Hopper Discharge Research Articles

Modeling the Discharge Rate of a Screw Conveyor Considering Hopper–Conveyor Coupling Parameters

Developing a flow rate model for the screw feeder and optimizing discharge performance are crucial for achieving automated intelligent precision feeding. This study constructs a mass flow rate model for screw conveyors, considering the coupled structural parameters of the hopper and screw conveyor. The model is developed using single-factor tests and central composite design (CCD) response surface tests and is validated through actual discharge tests. Results indicate that the discharge rate in the hopper–screw conveyor system is primarily influenced by the screw conveyor itself. Among the structural parameters, the hopper inclination angle and the hopper discharge opening length significantly affect the filling coefficient. Validation tests show an average error of 6.8% between the predicted and simulated mass flow rates and 5.0% with the actual mass flow rate, demonstrating the model’s high precision and accuracy.

Residual mass prediction of powder discharged from hopper at non-gravity directions

Residual powder often occurs when the hopper is inclined, which leads to material waste and reduces utilization efficiency. This paper carried out hopper discharge experiments of fine glass beads at non-gravity directions with hopper tilted from vertical to horizontal. The powder residual mass at different discharge directions was first analyzed. The criterion equation of powder residue was established in combination of experimental observation and force analysis, based on which the effect of the operation conditions on the utilization rate of powder was discussed. Second, based on the morphological characteristics of residual powder, the integral equation for calculating volume was established. Meanwhile, the error caused by the slip phenomenon was corrected. Finally, the residual mass prediction model was established. The model demonstrates precise prediction outcomes This study provides a reference for improving the utilization rate of powder in the aspects of hopper structure setting, powder flow properties, and discharge directions matching.

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.

Detection method of hopper discharge characteristics based on discharge time distribution combined with machine vision and neural network

A machine vision and neural network-based method for the quantitative detection of hopper discharge characteristics based on the discharge time distribution is proposed. Glass beads and quartz sand were utilized as test objects. The prediction model of the relationship between the particle mass and the pixel value of the image was established by an artificial neural network, and the mass flow rate (MFR) was calculated via image prediction. The average relative errors of the predicted MFR for glass beads and quartz sand were found to be −1.31 % and −2.02 %, respectively. Based on the particle marking method, a convolutional neural network was used to classify the image according to whether there were marked particles in the image, and the mass flow index (MFI) was calculated after error correction. The average relative errors of the predicted MFI values for glass beads and quartz sand were found to be −1.43 % and 0.82 %, respectively.

DEM and DEM-CFD modeling of systems with geometric constrictions using a new particle location based multi-level coarse graining approach

A popular Lagrangian approach for modeling granular systems is the discrete element method (DEM). Currently, the simulation of industrial granular systems often exceeds modern computer capacities. Therefore, the coarse graining (CG) approach bundles multiple particles into grains, which are less computationally demanding due to the reduced number of entities considered. In systems, where the maximum grain size is limited by local geometry constrictions, uniform grain sizes lead to inefficient computations since far from the constrictions larger grain sizes could be reasonably used. Multi-level coarse graining (MCG) addresses this by using multiple grain sizes, which are adapted to the geometric constrictions. In this study, geometrical non-uniform hoppers and a Wurster coater system were modeled using a new MCG approach. Results from literature regarding hopper discharge were matched. For the Wurster coater system MCG outperforms conventional CG by providing a higher resolution of the granular material close to the geometric constriction.

Systematic Calibration and Validation Approach for Discrete Element Method (DEM) Modeling of Corn Under Varying Moisture Contents (MC)

Abstract. Discrete Element Method (DEM) based simulation of grain threshing and conveyance processing at relatively dry to wet grain moisture content range has been limited. A comprehensive five-step framework of a DEM grain model calibration and validation of flow and grain impacts on equipment was investigated. The framework was examined by developing DEM models for corn grain moisture conditions sampled during crop harvesting, and simulated hopper discharge corn flow, and corn impact forces on a grain paddle elevator of a crop harvesting machine. Five bulk material response parameters were obtained from two calibration experiments of the angle of repose and direct shear test at the MC levels of 11%, 16%, and 26%. Latin hypercube sampling statistical design of experiment points, Gaussian Process Regression surrogate model, and optimization algorithms were successfully implemented to generate Hertz-Mindlin (HM) with Johnson-Kendall-Roberts (JKR) cohesive model of corn at three moisture content levels. The DEM simulation results predict the corn mass flow rate of hopper discharge with relative errors of -5%, -4%, and 1% for corn at 11%, 16%, and 26% MC levels, respectively. The DEM also predicts corn impact forces on a paddle elevator with a relative error of less than 11%. The established DEM calibration methodology, used for simulation of crop threshing, and harvested grain handling processes at extreme grain moisture content, can accelerate the simulation-based design of crop harvesting equipment. Keywords: Calibration, Corn, Discrete Element Method, Moisture Content, Sensitivity analysis, Validation.

Shape-changing particles for locally-resolved particle geometry in DEM simulations

Taking into account the complex shape of particles in discrete element method (DEM) simulations of large-scale granular systems is computationally demanding due to the time-consuming contact detection algorithms for polyhedral particles. In this short communication, a novel approach that locally resolves the particle shapes where needed and uses a simplified representation elsewhere, to accelerate simulations without compromising accuracy, is presented. For this purpose, a method employing a smooth transition of the particle shape representation from analytical spheres to shape-resolving polyhedra is introduced in DEM. The feasibility and correct implementation of this approach are demonstrated through simulations of hopper discharge involving spherical and dodecahedral particles from a flat bottom silo or shaft kiln. The model capabilities, in terms of accuracy as well as reduction in computational effort, are quantified for a moving bed with continuous outflow.

Vibro-fluidization of cohesive particles

The paper assesses the behavior of cohesive Geldart C-type particles, when fluidized by air with the aid of vibration. Together with their poor flowability and irregular hopper discharge, bubbling fluidization is very difficult to achieve due to the possible particle agglomeration and gas channeling. When trying to fluidize cohesive particles, the gas drag force cannot break the inter-particle bonds. Despite all these handling and operation problems, ultrafine particles of micron- or nanosize are increasingly applied in industrial processes. To disrupt the stable gas channels and cracks, a mechanical vibration is one of the easier and preferred methods to improve the fluidity of the cohesive particles. In the present study, several 2 to 40 μm particles were used. A comparison with Geldart A-type particles was also made. Experimental results were used to validate a more fundamental approach based upon the balance of forces acting on the particles. This resulted in a new delineation of the Geldart C/A boundary where the critical transition particle size for particles of given absolute density, ρp, Hamaker constant, H, and inter-particle distance, z0, decreases with an increasing vibration intensity, I, according to dcrit2ρp=8.03Hz021+Ig.

Discharge characteristics of conical and hyperbolic hoppers based on discharge time distribution

An experimental method based on the discharge time distribution (DTD) and the finite element method (FEM) simulation was applied to quantitatively evaluate the flow pattern, mass flow rate (MFR), and coefficient of variation (CV) of the MFR of a granular flow during the discharge of conical and hyperbolic hoppers with different initial inclination angles. The mass flow index (MFI) and MFR of the conical and hyperbolic hoppers appear to increase with the initial inclination angle. However, the MFI of the conical hopper exceeds that of the hyperbolic hopper while the MFR of the conical hopper is lower than that of the hyperbolic hopper. The CV of the MFR decreases as initial inclination angle increases for conical hoppers, but is less affected by the initial inclination angle for hyperbolic hoppers.

Modeling stratified segregation in periodically driven granular heap flow

We present a continuum approach to model segregation of size-bidisperse granular materials in unsteady bounded heap flow as a prototype for modeling segregation in other time varying flows. In experiments, a periodically modulated feed rate produces stratified segregation like that which occurs due to intermittent avalanching, except with greater layer-uniformity and higher average feed rates. Using an advection-diffusion-segregation equation and characterizing transient changes in deposition and erosion after a feed rate change, we model stratification for varying feed rates and periods. Feed rate modulation in heap flows can create well-segregated layers, which effectively mix the deposited material normal to the free surface at lengths greater than the combined layer-thickness. This mitigates the strong streamwise segregation that would otherwise occur at larger particle-size ratios and equivalent steady feed rates and can significantly reduce concentration variation during hopper discharge. Coupling segregation, deposition and erosion is challenging but has many potential applications.

Micromechanical analysis of granular dynamics and energy dissipation during hopper discharging of polydisperse particles

This paper presents a numerical study on the hopper discharging of widely polydisperse particles. It focuses on the effects of particle size distributions (PSDs) in the form of the log-normal distribution of the number (nPSD) and volume (vPSD) of particle constituents. In doing so, a recent GPU-DEM model suitable for large-scale simulations is adopted. The numerical results show that the mass discharge rate reduces with increasing nPSD spread but becomes larger at a wider vPSD spread. The discharging process is analyzed in terms of packing density, coordination number, velocities, and force network. It is observed that the packing density equally increases for both PSDs as the spread grows, whereas the coordination of the mixture reduces. Thus, a negative correlation between coordination and packing density is consistently observed. With increasing nPSD spread, the particle vertical velocities drop significantly, which are nearly unchanged for wider vPSDs. The particle-scale analysis is also extended to energy dissipation. The analysis reveals that the effect of PSD on the mass discharge rate is mainly attributed to the relative importance of different energy dissipation mechanisms. Irrespective of PSD type, the friction energy dissipation decreases with widening PSD, which becomes more pronounced near the outlet. In contrast, as the spread becomes wider, the collision dissipation near the outlet turns more important for nPSD but decreases for vPSD. These results account for different trends of discharge rates with respect to PSD type.

Hopper discharge flow dynamics of milled pine and prediction of process upsets using the discrete element method

Hopper discharge flow dynamics of milled pine and prediction of process upsets using the discrete element method

A Study of Contact Detection between Noncircular Particles in Discrete Element Method

One of the key points of modeling noncircular particles in the discrete element method is the contact detection of particles. In this study, a general contact detection algorithm of two-dimensional particles with analytic shape functions is provided. The contact detection of particles with strictly convex shape function, such as ellipses and superellipses, is solved by Newton–Raphson method, and a grid method is provided to deal with heart-shaped particles. The grid method can be generalized into a particle system, in which the shape function is not convex. The accuracy and stability of the algorithm are verified by a series of tests. For the collision of a pair of ellipses with an aspect ratio of α = a / b = 1000, the efficiency is not worse than the Newton–Raphson method. For random packing under gravity, no residual kinetic energy is observed, and the force that acts on the bottom is equal to the gravity, that is, the system reaches a mechanical equilibrium state. After equilibrium, the process of hopper discharge is also simulated. The present method is suitable for arbitrarily shaped particles with analytic shape functions in two-dimensional cases. In addition to superellipses, the method can also be applied to other particle systems as long as the shape functions are given.

A design method of hopper shape optimization with improved mass flow pattern and reduced particle segregation

A shape optimization method is presented in this paper to re-design hopper shapes for improving the flow patterns in silos. This method combines a continuum model of granular matter based on the Eulerian Finite Element Method, the optimization algorithms of genetic algorithm and the gradient descent method. Starting from a classic conical shape, the optimization method searches for the optimal shape of the hopper under given geometrical constraints. An optimized curve design can increase the mass flow zone in the hopper by more than 90%. The sensitivity of this method suggests that the shape optimization is of particular significance for initially funnel flow hoppers and granular materials with high internal friction. The optimized design was further characterized by using the Discrete Element Method. The DEM results demonstrate that the optimized hopper can also dramatically reduce particle segregation by around 70% during hopper discharge.

Hash Functions and GPU Algorithm of Infinite Grid Method for Contact Search

The paper presents the memory-saving GPU algorithm of the infinite grid method with various hash functionsfor contact search in discrete element computations. The implemented hash table of fixed size has the addedbenefit of allowing the grid to be potentially infinite in size, which is particularly suitable for a large numberof discrete particles, moving in large computational domains with empty regions. Research on the applicationof various hash functions and hash table sizes was performed to preserve the computational performance ofthe developed memory-saving GPU algorithm and its OpenCL implementation. The performance of the developed software was evaluated by solving the hopper fill and discharge as well as the artificial avalanche problemson the NVIDIA® Tesla™ P100 GPU. The performance achieved by using the memory-saving implementationof contact search was compared with that attained by using the standard implementation of the uniform gridmethod. The performed analysis revealed that the developed GPU algorithm and its OpenCL implementationreduced the GPU memory consumed by the uniform grid method up to 69.7 times, which resulted in the contactsearch memory equal to 1.86% of the total memory required by DEM computations. Moreover, the applicationof the Morton hash function and the proper hash table size allowed for preserving high computational performance of the infinite grid method and the developed GPU software.

Effect of outlet characteristics and particle properties on the flow characteristics inside conical hoppers

Precisely predicting the hopper discharge rate and trajectory is of great significance for industrial processing of granular materials. This study uses the DEM (Discrete Element Method)-based open-source software LIGGGHTS to analyze the flow behavior of spherical particles in six cone-shaped hoppers with different outlet shapes (circle, triangle, square, rectangle, pentagon and hexagon) with the various opening area. It was found that the particle flow velocity and mass flow rates are mainly determined by the outlet areas, while the outlet shape have an obvious influence on the particle trajectory which determines the stagnation area in the hopper. The results of the present study can provide meaningful guidance for the optimization of industrial hopper structure design and control.

Discrete element simulation of super-ellipse systems

There are two key problems in discrete element simulations of super-ellipse systems. One is the determination of contact point, and the other is the mechanical equilibrium with almost zero kinetic energy. The Newton–Raphson method or its modification used to determine the contact point is only sufficiently numerically stable for suitable deformation parameters, and the state of all particles with almost zero velocity is difficult to reach. In this paper, a novel contact detection method for all deformation parameters is used to determine the contact point, and a rolling resistance model is used to dissipate rotational kinetic energy for mechanical equilibrium. A series of tests are investigated to verify the validity of this method. For random packing under gravity, no residual kinetic energy (or almost 0) is observed, and the force that acts on the bottom is equal to the gravity, meaning that the system reaches mechanical equilibrium. After equilibrium, the process of hopper discharge, in which the kinetic energy remains stable for shape and material parameters, is also modeled. Furthermore, direct shear tests at different shear rates are simulated, and the results meet the rate independence, which is in agreement with experiments. The method is also suitable for investigation of sound propagation properties in the super-ellipse system, and the velocities of compressional and shear waves are calculated in uniaxial compression tests. In addition to super-ellipses, the method can be applied to other particle systems once the shape functions are given. After reaching the equilibrium state, a hole is opened at the bottom, and its width is 15 times the width of the particle. Figure shows the snapshots of particle flow at different times. Then, 0.372 seconds later, after 136 particles drop through the hole, a semi-circular structure of force arch occurs, and the particle flow stops. These findings are different from the results of the previous research and show that the shape has a significant effect on the flow rate.

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.

DEM based investigation of powder packing in 3D printing of pharmaceutical tablets

3D printing is emerging as one of the most promising methods to manufacture Pharmaceutical dosage forms as it offers multiple advantages such as personalization of dosage forms, polypill, fabrication of complex dosage forms etc. 3D printing came into existence in 1980s but its use was extended recently to pharmaceutical industry along with the approval of first 3D printed tablet Spritam by FDA in 2015. Spritam was manufactured by Aprecia pharmaceuticals using binder jetting technology. Binder jet 3D printing involves a hopper for powder discharge and printheads for ink jetting. The properties of tablets are highly dependent upon the discharge quality of powder mixture from the hopper and jetting of the ink/binder solution from the printhead nozzle. In this study, numerical models were developed using Discrete element method (DEM) to gain better understanding of the binder jet 3D printing process. The DEM modeling of hopper discharge was performed using in-house DEM code to study the effect of raw material attributes such as powder bed packing density (i.e. particle size, particle density etc) on the printing process, especially during powder bed preparation. This DEM model was further validated experimentally, and the model demonstrated good agreement with experimental results.

An error-controlled adaptive time-stepping method for particle advancement in coupled CFD-DEM simulations

Coupled Computational-Fluid-Dynamics (CFD) and Discrete-Element-Method (DEM) models provide an accurate description of multiphase physical systems where a solid granular particle phase exists in an underlying gaseous continuous medium. The time integration of the granular phase in these simulations is typically handled using an explicit scheme with a constant time-step among all particles that is invariant in time to resolve inter-particle collisions. A locally third-order accurate adaptive time integration technique for particles that employs an embedded locally second-order scheme for error determination is presented in this work. The particle time-step size is dynamically adapted based on solution error, thus leading to significant savings in computational time. The efficacy of our scheme is quantified using four test cases of varying complexity (binary collision, homogeneous cooling system, fluidized bed and hopper discharge). The adaptive time-stepping method exhibits improved performance (~ 2–3 times in most of the cases studied) compared to three commonly used non-adaptive time-step methods (first-order Euler-explicit, second-order Adams-Bashforth and third-order Runge-Kutta schemes), while maintaining the same level of accuracy and parallel scalability.