Hopper Flow Research Articles

Precursory arch-like structures explain the clogging probability in a granular hopper flow

The clogging phenomenon finds extensive application in both industrial processes and daily life events. While this broad spectrum of application motivated extensive research to identify the general factors underlying the clogging mechanism, it results in a fragmented and system-specific understanding of the entire clogging process. Therefore, it is essential to establish a holistic understanding of all contributing factors of clogging based on the microscopic physical mechanisms. In this paper, we experimentally investigate clogging of granular materials in a two-dimensional hopper flow and present a self-consistent physical mechanism of clogging based on precursory chain structures. These chain structures follow a specific modified restricted random walk, and clogging occurs when they are mechanically stable enough to withstand the flow fluctuations. We introduce a single-particle model that can explain the arch-forming probability. Our results provide insight into the microscopic mechanism behind clogging and a broader understanding of the dynamics of dense granular flow.

Repose angle prediction of railway ballast based on Hopper Flow Test and PCA-Stacking ensemble learning method

The deterioration of track ballast is mainly reflected in the fragmentation of ballast particles and the evolution of grading. The repose angle of the ballast is the internal friction angle, reflecting the shear strength of the track ballast. The angle of repose of 158 ballast samples with varying gradation parameters was tested by conducting hopper flow tests on ballast particles. Then, based on this database, a stacking ensemble regressor-based principal component analysis (PCA) was proposed for the repose angle prediction. The data are first processed by PCA and then randomized into the train (80%) and test (20%) data. Besides stacking ensemble regressor, five different individual regressors, including support vector regressor, k-nearest neighbors, random forest, gradient boosting decision tree, and adaptive boosting, are compared and analyzed. The results indicate that the stacking ensemble regressor performs better than single regressors and demonstrates enhanced robustness and generalization capabilities. Additionally, the Effect of the number of principal component indicators on the prediction accuracy is determined, and the difference in stacking ensemble prediction performance with and without PCA is discussed. Finally, a computer prediction system for ballast repose angle was developed to make the proposed stacking ensemble regressor directly applicable to the railroad construction site. This model can be used in practical track maintenance decisions, whereby the ballast gradation can facilitate rapid assessment of the angle of repose.

Identification of dominant DEM parameters for multi-component segregation during heap formation, hopper discharge and chute flow

Segregation of granular materials is a critical phenomenon in various industries, such as food processing, pharmaceuticals, and mining. The Discrete Element Method (DEM) is an effective tool for gaining insight into granular segregation by providing particle-level information and the freedom to model mixtures that are often difficult or impossible to achieve through experiments. To ensure realistic material behaviour and correct representation of segregation, it is essential to calibrate the model parameters systematically. However, in the context of multi-component segregation, it is extremely challenging and computationally expensive to consider all parameters in the calibration procedure since interaction parameters between components must also be considered. This work aims to identify the dominant DEM parameters for modelling multi-component segregation during hopper discharge, chute flow and heap formation in a mixture of pellet and sinter. Utilising a representative example of a multi-component mixture with different sizes, densities and shapes used in blast furnaces, the investigation is done for various initial configurations as well as various mass ratios of the mixture. Our findings revealed that, while only particle-geometry interaction parameters dominate the segregation after the hopper and chute flow, particle-particle parameters are also significant for segregation in the heap. We also demonstrated that the downstream segregation is significantly influenced by the segregation upstream. Moreover, we found that the effect of pellet-sinter interactions is negligible. This research provides insights into the dominant DEM parameters, facilitating more efficient and robust calibration of multi-component models in future research endeavours.

Application of fluid rheology models for milled woody biomass and non-recyclable municipal solid waste particles

Biofuels from biomass and non-recyclable municipal solid waste (N-MSW) can potentially replace aviation fossil fuels. However, the cost-effectiveness is impeded by feedstock handling issues, such as unstable flow or jamming in hoppers and feeders. This issue can be solved mainly based on enhanced understanding of the rheology of biomass and N-MSW particles, which remains poorly understood. Leveraging discrete and continuum-based granular rheology models, in this study, we conduct industry-scale hopper flow testing of milled woody biomass, paper, cardboard, foam, thin film, and plastic particles, and investigate the potential of using fluid rheology models to characterize the hopper flow behavior. The hopper flow tests demonstrate different flow behaviors of tested materials, including fast flow, stable-to-unstable flow, and varying flow rates. Numerical simulation of hopper flow tests utilizing the Gudehus-Bauer hypoplastic model demonstrates good agreement with experimental data for the biomass and rigid plastic particles, and those using non-Newtonian fluid models exhibit promising agreement with experimental data with low computational cost. However, new fluid rheological models are required to capture the unstable and varying rate flows of highly compressible particles such as paper and foam. This study advances the knowledge on the rheology of particulate biomass and N-MSW materials for biofuel production.

Experimental research of product flow in gravity loading hopper

Experimental research of product flow in gravity loading hopper

Discrete element modeling of granular hopper flow of irregular-shaped deformable particles

Many natural and engineered granular materials have relatively deformable particles. Besides particle size and shape, particle deformability is another salient factor that significantly impacts the material’s flow behavior. In this work, the flow of irregular-shaped deformable particles in a wedge-shaped hopper is investigated using discrete element simulations. A bonded-sphere model is developed to simultaneously capture irregular particle shapes and particle-wise deformations (e.g., compression, deflection, and distortion). Quantitative analysis of the effects of irregular shapes and particle deformations shows that the increase in particle stiffness tends to increase initial packing porosity and decrease the flow rate in the hopper. Rigid particles tend to have clogging issues, whereas deformable particles have less chance to, indicating particle deformation reduces the critical bridging width in the hopper flow. Detailed analysis of stress fields is also conducted to provide insights into the mechanism of particle flow and clogging. Stresses and discharge rates calculated from numerical simulations are compared and show good agreement with Walker’s theory and the extended Beverloo formula. Simulations with various particle shape combinations are also performed and show that the initial packing porosity decreases with an increasing percentage of fibers while the discharge rate has a complex dependency on particle shapes.

Finite element modeling of biomass hopper flow

Hoppers are widely used biomass handling devices that channel bulk biomass from storage to subsequent handling equipment. Jenike’s longstanding approach, based on the Mohr-Coulomb model, has been successfully used to design hoppers handling cohesionless granular materials such as grains and other agricultural produces. However, designing a hopper to ensure reliable biomass flow is found to be challenging due to cohesion, irregular particle shape, and bulk material elastoplasticity. This study aims to address the biomass handling engineering challenge with alternative constitutive material models concerning the flow behavior of bulk solids. Finite element modeling is an approach that allows for implementation of different material models, whose underlying constitutive theories assist in investigating the origin and manifestation of bulk mechanical behavior of granular materials. This study focuses on the incipient gravity hopper flow of two types of biomass feedstocks, i.e., ground corn stover and Douglas fir wood. Three widely used constitutive material models, i.e., Mohr-Coulomb model, modified Cam-Clay model, and Drucker-Prager/Cap model, are implemented. Using the flow pattern represented by the volume of biomass exhibiting more than 7% of axial strain (Kamath and Puri, 1999), the finite element model predicts that the bulk corn stover particulate material forms an arch, which represents a hampered transition from the static state to the dynamic flow-state out of the hopper, whereas bulk Douglas fir wood particulate material develops a reliable mass flow pattern. A laboratory scale hopper was used to experimentally determine the biomass flow conditions, which were subsequently compared with the predicted onset of flow by a finite element model (FEM). The developed FEM was found to correctly predict the initiation of mass flow for the milled Douglas fir wood, whereas corn stover was predicted to establish a strong core flow suggesting an unreliable handling characteristic. This observation aligns with the reported poor handling of milled corn stover.

Investigating the compressibility and flowability of cocoa powders: A solution for chocolate industry

AbstractThe flowability and compressibility properties were determined for two types of cocoa powders, which are used commercially in chocolate industries; alkalized and natural cocoa powders. Physical and flow properties have a very significant role in the flow behavior, which relates to the handling, transportation, and storage of bulk powders. Throughout the research, it was observed that the properties of both cocoa powders are similar. The objectives of this work are to compare the compressibility and flowability between alkalized and natural cocoa powders and to design the minimum opening size of hopper for mass flow based on their flow properties. Jenike's mathematical methodology is applied during the research for the design of conical hoppers for mass flow. Besides, powder flow analysis using powder flow analyzer is one of the testing methodologies in this research. In addition, direct shear box tests were performed with three different normal stresses. The alkalized cocoa powder needs 1.366 m in diameter for the opening of the hopper, while the natural cocoa powder needs 1.531 m. From the results of the study conducted, it was concluded that both cocoa powders are very cohesive and have poor flow properties. This research reveals that the physical and flow properties of two main types of cocoa powder contributed a lot to the process of hopper design, enhance process understanding, and also applicable for analyzing the powder behavior at any stage in industry.Practical applicationsCocoa powder is the essential ingredient of chocolate manufacturing and other food industry having a chocolate‐like flavor including beverages, biscuits, desserts, and so forth. In chocolate industry, the flow behavior of cocoa powders can affect manufacturing efficiency, which directly affects the production capacity and product quality in terms of its weight and content uniformity. In this study, the critical design parameters such as hopper angle and size of opening were determined to improve the flowability of cocoa powders when passes through hopper. The findings of the present study make it possible for an accurate estimation of a correct intersection with the hopper flow factor line and effective angle of internal friction (δ), extrapolating the powder flow function ff curve to obtain hopper opening size for each cocoa powder for better flowability.

Segregation in inhalable powders: Quantification of the effect of vibration on adhesive mixtures

The objective of this investigation was to study the effect of induced vibrations on adhesive mixtures containing budesonide and salbutamol sulphate as active pharmaceutical ingredients (APIs) and InhaLac 70 as carrier. A series of adhesive mixtures with varied API concentration (1–4%) was prepared for each API. Half of the adhesive mixture was stressed on a vibrating sieve under conditions resembling hopper flow. Based on scanning electron micrographs, it was concluded that InhaLac 70 contains particles of two distinct shapes, one irregular with groves and valleys and the other more regular with well defined edges. The dispersibility of the control and stressed mixtures was studied using a next generation impactor. The stressed mixtures containing 1 and 1.5% API displayed a significant reduction in fine particle dose (FPD) compared to the control. The reduction in FPD resulted from a loss of API from the adhesive mixture during vibration and as a consequence of restructuring and self agglomeration resulting in reduced dispersibility. However, no significant difference was observed for mixtures with larger weight fractions of API (2 and 4% API) but these have a drawback of reduced fine particle fraction (FPF). It is concluded that vibrations induced on the adhesive mixtures during handling potentially have a significant effect on the dispersibility of the API and the total amount of drug delivered to the lungs.

Moisture dependent engineering properties of Musa balbisiana seeds

AbstractEngineering properties of wild banana seeds at different moisture content (8.66%, 12%, 16%, 20%, and 24% db) were investigated. Physical dimensions, seed surface area (SA), seed volume (SV), and thousand seed mass (M1000) increased linearly with increase inmoisture content. While porosity decreased linearly from 42.33% to 38.89%, bulk density (ρb) and true density (ρt) increased from 513.59 to 564.72 and 890.56–924.09 kg m−3, respectively. The angle of repose increased linearly from 29.84 to 36.48 with moisture content. The increased moisture content also caused an increase in static coefficient of friction for surfaces made of stainless steel, glass, and plywood. The thermal conductivity (λ) and volumetric specific heat (ρcp) were found to increase linearly from .17 to .20 Wm−1 K−1, and .58 to .99 MJ m−3 K−1, and thermal diffusivity (α) decreased from .31 to .19 (×10−6 m2 s−1) with a increase in moisture content.Practical applicationsThe research aimed to study the engineering properties of wild banana seeds as a function of moisture content as they are necessary to design equipment for handling, aeration, storage, and processing. Moreover, it helps in predicting flow and handling behavior during processing, including hopper flow, and conveying through feeders and other handling equipment. Furthermore, thermal properties are helpful in engineering, process design and modeling the thermal behavior of food products during storage, processing, and transportation.

Wedge-Shaped Hopper Design for Milled Woody Biomass Flow

The bioenergy industry has been challenged by unstable flow and transport of milled biomass in material handling operations. Handling issues such as hopper clogging and auger jamming are attributed to knowledge gaps between existing handling units designed for bulk solids and their suitability for milled biomass with high compressibility. This work investigates various flow behaviors of granular woody biomass in wedge-shaped hoppers. Hopper flow physical experiments and numerical simulations are conducted to study the influence of the critical material attributes and critical processing parameters on the flow pattern, arching, and throughput. The results show that (1) the preferred flow pattern, mass flow, can be achieved by controlling the material’s internal friction angle, hopper inclination, and hopper wall friction; (2) hopper arching, governed by the competing gravity-driven force against flow resistance from material internal friction and material–wall friction, can be controlled by the hopper wall friction angle and the inclination angle; and (3) flow throughput can be accurately estimated from our empirical equation with inputs of hopper outlet geometry and particle-scale to bulk-scale material attributes. This study elucidates woody biomass flow physics and provides guidance for industrial equipment design.

Predicting powder feedability: A workflow for assessing the risk of flow stagnation and defining the operating space for different powder-feeder combinations

Powder feeding is of critical importance for continuous manufacturing (CM) since next to in-process segregation it is the phenomenon primarily responsible for fluctuations in content uniformity and for content deviations in the final drug product. So far, feeding studies have focused on the characterization of specific feeders and the prediction of their performance for various materials. This work presents a more holistic approach, an early general assessment of the “feedability” of raw materials. With that regard, we established a workflow to: i) predict potential feeding issues, such as the flow stagnation in the hopper based on both the material attributes and the feeder’s geometry; and ii) predict the feed rate space using various feeder/screw combinations for powders with an acceptable risk of hopper flow stagnation. Statistical models were developed for this twofold approach using a dataset comprising nine powders and four different feeders. In order to include different feeding equipment into the statistical models, novel equipment descriptors (capturing the effect of different geometries) and performance indicators (the end fill level as indicator for the risk of powder flow stagnation) were introduced. The application of the workflow was demonstrated for a simple formulation, and model validation was successfully performed for an additional powder that was not contained in the original dataset. Finally, the most relevant material attributes were identified, and reduced material characterization data sets were investigated in terms of effects on the model’s prediction performance. The workflow presents a promising tool for initial process assessment in early-phase development.

Numerical investigation on the clogging-collapsing events in granular discharge

Granular flow in hoppers is widely encountered in industries and daily life. Despite its ubiquity, understanding on its basic flow behavior is still limited. Typically, the flow may be interrupted by the formation of arches and the phase transition ensues, and in general these arches may not collapse without external energy input such as vibration. However, in this study, the rare events of granular flow arrested by the formation of unstable arches and then restarted by their spontaneous collapsing, or the clogging-collapsing events, were observed in both lab experiments and numerical simulations in the discrete element method (DEM). It was demonstrated that the clogging may result from the coordinated evolution of the entire force chain system and the kinetic energy dissipated incompletely in bulk is mainly responsible for the collapsing. The evolution of the kinetic energy displays different modes in the clogging-collapsing and permanent clogging events, suggesting that the collapsing can be predicted by monitoring the variance of the kinetic energy. • Experimental and numerical study on the clogging-collapsing events in hoppers. • Imperfect arches with concave links found in temporal clogging. • Temporal arches bearing light load and supported by tangential contact forces. • Kinetic energy fluctuating at fine amplitude during temporal clogging. • Kinetic energy level and its fluctuation may indicate instable packing.

Multiscale Shear Properties and Flow Performance of Milled Woody Biomass

One dominant challenge facing the development of biorefineries is achieving consistent system throughput with highly variant biomass feedstock quality and handling performance. Current handling unit operations are adapted from other sectors (primarily agriculture), where some simplifying assumptions about granular mechanics and flow performance do not translate well to a highly compressible and anisotropic material with nonlinear time- and stress-dependent properties. This work explores the shear and frictional properties of loblolly pine at multiple experimental test apparatus and particle scales to elucidate a property window that defines the shear behavior over a range of material attributes (particle size, size distribution, moisture content, etc.). In general, it was observed that the bulk internal friction and apparent cohesion depend strongly on both the stress state of the sample in granular shear testers and the overall particle size and distribution span. For equipment designed to characterize the quasi-static shear stress failure of bulk materials ranging from 50 to 1,000 ml in test volume, similar test results were observed for finely milled particles (50% passing size of 1.4 mm) with a narrow size distribution (span between 10 and 90% passing size of 0.9 mm), while stress chaining and over-torque issues persisted for the bench-scale test apparatus for larger particle sizes or widely dispersed sample sizes. Measurement of the anisotropic particle–particle friction ranged from coefficients of approximately 0.20 to 0.45 and resulted in significantly higher and more variable friction measurements for larger particle sizes and in perpendicular alignment orientations. To supplement these laboratory-scale properties, this work explores the flow of loblolly pine and Douglas fir through a pilot-scale wedge-shaped hopper and a screw feeder. For the gravity-driven hopper flow, the critical arching distance and mass discharge rate ranged from approximately 10 to 30 mm and 2 to 16 tons/hour, respectively, for both materials, where the arching distance depends strongly on the overall particle size and depends less on the hopper inclination angle. Comparatively, the auger feeder was found to be much more impacted by the size of the particles, where smaller particles had a more consistent and stable flow while consuming less power.

Self-similarity of density and velocity profiles in a 2D hopper flow of elliptical particles: Discrete element simulation

Two-dimensional discharge flow of elliptical particles with different aspect ratios from a silo is investigated by using discrete element simulation. The measured flow rate of the particles is well fitted via Beverloo's law. The flow rate shows a monotonic decrease with increasing aspect ratio. The density and velocity profiles of particles at the outlet were systematically measured. At an identical outlet size, the speed of particles through the aperture decreases with increasing aspect ratio. The velocity profiles in all cases follow the same definite self-similar law and are in good agreement with the reported experimental results, thereby showing compatibility with the free fall arch postulation. The density profiles show obvious self-similar feature and can be fitted conveniently by using a fractional power law. Based on these observations and the results of the previous work, the flow rate for elliptical particles is calculated and is in agreement with the simulated results.

Effect of the Hopper Angle of a Silo on the Vertical Stress at the Cylinder-to-Hopper Transition

Silos are used worldwide to store granular and powdered materials. Agricultural, food and feed products are commonly stored in silos. However, many questions remain unanswered about how to estimate the pressures applied by the bulk material, which are needed to design and calculate the structure of the silo. The complexity of the laws that govern the mechanical behavior of the stored material along with the low number of experimental stations in the world hinder progress in this field. The aim of this study was to elucidate the relationship of the hopper angle, flow pattern and vertical stress at the cylinder-to-hopper transition in slender silos. Therefore, a set of experiments was conducted on a test station to measure the vertical stress produced by maize at the cylinder-to-hopper transition. Five different hopper angles were used. The experiments comprised the filling, the static phase and the discharge. The results obtained show that the hopper angle influences the vertical stress at the cylinder-to-hopper transition. Some bottom configurations (flat bottom and bottom with an angle of 30°) led to vertical stresses that exceeded the value calculated according to Eurocode 1. It is clear that further experimental studies are still necessary to understand the underlying physical phenomena and the relations between pressures, silo geometry and flow pattern of the stored material.

Influence of grain bidispersity on dense granular flow in a two-dimensional hopper

This work uses the discrete-element method to investigate bidisperse dense granular flow with large and small grains in a two-dimensional hopper. A half-circular dynamical force arch forms above the outlet, and the robustness of Beverloo's law is verified to describe the relationship between flow rate and outlet size. The bidisperse flow peaks when monodisperse flow of small grains is supplemented with a small fraction of large grains. The dense flow rate relates closely to the local flow characteristics of a key area. However, the interior packing structures (i.e., an ordered arrangement for monodisperse flow and a disordered arrangement for bidisperse flow) dominate the flow-pattern transition from mass flow to funnel flow. The earlier occurrence of the transition increases the grain velocity and therefore the flow rate. This discovery of interior flow rheology provides a plausible basis for constructing a general constitutive framework for dense granular flow.

Flow and heat transfer simulation in the ADS Dense Granular-flow Target using the Material Point Method

The Dense Granular-flow Target (DGT) proposed by Chinese Academy of Sciences has great potential compared with solid target and liquid metal target. In DGT, the number of metal grains is up to ten million. To study the flow and heat transfer behavior of such a large number of particles, experiments and Discrete Element Method (DEM) simulations are extremely expensive. Therefore, this paper focus on develop a continuum approach suitable for simulating the flow and heat transfer behavior in DGT. This approach is based on the Material Point Method (MPM) and chose the μ(I) rheology as the constitutive model for granular material. It can be concluded from this work that the μ(I) rheology implemented in MPM is able to reproduce quantitatively the granular behavior in hopper flow. The velocity distributions calculated by MPM are in good agreement with those calculated by DEM, although the fluctuation information in particle scale is filtered. The temperature results of MPM are basically consistent with DEM in mesoscopic scale, which is a great improvement compared with the results from uniform velocity estimation. The influences of the effective thermal conductivity, proton current and flow rate on the temperature field are investigated. According to the MPM calculation, the maximum proton current that the target can withstand and the minimum velocity that the granular needs to be met can be estimated quickly. The MPM procedure developed in this paper would be of considerable help in predicting the flow and heat transfer behavior for DGT.

Clogging and avalanches in quasi-two-dimensional emulsion hopper flow.

We experimentally and computationally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions are above jamming such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets often clog and thus exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power-law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. Our computational studies reproduce the experimental observations by adding a flexible compliance to the system (in other words, a finite stiffness of the sample chamber). The compliance results in continuous flow at high flow rates, and allows the system to clog at low flow rates leading to avalanches. The computational results suggest that the interplay of the flow rate and compliance controls the presence or absence of the avalanches.

Hopper flows of deformable particles.

Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w: Q ∼ (w/σavg - k)β, where σavg is the average particle diameter, kσavg is an offset where Q ∼ 0, the power-law scaling exponent β = d - 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent β. We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent β varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, λ = ζ/μ. β = d - 1/2 in the λ → 0 limit and d - 3/2 in the λ → ∞ limit, with a midpoint λc that depends on the hopper opening angle θw. We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent β. The offset k increases with particle stiffness until k ∼ kmax in the hard-particle limit, where kmax ∼ 3.5 is larger for λ → ∞ compared to that for λ → 0. Finally, we show that the simulations of hopper flows of deformable particles in the λ → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.