Hopper Flow Research Articles

Critical numerical analysis of quasi-two-dimensional silo-hopper discharging

We present a critical comparative analysis between numerical and experimental results of quasi-two-dimensional silo and hopper flows. In our approach, the Discrete Element Method was employed to describe a single-layer mono-disperse sphere confined by two parallel walls with an orifice at the bottom. As a first step, we examined the discharge process, varying the size of the outlet and the hopper angle. Next, we set the simulation parameters fitting the experimental flow rate values obtained experimentally. Remarkably, the numerical model captured the slight non-monotonic dependence of the flow rate with the hopper angle, which was detected experimentally. Additionally, we analyzed the vertical velocity and solid fractions profiles at the outlet numerically and experimentally. Although numerical results also agreed with the experimental observations, a slight deviation appeared systematically between both approaches. Finally, we explored the impact of the system’s confinement on this process, examining the consequences of particle-particle and particle-wall friction on the system macroscopic response. We mainly found that the degree of confinement and particle-wall friction have a relevant impact on the outflow dynamics. Our analysis demonstrated that the naive 2D approximation of this 3D flow process fails to describe it accurately.

Triggering flow of jammed cohesive granular materials using modulated pulsed airflow

AbstractRealizing the stable high‐flux flow of cohesive granular materials is a complicated subject. We experimentally studied the dynamic characteristics of cohesive granular materials discharged from hopper under modulated pulsed airflow. Results show that pulsed airflow with a smaller duty cycle can effectively trigger the stable flow of jammed cohesive granular materials. Furthermore, under proper working conditions, the hopper flow will change from the classic arch breaking mode to a free flowing mode like liquid. The flow rate of the powder in the free flowing mode will decrease as powder bed height decreases, which overturns the consistent recognition. The oscillating shear provided by the pulsed airflow eliminates the Janssen effect and achieves a liquid‐like stress transmission, which supports the above findings. Through energy analysis, we gave the scaling relationship between the pressure gradient and the pulse parameters to cover the experimental data and revealed the internal mechanism.

Techniques to Determine Powder Flow Properties

The goal of the current work was to do an orderly assessment of flow of powders and granules using compendial and non-compendial procedure. Angle of repose, Tapped density, Carr's compressibility file, Bulk density, Hausner’s ratios were assessed. Moreover, flow was described utilizing powder rheometer wherein delicate force transducer screens the forces created as consequence of the sample displacement, another technique FT4 powder rheometer. The Freeman Technology (FT4 powder rheometer) is intended to describe powders undergoing different circumstances in manners that look like wide scale creation climate. Techniques incorporate security and irregular flow rate, compressibility, shear cell, air circulation, porousness, divider contact and union. The FT4 has demonstrated application on the whole powders preparing ventures, including drugs, fine synthetic substances, cosmetics, food, additives and powder covering. The FT4 application connect to filling, hopper flow, Tablet pressure, wet granulation, end point, flow added substance determination and enhancement, moisture impacts, static change, feeding, stirring, separation, caking, processing, Wall grating, grip, hopper configuration etc.

Static and dynamic pressure measurements of maize grain in silos under different conditions

Silos are used worldwide to store products of high commercial value. However, many questions remain unanswered regarding storage and estimation of pressures in silos. Furthermore, there are few full-scale experimental stations in the world to facilitate the study of silo pressures, hindering progress in this area. The aim of this paper is to describe the setup, calibration, and validation of a pilot-scale test facility. The pilot silo described here contains 59 measurement cells capable of measuring loads and pressures throughout the silo. In addition, it can be used to study maximum and dynamic pressures in the filling, static, and discharge phases using a range of stored products. Validation of this test facility using maize yielded reliable and novel results, which were compared with Eurocode 1, part 4 (CEN, 2006). Pressures were obtained in the pilot silo at two different grain heights: 2.77 m and 5.30 m, and were evaluated in all three filling, static, and discharge phases. Normal and friction pressures in the silo, vertical stress at the silo–hopper transition, product weight, flow rate, and test time were recorded. The results obtained were consistent with the standard and the findings reported in other studies, demonstrating the accuracy of the pilot silo calibration and thus validating the experimental model. Some of the novel findings obtained include the moment of maximum pressure at the transition during discharge and the influence of silo slenderness on settling of the material during filling and under static conditions. • Product accommodation is influenced by the slenderness of the silo. • The moment of maximum pressure in the transition is influenced by the slenderness. • The slenderness of the silo influences the moment of the maximum friction pressure. • The greater the slenderness of the silo, more maximum normal pressure points. • Normal and friction pressures on the wall are influenced by slenderness.

Bimodal frequency distribution of granular discharge in 2D hoppers

As a classical example of granular flow, gravity-driven hopper flow has been studied for decades, but an in-depth understanding of its fluctuation is still lacking, especially at small-scale and short-term. In this experimental and numerical study, the time interval (tΔ) between the discharging of two consecutive grains from hoppers under a series of geometrical and operating conditions is characterized by its probability density function (PDF). By ensemble averaging over a large number of cases, the PDF from simulation and experiments was found to be consistent but totally different for small and big orifices. Three modes of particle discharging were found and each matches a section of the PDF, with two of the modes found in simulating the discharging of hard sphere gas through an orifice, which suggests a similar mechanism behind the two phenomena. These findings may be helpful to the designing and operation of high-precision feeding system, such as in pharmaceutical industries.

Measurement of granular temperature and velocity profile of granular flow in silos

In this paper we report experimental results on the granular temperature and velocity profile of glass beads in steady-state flow inside a flat-bottomed silo. We found that the dynamics of the granular system during the discharge is stable on the mesoscopic scale. In particular, the ordered directional movement of particles can occur near the orifice. In addition, the correlation between the granular temperature distribution and velocity vector field is opposite in the radial and axial directions. According to the kinetic model, the main cause for the reversal of spatial correlation is that the intensity of the particle diffusion decrease with the decrease of silo height. This highlights a surprising and unrecognized role that the diffusion motion of particles plays in energy dissipation for hopper flow.

Strategic placement of an obstacle suppresses droplet break up in the hopper flow of a microfluidic soft crystal

When granular materials, colloidal suspensions, and even animals and crowds exit through a narrow outlet, clogs can form spontaneously when multiple particles or entities attempt to exit simultaneously, thereby obstructing the outlet and ultimately halting the flow. Counterintuitively, the presence of an obstacle upstream of the outlet has been found to suppress clog formation. For soft particles such as emulsion drops, clogging has not been observed in the fast flow limit due to their deformability and vanishing interparticle friction. Instead, they pinch off each other and undergo break up when multiple drops attempt to exit simultaneously. Similar to how an obstacle reduces clogging in a rigid particle system, we hypothesize and demonstrate that an obstacle could suppress break up in the two-dimensional hopper flow of a microfluidic crystal consisting of dense emulsion drops by preventing the simultaneous exit of multiple drops. A regime map plotting the fraction of drops that undergo break up in a channel with different obstacle sizes and locations delineates the geometrical constraints necessary for effective break up suppression. When optimally placed, the obstacle induced an unexpected ordering of the drops, causing them to alternate and exit the outlet one at a time. Droplet break up is suppressed drastically by almost three orders of magnitude compared to when the obstacle is absent. This result can provide a simple, passive strategy to prevent droplet break up and can find use in improving the robustness and integrity of droplet microfluidic biochemical assays as well as in extrusion-based three-dimensional printing of emulsion or foam-based materials.

The role of the hopper angle in silos: experimental and CFD analysis

In this work, we reported experimental and numerical results of granular flows in silos and hoppers. We used a very flexible experimental setup, allowing us to explore the entire domain of the hopper angles. In addition, the granular flow was also studied numerically using Computational Fluid Dynamics. First, the numerical protocol was validated, comparing the output with experimental data of mass flow rate. In general, we obtained a good quantitative agreement between numerical and experimental results using a single set of the model parameters. Remarkably, the numerical results reproduced very well the weak non-monotonic behavior of the mass flow rate dependence on the hopper angle obtained experimentally. Stepping forward, we examined the scaling properties of the simulated velocity v(r) and density $$\phi (r)$$ profiles at the outlet region. Finally, we also analyzed the velocity and volume fraction field inside the silo. The outcomes suggested that fast dynamics at orifice perturbs the system distinctly, depending on the hopper angle. Interestingly, small and large angles showed a larger zone of influence in comparison with intermediate angles.

Discrete Element Modeling (DEM) based investigation of tribocharging in the pharmaceutical powders during hopper discharge

Triboelectric charging is defined as the phenomenon of charge transfer between two different material surfaces when they are brought into contact and separated. The focus of this research is the development of a Discrete Element Method (DEM) based simulation model to predict tribocharging during hopper discharge. Due to decreased particle-wall interactions and reduced particle wall contact times, net charges generated during hopper discharge are low. The simulation model confirmed this effect and was implemented to predict the triboelectric behavior of glass beads and MCC particles during hopper flow, along with the prediction of percent charged and uncharged particles. Approximately one-third of the particles were predicted to remain uncharged during the hopper discharge simulations for mono-dispersed particles, thus rendering a comparatively high amount of charge distribution into a small concentration of materials. The DEM model acted as a tool to predict charges that can be generated during hopper discharge at a specified geometry, with a potential to mitigate particle charging, when used for appropriate selection of hopper angles, and hopper wall materials.

Flow characterization of compressible biomass particles using multiscale experiments and a hypoplastic model

Poor flowability of compressible biomass particles poses severe handling challenges in all processes of biorefineries, which results in poor energy-yielding in conversion. This paper presents the characterization of the flow behavior of a widely used compressible biomass material (ground loblolly pine) using a combination of physical characterization and numerical simulation. An advanced hypoplastic model with implementation and validation in Abaqus VUMAT is adopted. A workflow is established to calibrate material parameters directly from index tests, an oedometer test, and a Schulze ring shear test, and indirectly from numerical simulations of those tests. The finite element simulation of axial shear tests and hopper flow tests using the calibrated hypoplastic model is shown to capture key flow attributes, such as the maximum shear stress in shear tests, as well as the mass flow rate and flow pattern in hopper. The results demonstrate that a subset of the laboratory tests needs to allow large strains for adequate characterization of compressible granular flow, and numerical models developed for non-compressible materials can accurately predict the flow behavior of compressible biomass material, even though strain magnitudes are not scaled correctly. This study provides a potent tool to decipher and resolve material handling upsets in biorefineries and other energy industries that utilize forest products.

Quantitative measurement of hopper flow using MRI

To gain fundamental insight into granular flow behaviour, quantitative measurements of velocity and solid fraction are required. The aim of this study is to measure the solid fraction and velocity of 3D granular flows quantitively using a recently developed MRI method. Time-averaged spatial maps of the solid fraction and velocity are obtained for hoppers with wall angles of 30°, 60°, and 90°. From these maps, the mass flow rate of the material was calculated along the height of the hoppers. Excellent agreement was observed between the MRI and gravimetric mass flow rate measurements, confirming the quantitative nature of the measurements. The resulting solid fraction and velocity measurements provide insight into the dynamics of granular flow.

Influence of an inserted bar on the flow regimes in the hopper* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11705256 and 11905272), National Postdoctoral Program for Innovative Talents, China (Grant No. BX201700258), and West Light Foundation of the Chinese Academy of Sciences (Grant No. 2018-98).

We investigated the influence of an inserted bar on the hopper flow experimentally. Three geometrical parameters, size of upper outlet D 1, size of lower outlet D 0, and the height of bar H, are variables here. With varying H we found three regimes: one transition from clogging to a surface flow and another transition from a surface flow to a dense flow. For the dense flow, the flow rate follows Beverloo’s law and there is a saturation of inclination of free surface θ. We plotted the velocity field and there is a uniform linear relation between the particle velocity and depth from the free surface. We also found that the required value of D 1 to guarantee the connectivity of flow is little smaller than D 0. For the transition from a surface flow to a dense flow, there is a jump of flow rate and the minimum θ for flowing is two degrees larger than the repose angle.

Analysis of particle shape effect on the discharging of non-spherical particles in HTR-10 reactor core

The discharge flow characteristics of particles are crucial in many industrial applications, and the shape of particle is an important influencing factor to the particle flow behavior. In this study, the discrete element method (DEM) was adopted to analyze the discharge flow of non-spherical particles in HTR-10 reactor core. After model validation, the shape effect on particle flow in hopper was analyzed. The super-ellipsoid model was used to the comparative study of particles with 5 different shapes which can represent a large number of shapes, including oblate ellipsoidal particles, prolate ellipsoidal particles, circular cylindrical particles, elliptical cylindrical particles, and cubical particles, respectively. The results showed that the more stable the packing structure, the higher the efficiency of the stacked volume. But the mobility of these particles was worse than particles with good flow properties. The increase in the blockness (n1 and n2) will make the fluidity of the particles worse, and the particles with aspect ratio (Ra) between 1.5–2 show better discharge behavior. Both the axial and radial velocity can be influenced by particle shape significantly, which will result in different discharge behavior. Rotation angle and direction angle distribution are introduced to analyze the rotation motion. Cylindrical particles showed the most obvious rotation, while the ellipsoidal particles rotated in a relatively small range.

Beverloo law for hopper flow derived from self-similar profiles

We use particle simulations to investigate the mass flow in two-dimensional hopper flow and to analyze the dependency of the flow rate with the bottleneck width and the particle diameter. A flow rate law is derived from self-similar velocity and density profiles at the neck. The resulting relation is an enhancement of the Beverloo relation that incorporates the dependency of the density with the neck width. The parameters of the Beverloo relation are interpreted by coupling the hourglass theory with the free-fall arch theory using non-zero arch velocity as accounted by the hourglass theory.

Jamming probability of granular flow in 3D hopper with shallow columns: DEM simulations

We performed a numerical study of the jamming that stops the flow of granular material from a three-dimensional hopper discharging due to gravity. When the hopper outlet is not much larger than the particles, granular material clogs the hopper outlet due to the formation of an arch or dome. For a wide range of particle diameters, we obtained the size distribution of the “avalanche,” defined as the number of particles that fall before jamming. We repeated this process through a discrete element method model verified with a simple experiment. From these distributions, we determined the probability of the flow jamming before N particles pass through the hopper. As the ratio between the hopper outlet diameter and the particle diameter increases, the probability that an arch will block the outlet decreases. We show here that the probability of one particle passing through the hopper is not constant when there are not sufficient particles. Then, we propose a new model that can quantify changes in particle passing probability. Using this model, we derive the particle passing probability in a hopper with shallow columns and confirm that the probability of one particle passing through the hopper is closely related to the pressure acting on the bottom of the hopper.

The effects of physical factors on the granular hopper flow

The flowing behavior of granular materials is known as granular flow, which is ubiquitous in nature, industry and daily life. The behavior is not only related to flowing particles’ properties such as size, shape, density, and coarseness, but also to the external environments such as the flow channel and outlet. Therefore, the granular flow exhibits abundant non-linear phenomena. By now, great achievements have been made in the engineering field, but a unified theoretical framework is still absent. Consequently, it is very necessary to systemically investigate the effects of different parameters on the granular flow. This will be beneficial to deepen the understanding of flowing behavior, uncover the flowing mechanism, as well as potentially open a new avenue of establishment of the constitutive equations. This paper mainly focuses on the hopper flow including gravity-driven hopper, inclined hopper and velocity-driven horizontal hopper, and presents the dependence of the flow rate, flow pattern, particle velocity and packing fraction on various physical factors. These factors involve the outlet size, outlet position, outlet shape, coefficient of friction of inter-particles, particle shape, outlet number, external stimulus, obstacles, and hopper angle. The results can provide significant reference for tuning the flow rate and transportation efficiency, as well as serve as the basis for the future research.

TO THE SUBSTANTIATION OF THE STORAGE BUNKER DESIGN FOR A HIGH-ACCURACY VOLUMETRIC DOSING DEVICE

The paper substantiates the design of one of the main components of a high-precision volumetric dosing device for bulk materials - its storage hopper. It is determined that hopper structural design should avoid possible hang-ups of the product processed and maintain rather uniform dense packing of the material on its way to the dosing area. The process of bulk material flow in a storage hopper was studied numerically by discrete element method. It is concluded that hopper design should be axially symmetric, with defect-free walls, and expanding at an angle of 2-4° to its base.

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.

DEM study on the effects of pellet characteristics on particle flow in rectangular hopper

In this work, a non-cohesive and multi-element particle model of discrete element method (DEM) was constructed, which was used in combination with experiments to investigate the particle flow characteristics in retangular hopper equipped with the screw discharging machine. On this basis, different diameter pellets (dp = 20 mm, 25.02 mm) with various sphericities (φ = 0.868, 0.985, 1) and particle size distribution (a = 0:1, 0.1:0.9, 0.15:0.85, 0.2:0.8) were selected to examine the effects of sphericity and particle size distribution on the distribution of particle average velocity, motion distance and voidage. Our results showed that as the a increased, the particle average vertical velocity was first decreased and then increased. The motion distance of particles at 1/2 bed height was relatively stable. Furthermore, the average voidage of cylindrical particles was the largest and that of ellipsoidal particles was the smallest. Finally, the specific position of the lag of particle motion is revealed.

Periodic instationarities of granular flows in conical hoppers

Granular flows through converging sections such as conical hoppers have been reported to be submitted to instationarities, which in certain circumstances can appear to be organized and periodic. In this paper, we explore this phenomenon by conducting discrete element modelling simulations of a 3D gravity-driven hopper flow and varying a large number of parameters such as hopper geometry and granular sample properties. Dedicated postprocessing techniques are developed and used to investigate the spatial and temporal patterns of these instationarities and to bring some understanding on the physics of this spontaneous phenomenon. Numerical results show that a clear structure appears for these instationarities, under the form of rapidly propagating waves relating variations in velocity magnitude and coordination number. While very faint, periodic variations of the sample density are also detected. The parametric study reveals that the self-organization of these variations requires a narrow set of conditions in terms of hopper geometry and intergranular contact friction coefficient.