diameter ≥25), while larger scaling factors gave inconsistent results. This calibrated parameter set was then used in modelling hopper discharge of the scaled particles. Here the results indicated that the maximum scale factor was independent of the size of the hopper opening and should be less than 1.3 and 2.5 to accurately model the rate of discharge and the velocity field respectively. This demonstrated that the maximum scale factor is application dependent and should be carefully selected. The correlations of Beverloo [1] and Villagran Olivares et al. [2] to predict the rate of discharge were compared to the experimental and DEM results. Beverloo's correlation could be accurately fitted for scaling of the hopper opening and the particles by factors of 2 and 4 respectively, however, the correlation by Villagran Olivares et al. failed to fully take the particle scale into account. It was shown that the parameter in this correlation is particle size dependent.

Effect of surface compositional difference on powder flow properties

Surface composition plays an important role in the cohesion/adhesion behavior of powders. Yet, the quantification of the major factors that affect powder kinematics is a challenge because of the surface composition heterogeneity of granular materials. This study aims to understand the mechanisms that drive cohesiveness in dry powders by evaluating the bulk flow performance of uniform size glass beads coated with distinct chemical components. Silica beads of 125, 180, and 250 μm were coated with corn starch, molasses, butter, or wheat gluten to reproduce the surface composition of food powders. Particle size and shape distributions, dynamic flow properties, shear flow properties, and compressibility profile of the coated materials were evaluated and compared with uncoated silica beads. The stability index, a dynamic flow property, ranged from 0.9 to 1.1 for all samples, which indicated a stable flow. Surface modified powders showed increasing bulk cohesion and higher compressibility indexes in comparison with the control samples. Specifically, butter and molasses coated powders had the highest specific energy, cohesion, and compressibility indexes, primarily, due to the higher magnitude of interparticle interactions, lower bulk densities, and poor bed dilatancy. This study provides quantitative understanding on powder flow that will be important for smoother powder processing operations in which the surface compositional difference is of major interest such as hopper discharge, high shear mixing, and tablet compaction processes.

Understanding the varying discharge rates of lognormal particle size distributions from a hopper using the Discrete Element Method

The focus of this study is on understanding the varying discharge rates of lognormal particle size distributions (PSDs) with the same mean particle diameter. Discrete element method (DEM) is used to simulate lognormal PSDs with the same arithmetic mean of the particle diameter of 5 mm but varying PSD widths (σ/μ = 10% to 70%) in a 3D conical hopper. Four highlights are noted: (i) the Beverloo correlation and others modified to account for various particle properties predict the discharge rates of lognormal PSDs poorly, which underscores the need for more understanding on the influence of PSD width; (ii) the velocity vectors are less uniformly downwards in the hopper for the wider PSDs, which results in the slowing down of the discharge rate; (iii) the radial particle velocity, and both the radial and vertical particle angular velocity increase with PSD width throughout the first half of the hopper discharge; and (iv) the collision force magnitudes are greater for the wider PSDs, and the cross-sectional fluctuations of the collision forces at the cone height increases with PSD width. The increase of the magnitudes of these particle characteristics (namely, radial particle velocity, angular velocity, and collision force) with PSD width underlies the decreasing hopper discharge rate.