Hopper Flow Research Articles

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.

DEVELOPMENT OF SOFTWARE TO DETERMINE PRESSURES IN MULTICELULARSILOS WITH CONCENTRIC AND ECCENTRIC DISCHARGE

A computer program for determining the pressures, horizontal and friction, in prismatic slender silos, with square section, eccentric hopper and mass flow, international codes taken as basis were: AS 3774 (1996), DIN 1055-6 (2005) and BS EN 1991-4 (2006) and the theories proposed by Safarian (1969) and Walker (1966). The development application was made possible by the development of a computational algorithm in programming “Borland Delphi”. The program was carried out for five silos projects with truncated pyramid form hopper considering the following eccentricities: 25%, 30%, 35% and 43%, as well as a concentric model for comparison. The computer program allowed SILOEXCENTRIC easily and quickly be applied to slender prismatic geometry of silos with concentric and eccentric hoppers. The results demonstrated the efficiency of the computer program for the proposed objectives So SILOEXCENTRIC results in pressures that are stored in files in “Notepad” format that may be accessed are generated. Besides files, various data are presented in graphical form, facilitating the assessment of horizontal pressures and friction, which proved adequate to international standards, considering the limit states.

A numerical study of dynamics in thin hopper flow and granular jet**Project supported by the National Natural Science Foundation of China (Grant Nos. 11705256 and 11905272), the National Postdoctoral Program for Innovative Talents, China (Grant No. BX201700258), Young Scholar of CAS "Light of West China" Program for Guanghui Yang (Grant No. 2018-98), and the Strategic Priority Research Program of the

The dynamics of granular material discharging from a cuboid but thin hopper, including the hopper flow and granular jet, are investigated via discrete element method (DEM) simulations. The slot width is varied to study its influence on the flow. It is found the flow in the cuboid hopper has similarity with the flow in two-dimensional (2D) hopper. When the slot width is large, the flowrate is higher than the predicted value from Beverloo’s law and the velocity distribution is not Gaussian-like. For granular jet, there is a transition with varying slot width. For large slot width, there is a dense core in the jet and the variations of velocities and density are relatively small. Finally, the availability of continuum model is assessed and the results show that the performance with large slot width is better than that with small slot width.

Capillary forces on wet particles with a liquid bridge transition from convex to concave

The transition of a liquid bridge profile from convex to concave and the associated capillary forces are experimentally studied via particle-particle and particle-plane pairs. The results demonstrate that a convex liquid bridge appears at a relatively large water volume and small separation distance, where the capillary force remains approximately constant. As the separation distance increases, the liquid bridge is stretched from convex to concave, and the capillary force initially doesn't change much but increases to the maximum value and then decreases gradually. By combining analytical analysis and experimental data, a framework is proposed for predicting the evolution of liquid bridge profiles. Additionally, a capillary force model that is applicable to both convex and concave liquid bridges is formulated. The applicability of this force model to multiple-particle systems is demonstrated by comparing DEM predictions of repose angles of sandpile and hopper flow discharge rates with experimental measurements at various water contents.

Effect of Particle Shape on Repose Angle Based on Hopper Flow Test and Discrete Element Method

The repose angle of granular material is an essential parameter to understand the microbehavior of the granular material and, then, to relate it with the macrobehavior. In this study, a self‐design large‐scale hopper flow test apparatus has been developed to measure the repose angle of the ballast using a fixed funnel method. Then, the numerical simulation using the realistic clump is compared with the experimental test to prove its validity. Meanwhile, the idealized clumps with custom shape parameters, including roughness of particle and ground, angularity, aspect ratio, and sphericity, were chosen to analyze the influences of particle shape on the repose angle. The results show that the angle of repose generally tends to increase with the increase of the friction coefficient of particles and the roughness of the ground. With the increase of the angularity from 0 to 4, the pile height and the repose angle increase. Meanwhile, the extended area decreases accordingly. For cuboid particles, with aspect ratio increasing from 1.0 to 1.67, the angle of repose increases firstly and then maintains a constant between aspect ratio 1.25–1.67. For ellipsoid particles, the angle of repose decreases, then reaches a minimum at aspect ratio around 1.3, and finally increases.

Hopper flows of mixtures of spherical and rod‐like particles via the multisphere method

AbstractThe discharge of granular media from hoppers plays a vital role in many solids handling operations. The dynamic flow of poly‐disperse nonspherical particles differs markedly from mono‐disperse spheres and highlights the need to rigorously account for particle shape effects. The multisphere discrete element method (MS‐DEM) was utilized here to examine the bulk packing fraction, discharge rate, collisional stress tensor, and order parameter of a bi‐disperse sphere‐rod mixture evacuating a hopper. A modified form of the Myers and Sellers correlation with variable shape factor is capable of replicating the MS‐DEM discharge data. The collisional stress tensor is observed to be highly symmetric for mono‐disperse spheres but becomes asymmetric when rod‐like particles are introduced. The order parameter within the hopper increases significantly during discharge and the rod‐like particles undergo shear induced alignment with their long dimensions orthogonal to the outflow plane.

Influence of particle packed pattern on the transient granular flow in a wedge-shaped hopper

A hopper has very wide and vital applications in handing the granular materials in daily life and industrial production, and the full understanding of the granular flow inside a hopper is of great importance to control and optimize the discharge process. By employing experimental and numerical methods, the influence of particle packed pattern on the transient granular flow is investigated in terms of the particle-scale kinetics and structure. For the mono-sized particles packed pattern, despite the similar particle-scale structure, smaller particles achieve greater kinetic energy conversion efficiency, which helps shorten the discharge time. For the binary-sized particles uniform mixing pattern, the interaction between particles increases the individual kinetic energy and transient average coordination number (CN) of large particles, while decreases that of small ones. Then the in-between kinetic energy and the disperse structure are reached. For the layer by layer mixing pattern, the strong percolation effect caused by the upper small particles hinders the increase of the individual kinetic energy at the beginning of the discharge process, and the transient average CN at the layer interface abruptly reaches 8. By contrast, when the small particles are placed at the bottom, more particles are active in the larger space, and subsequently, a looser structure is achieved in a shorter period.

A novel particle tracking velocimetry method for complex granular flow field**Project supported by the National Natural Science Foundation of China (Grant Nos. 11572201 and 91634202).

Particle tracking velocimetry (PTV) is one of the most commonly applied granular flow velocity measurement methods. However, traditional PTV methods may have issues such as high mismatching rates and a narrow measurement range when measuring granular flows with large bulk density and high-speed contrast. In this study, a novel PTV method is introduced to solve these problems using an optical flow matching algorithm with two further processing steps. The first step involves displacement correction, which is used to solve the mismatching problem in the case of high stacking density. The other step is trajectory splicing, which is used to solve the problem of a measurement range reduction in the case of high-speed contrast The hopper flow experimental results demonstrate superior performance of this proposed method in controlling the number of mismatched particles and better measuring efficiency in comparison with the traditional PTV method.

Wall stress analysis in an unsteady hopper flow with ellipsoidal particles

Design of bulk solid storage vessels requires the knowledge of wall stress distribution in static and moving beds of granular materials. Most previous studies have shown that for spheres, side wall stress developed in hoppers increases with the distance from the top surface but there is hardly any limited value. Theoretically, the wall stress profile can be predicted by Jessen-Walker-Walters theory. However, wall stress is affected by many variables, particularly the shape of granular materials. In this work, ellipsoids which can represent a large number of particle shapes are used to investigate the effect of particle shape on the wall stress profile developed in a cylindrical hopper. The results show that due to the better flowabilities, spheres exert higher maximum stress on walls than ellipsoids. Wall stress for ellipsoids approaches a constant value quickly. It is also found that the wall stress distribution is not affected much by orifice size, but solid bed height. Further, an attempt is made to characterize the two parameters of wall friction coefficient μ and the lateral stress ratio KA in Jessen-Walker-Walters theory, indicating that both μ and KA vary with aspect ratio of ellipsoids. The assumption of the constant μ and KA may bring significant error in the wall stress prediction.

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.

Wireless detector for translational and rotational motion of spherical-particle flow

To measure the translational and rotational motion of spherical particles in a three-dimensional granular flow, a wireless spherical detector with a built-in wireless module and a three-axis gyroscope and three-axis accelerometer was developed. The three-axis acceleration and three-axis angular velocity can be measured and stored by the detector in real time. The attitude angle, the spatial rotation of the detector coordinate system relative to the laboratory coordinate system, described via the Euler angle is obtained with a Quaternion algorithm and Kalman filter. The gravity acceleration component in the acceleration data can be removed with the attitude angle. The test results show that the acceleration error is ±0.02G, and the average cumulative angle error is 0.02°/s. Finally, the detector was tested as a tracer particle in hopper flow. According to the results, the variation value of the rotation angles of the spherical detector obeys an exponential distribution.

Effects of aspect ratio and component ratio on binary-mixed discharging pebble flow in hoppers

As an important class of particle flows in industrial applications, hopper flows, particularly those using pebbles (diameters dp ~O(10-2) m), play a significant role in nuclear reactor engineering, e.g. HTGR and ADS reactors. However, the features and influencing factors of the binary mixture discharge have not yet been widely investigated. In this study, the discrete element method (DEM) simulation was adopted to analyze the discharge flow of binary mixtures consisting of ellipsoids and spheres in a hopper. After a model validation, the effects of particle aspect ratio (Ra, the ratio of the major axis to the minor axis) of ellipsoids and component ratio (Rn, the ratio of the ellipsoid number to the sphere number) of ellipsoids to spheres were analyzed. Flow patterns were visualized by colored pebble stripes according to pebbles' initial heights. Particle discharge flow rates were computed to examine their relations to particle aspect ratios and component ratios. The force structure and distributions of the binary mixtures were also explored. Results showed that pebble stripes followed quadratic function profiles. Adding ellipsoids was advantageous for particles discharging at lower particle aspect ratios (Ra≤2), while impedimental at large particle aspect ratios (Ra≥3). The discharge flow rate was inversely proportional to the particle aspect ratio at fixed component ratios, and linearly proportional to the 1/4th power of the component ratio at fixed particle aspect ratios. In addition, the discharge flow rate showed low sensitivity to the initial packing states of particles when the particle aspect ratio and component ratio were fixed.

Improved PTV measurement based on Voronoi matching used in hopper flow

To improve the particle-matching accuracy of the particle tracking velocity (PTV) measurement method, this paper proposes a PTV measurement technology called V-PTV technology. The method first extracts the coordinates of the particle points in two consecutive frames, and then constructs a Voronoi diagram for the obtained particle-point data set. Precise matching among different particles is achieved by establishing a matching relationship with the largest cross-correlation coefficient because of the high similarity of the Voronoi grid structure. It can be seen from the results of the numerical simulation experiment that the particle tracking accuracy of V-PTV is always above 95% compared with other traditional methods. Finally, the particle-velocity distribution in the different regions in the hopper, and that of the velocity with time before blockage, are observed using V-PTV measurement.，which verifies the effectiveness of the method proposed in this paper.

Understanding the local flow rate peak of a hopper discharging discs through an obstacle using a Tetris-like model

Placing a round obstacle above the orifice of a flat hopper discharging uniform frictional discs has been experimentally and numerically shown in the literature to create a local peak in the gravity-driven hopper flow rate. Using frictionless molecular dynamics (MD) simulations, we show that the local peak is unrelated to the interparticle friction, the particle dispersity, and the obstacle geometry. We then construct a probabilistic Tetris-like model, where particles update their positions according to prescribed rules rather than in response to forces, and show that Newtonian dynamics are also not responsible for the local peak. Finally, we propose that the local peak is caused by an interplay between the flow rate around the obstacle, greater than the maximum when the hopper contains no obstacle, and a slow response time, allowing the overflowing particles to converge well upon reaching the hopper orifice.

A Tetris-like Model Showing a Universal Enhanced Flow Rate of a Hopper Discharging Hard Discs Through an Adjustable Inclusion

In the literature, placing an inclusion near the orifice of a hopper, containing disc particles, has been experimentally and numerically reported to locally enhance the gravity-driven hopper flow rate. Moreover, the peaked flow rate can happen regardless of the interparticle friction, the inclusion geometry, or the disc dispersity. To reveal the fundamental reason causing this local effect, we propose a Tetris-like model that sequentially moves one disc particle at a time towards the hopper orifice. A Gaussian displacement function that independently controls a disc's movement in the horizontal or vertical direction, and the algorithm of the model accepts a movement as long as it creates no overlap between objects in the system. Our model creates an artificial steady probability-driven hopper flow without knowing the Newtonian dynamics which allows interparticle collaborative motion. Under specific conditions, we reproduce the enhanced flow rate and show that a moderate response time of the system and a flow rate difference between its value around the inclusion and its maximum without an inclusion are sufficient to explain this local effect with no Newton's laws involved.

Surface breakage of fired iron ore pellets by impact

Surface breakage or attrition occurs when iron ore pellets are subjected to handling stages in which the stressing level is insufficient to cause their massive fracture. This breakage mechanism has been investigated for five types of industrial iron ore pellets from impacts against a steel target, leading to a model that accounts for the effect of pellet size, impact energy and angle. The model is then validated on the basis of two different tests. First, a tumbling test on a small drum (0.305 m diameter) is used to demonstrate the validity of the model to describe surface breakage by motion of the pellets at comparatively low velocities, such as those that are found during flow in hoppers and silos. The model is also validated on the basis of simulations of a RO-TAP® sieve shaker. It is demonstrated that it is able to predict with confidence results from the tests, proving to be a powerful tool when used in combination with simulations using the discrete element method, to predict mechanical degradation due to surface breakage during handling.

Low cost irregular feed stock for laser powder bed fusion

Spherical powders are almost exclusively deployed for metal laser powder bed fusion (LPBF) additive manufacturing (AM). In this work, low-cost irregular powder feedstock is studied for its potential in three key areas to meet minimum AM process requirements, namely: (1) hopper flow, (2) layer spreading, and (3) de-powdering. Irregular water-atomized Iron powder was used as the study population, while spherical plasma-atomized Inconel 625 powder was used as the control. Powder flow characteristics were obtained using a FT4 Powder Rheometer (Freeman Technology). Layer spreading was evaluated indirectly via powder bed density measurements. Measurements were quantified by using printed artifacts for captive powder and evaluated using isopropanol infiltration and three-dimensional computed tomography (CT) imaging (Zeiss Xradia 520 Versa). Powder clearing from fine channels was quantified through vision-based measurements of printed artifacts (Dino-Lite DinoCapture 2.0). The results from this work demonstrated that: (1) A larger opening and steeper hopper angle are necessary to maintain a mass flow regime with the irregular powder. (2) Powder bed density is similarly consistent across the bed indicating adequate spreadability. (3) Water-atomized Iron powder has better de-powdering characteristics in the smallest cleared 0.6 mm diameter features, likely due to its 15% lower bed density.

A counterintuitive way to speed up pedestrian and granular bottleneck flows prone to clogging: can ‘more’ escape faster?

Dense granular flows through constrictions, as well as competitive pedestrian evacuations, are hindered by a propensity to form clogs. We use simulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contact-averse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar effect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individual pedestrians.

Hopper flow of irregularly shaped particles (non-convex polyhedra): GPU-based DEM simulation and experimental validation

Numerous practical applications of the Discrete Element Method (DEM) require a flexible description of particles that can account for irregular and non-convex particle shape features. Capturing the particle non-convexity is important since it allows to model the physical interlocking when the particles are in contact. To that end, the most flexible approach to capture the particle shape is via a polyhedron, which provides a faceted representation of any shape, albeit at a significant computational cost. In this study we present a decomposition approach to modeling non-convex polyhedral particles as an extension of an existing open source convex polyhedral discrete element code, BlazeDEM-GPU, which computes using general purpose graphical processing units (GPGPUs). Although the principle of decomposition of non-convex particles into convex particles is not new, its application by the discrete element modeling community has been rather limited. The non-convex extension of BlazeDEM-GPU was validated using a hopper flow experiment with identical convex and identical non-convex 3D printed particles. The experiment was designed around two sensitive flow points, with the convex particles following the intermittent flow and the non-convex particles forming stable arches. It was demonstrated that the DEM simulations can be applied to reproduce both the convex and the non-convex flow behavior using the same parameter set. This study is a significant step towards general computing of non-convex particles for industrial-scale applications using the GPGPUs.

Trap Model for Clogging and Unclogging in Granular Hopper Flows.

Granular flows through narrow outlets may be interrupted by the formation of arches or vaults that clog the exit. These clogs may be destroyed by vibrations. A feature which remains elusive is the broad distribution p(τ) of clog lifetimes τ measured under constant vibrations. Here, we propose a simple model for arch breaking, in which the vibrations are formally equivalent to thermal fluctuations in a Langevin equation; the rupture of an arch corresponds to the escape from an energy trap. We infer the distribution of trap depths from experiments made in two-dimensional hoppers. Using this distribution, we show that the model captures the empirically observed heavy tails in p(τ). These heavy tails flatten at large τ, consistently with experimental observations under weak vibrations. But, here, we find that this flattening is systematic, which casts doubt on the ability of gentle vibrations to restore a finite outflow forever. The trap model also replicates recent results on the effect of increasing gravity on the statistics of clog formation in a static silo. Therefore, the proposed framework points to a common physical underpinning to the processes of clogging and unclogging, despite their different statistics.