Scale-up and flow behavior of cohesive granular material in a four-bladed mixer: effect of system and particle size

Flow of cohesive granular materials with different moisture contents was examined in a four-bladed mixer via the discrete element method (DEM). Firstly, the mixer diameter (D) was increased while keeping the particle diameter (d) constant. It was observed that when the mixer diameter to the particle diameter ratio (D/d) was larger than a certain critical size (D/d ≥ 75), granular flow behaviors and mixing kinetics followed simple scaling relations. For D/d ≥ 75, flow patterns and mixing kinetics were found to be independent of system size, and velocities of particles scaled linearly with the tip speed of the impeller blades and particle diffusivities scaled with the tip speed of the blades and mixer diameter. These results suggest that past a certain system size the flow and mixing of cohesive particles in large-scale units can be predicted from smaller systems. Secondly, system size was kept constant and particle diameter was changed and it was observed that by keeping the Bond number constant (by changing the level of cohesion) the flow behavior and mixing patterns did not change, showing that larger particles can be used to simulate flow of smaller cohesive particles in a bladed mixer by matching the Bond numbers.     

The effect of liquids on radial segregation of granular mixtures in rotating drums

The presence of liquids can significantly affect the dynamics of granular flow. This paper investigates the effect of liquids on radial segregation of granular mixture in a rotating drum using the discrete element method. The wet granular mixture, due to differences in particle size and density, segregates in a similar way to that of dry particles: lighter/larger particles move to the periphery of the bed while heavier/smaller particles stay in the centre. An index based on the variance of local concentration of one type of particles was proposed to measure the degree of segregation. While the liquid induced capillary force slows down the segregation process, its effect on the final state is more complicated: small cohesion shows no or even positive effect on segregation while high cohesion significantly reduces particle segregation. The effect can be explained by the change of flow regimes and the competing effects of mixing and segregation (un-mixing) in particle flow which are both reduced by the interparticle cohesion. A diagram is generated to describe the combined effect of particle size and density on segregation of wet particles. A theory is adopted to predict the segregation of particles under different density/size ratios.     

A DEM Analysis of Flow Characteristics of Noncohesive Particles in Hopper

Flow characteristics of material in hoppers, silos, and bins are critical issues for operational stability as well as structural integrity of these units. In this work, flow of noncohesive particles in hopper is studied using the discrete element method (DEM) where each particle is tracked for its position, velocity, and acceleration. Material properties tend to alter during hopper flow due to compaction, expansion, and segregation. These features are difficult to model with a continuum approach. In the first part, material flow patterns are correlated with hopper angle and hopper opening, the two main design parameters. The typical shift from mass flow to funnel flow depending on the hopper angle was successfully simulated. In the second part, the discharge rate of material was quantitatively analyzed as function of hopper design parameters. Beverloo model 1 was tested on these simulated flow rates and it was shown that the simulated flow rates follow the model for this specific granular system. However, the DEM analysis was also able to demonstrate the failure of the traditional Beverloo model in the restricted flow regime. Simulated flow rates also follow the empirical correlations with hopper angle as stated in literature. DEM simulations were validated with experimental data for both material flow pattern and discharge rates.     

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.     

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.     

DEM simulations: mixing of dry and wet granular material with different contact angles

In solid mixing the raw materials typically differ at least in one material property, such as particle size, solid density and wetting properties, which in turn influence particle mobility. For example, smaller particles can percolate through the voids of larger ones under the influence of strain and gravity. This may produce fine particle accumulation at the bottom of the mixing vessel which results in undesired, inhomogeneous final products. When wet particles with different wetting properties need to be mixed, heteroagglomeration may occur as another segregation mechanism. We present a new capillary bridge force model to study segregation in moist cohesive mixing processes using DEM. New analytical equations of best fit are derived by solving the Young–Laplace equation and performing a regression analysis, in order to investigate discontinuous mixing processes of dry and moist materials with different particle sizes and different contact angles. Compared to a dry mixing process, mixing efficiency is improved by the addition of a small amount of liquid. While percolating segregation is reduced, heteroagglomerates occur in the wet mixing process.     

Analysis and DEM simulation of granular material flow patterns in hopper models of different shapes

By using the discrete element method (DEM) a comparison and observations on material flow patterns in plane-wedged, space-wedged, and flat-bottomed hopper were accounted for. Numerical results obtained by combining data of individual particles, statistical processing of particle assemblies and evaluation of the field variables provided the essential characteristics for different regimes of the discharge flow (within steady or unsteady state of flow) and the differences in differently shaped hoppers due to different microscopic inter-particle friction. For validation of the performed simulations, velocity patterns developed in three-dimensional flat-bottomed hopper containing 20,400 pea grains were also analysed. To represent the continuum by avoiding the local effects produced by the individual grains, the simulation results were focused on the mean velocity distributions with data smoothening. The effect of rolling resistance on granular material flow was also considered.     

Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation

In order to test the effect of material properties on flowability of particulate materials, discharge procedures of spherical particles within a flat-bottomed model silo with three sets of material properties, i.e., soft and hard without adhesion and adhesive hard, were simulated using the Discrete Element Method. For each system, three particles on the center line were selected and their instant vertical velocity components were traced. In addition, both discharge and the rate were recorded throughout the procedure. The predicted results show that, for both the systems without adhesion, though the soft has a material modulus only 1/1000 of the hard, there are no significant differences in f low pattern and discharge rate. This suggests that a soft system can be used to predict the behavior of a hard one to save CPU time in a gravity-driven granular flow. On the other hand, comparison between both hard systems shows that adhesion can significantly reduce the flowability in granular flow. By analyzing the velocity plot for the traced particles, free fall was clearly detected above the decompression zone, indicating the motion of a particle in a granular flow can be resolved as free fall together with the movement due to particle collision. In addition, select dynamic behavior related to the kinetic fluctuations affecting flow was observed. discrete element method silo granule flow particulate material     

Development and validation of calibration methods for discrete element modelling

Discrete element method (DEM) is proving to be a reliable and increasingly used tool to study and predict the behaviour of granular materials. Numerous particle-scale mechanisms influence the bulk behaviour and flow of bulk materials. It is important that the relevant measurable input parameters for discrete element models be measured by laboratory equipment or determined by physical calibration experiments for rational results. This paper describes some of the bench-scale experiments that have been developed to calibrate the DEM simulations to reflect actual dynamic behaviour. Relevant parameters such as static and rolling coefficients of friction, coefficient of restitution and inter-particle cohesion forces from the presence of liquid bridges have been investigated to model the bulk behaviour of dry and moist granular materials. To validate the DEM models, the results have been checked against experimental slump tests and hopper discharge experiments to quantitatively compare the poured and drained angles of repose and solids mass flow rate. The calibration techniques presented have the capability to be scaled to model and fine tune DEM parameters of granular materials of varying length scales to obtain equivalent static and dynamic behaviour.     

A concise treatise on model-based enhancements of cohesive powder properties via dry particle coating

This paper presents a review of our key advances in model-guided dry coating-based enhancements of poor flow and packing of fine cohesive powders. The existing van der Waals force-based particle-contact models are reviewed to elucidate the main mechanism of flow enhancement through silica dry coating. Our multi-asperity model explains the effect of the amount of silica, insufficient flowability enhancements through conventional blending, and the predominant effect of particle surface roughness on cohesion reduction. Models are presented for the determination of the amount and type of guest particles, and estimation of the granular Bond number, used for cohesion nondimensionalization, based on particle size, particle density, asperity size, surface area coverage, and dispersive surface energy. Selection of the processing conditions for LabRAM, a benchmarking device, is presented followed by key examples of enhancements of flow, packing, agglomeration, and dissolution through the dry coating. Powder agglomeration is shown as a screening indicator of powder flowability. The mixing synergy is identified as a cause for enhanced blend flowability with a minor dry coated constituent at silica < 0.01%. The analysis and outcomes presented in this paper are intended to demonstrate the importance of dry coating as an essential tool for industry practitioners.     

Segregation behavior of particles with Gaussian distributions in the rotating drum with rolling regime

The mixing and segregation of granular materials are essential to provide valuable insights and references for practical industrial production. In this paper, the segregation behaviors of particles with Gaussian distributions and 40% filling level in the rotating drum with rolling regime were numerically studied by the discrete element method. The effects of rotation speed and particle size parameter λ (size ratio of the largest versus smallest particles) on the segregation behavior (mixing index, segregation rate), flow characteristics (particle velocity and trajectory, gyration degree and radius, particle size distributions) and the microscopic properties (collision, contact force, axial diffusion, and kinetic energy) of granular systems were systematically investigated. The results show that the segregation rate and degree of particles with Gaussian distributions gradually increase with the increase of the rotation speed and particle size parameter λ. The radial and axial segregation patterns become more obvious with the increase of λ. And the variation of the flow characteristics of particles with different sizes in the same system is also inconsistent. The microscopic properties of Gaussian-dispersed particles change with the rotation speed and λ. The rapid radial segregation depends on the larger pores existed in the granular system, which leads to a gradual increase of the axial dispersion coefficient of large particles and a gradual decrease of the axial dispersion coefficient of small particles.     

Effects of Material Properties on Granular Flow in a Silo Using DEM Simulation

In order to test the effect of material properties on flowability of particulate materials, discharge procedures of spherical particles within a flat-bottomed model silo with three sets of material properties, i.e., soft and hard without adhesion and adhesive hard, were simulated using the Discrete Element Method. For each system, three particles on the center line were selected and their instant vertical velocity components were traced. In addition, both discharge and the rate were recorded throughout the procedure. The predicted results show that, for both the systems without adhesion, though the soft has a material modulus only 1/1000 of the hard, there are no significant differences in f low pattern and discharge rate. This suggests that a soft system can be used to predict the behavior of a hard one to save CPU time in a gravity-driven granular flow. On the other hand, comparison between both hard systems shows that adhesion can significantly reduce the flowability in granular flow. By analyzing the velocity plot for the traced particles, free fall was clearly detected above the decompression zone, indicating the motion of a particle in a granular flow can be resolved as free fall together with the movement due to particle collision. In addition, select dynamic behavior related to the kinetic fluctuations affecting flow was observed.

discrete element method silo granule flow particulate material     

Particle screening phenomena in an oblique multi-level tumbling reservoir: a numerical study using discrete element simulation

Due to their wide usage in industrial and technological processes, granular materials have captured great interest in recent research. The related studies are often based on numerical simulations and it is challenging to investigate computational phenomena of granular systems. Particle screening is an essential technology of particle separation in many industrial fields. This paper presents a numerical model for studying the particle screening process using the discrete element method that considers the motion of each particle individually. Dynamical quantities like particle positions, velocities and orientations are tracked at each time step of the simulation. The particular problem of interest is the separation of round shape particles of different sizes using a rotating tumbling vertical cylinder while the particulate material is continuously fed into its interior. This rotating cylinder can be designed as a uniform or stepped multi level obliqued vertical vessel and is considered as a big reservoir for the mixture of particulate material. The finer particles usually fall through the sieve openings while the oversized particles are rebounded and ejected through outlets located around the machine body. Particle–particle and particle–boundary collisions will appear under the tumbling motion of the rotating structure. A penalty method, which employs spring-damper models, will be applied to calculate the normal and frictional forces. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. The particle distribution, sifting rate of the separated particles and the efficiency of the segregation process have been studied. It is recognized that the screening phenomenon is very sensitive to the machines geometrical parameters, i.e. plate inclinations, shaft eccentricities and aperture sizes in the sieving plates at different levels of the structure. The rotational speed of the machine and the feeding rate of the particles flow have also a great influence on the transportation and segregation rates of the particles. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies for achieving optimal operation have been performed.     

Investigation of spherical and non-spherical binary particles flow characteristics in a discharge hopper

The particulate flow characteristics of granular particles including mung beans, wooden spheres, wooden cylinders, wooden cubic, plastic spheres, plastic cylinders, and their binary mixtures in a flat bottom hopper were studied experimentally using high-speed high-resolution camera recordings. An image processing method based on the color threshold was developed to calculate the area ratio for binary mixtures. The mass discharge rates, the residue inclination angles, and the changes in edge height and center height with time were also investigated. In addition, the effects of different initial packing patterns on the particulate flow, mixing and segregation behaviors were analyzed and compared. It is interesting to find that the shape of particles and the initial binary particle packing patterns have significant effects on the discharging characteristics. The results of this study provide helpful guidance for industrial applications and provide experiment data for computational model validation.     

Simulation of cutting processes using mesh-free Lagrangian particle methods

This contribution presents the model of a ‘granular solid’ based on the Discrete Element Method which is used to model cutting processes of cohesive and ductile materials, e.g. aluminum. The model is based on a conventional three-dimensional Discrete Element approach which employs rigid spheres as it is used to model granular media. Including cohesive interactions besides the repulsive interactions of the basic model allows for the particle agglomerate to display cohesive and ductile behavior. Using the thus generated granular solid the failure modes of ductile engineering materials like aluminum can be qualitatively and quantitatively reproduced. This is shown by comparison with experiments of a tensile and a Charpy impact test. To show the applicability of the approach for manufacturing problems an orthogonal cutting process of steel and aluminum is modelled and the cutting forces are compared to experiments. To further enhance the model thermal interactions between particles are included. The thermodynamics during cutting due to dissipative phenomena is evaluated and compared to experiments.     

Multi-scale study of particle flow in silos

The flow characteristics of solid particles in a silo were studied experimentally and theoretically. A multi-scale study of the particles flow was performed by means of discrete element method (DEM). The dependence of flow behaviors on the particles diameter distribution and silo geometry was analyzed to establish the spatial and statistical distributions of microdynamic variables related to flow and silo structures such as velocity, porosity, coordination number, and interaction forces between particles. The results show that the distribution of particle diameter has great effects on particles flow, and the mixing of multi-sized particles is propitious to granular flow. The geometry of silos has greater effects on granular flow than particle size distribution, and inserts can improve the flow behaviors of “funnel flow” type to “mass flow”. Linear equations can be used to describe the relationship between discharge rate and orifice size by G^2/5 vs. D_o for the same distribution of particles diameter. The flow structure of particles in the silos is spatially non-uniform, which is illustrated by spatial and statistical distributions of porosity and coordination number. Both porosity and coordination number are affected by the mode of particles packed, which is affected by the geometry of silos and particle size distribution. The distribution of contact forces between particles is spatially non-uniform too. In flat-bottomed silo, there are arched stress chains in the vicinity of the orifice under the “bridging action”, which disappeared in wedge-shaped hopper silo.     

DEM study of monodisperse granular flow in a pipe

Flow of granular material through a pipe has several industrial applications but maintaining a uniform mass flux is quite challenging. In this work, monodisperse granular flow (non-turbulent and non-dense phase particle transport) through a vertical pipe was simulated using discrete element method (DEM). Effects of different geometric and granular parameters on mass flux of cohesive and non-cohesive solids were analyzed and evaluated. Several important parameters and their effects on mass flux were studied like: L/D ratio, pipe diameter to particle diameter ratio (D/D_p), Poisson ratio, and pipe inclination angle. Furthermore, effects of moisture content and Bond number on mass flux were also investigated. These parameters influenced mass flux except Poisson ratio which showed no significant improvement in mass flux upon increasing the value of this ratio.     

Effects of process parameters and hopper angle on segregation of cohesive ternary powder mixtures in a small scale cylindrical silo

Segregation of two ternary powder mixtures at filling and at discharge of a 0.4 m³ cylindrical silo has been investigated experimentally. The material distribution at silo filling was determined by sampling from the upper layers of the heap at different radial positions and with varying levels of fill. Discharge flow patterns were elaborated with tracer objects in the majority of experiments and the composition of the bulk solids during emptying was determined by sampling across the entire discharge stream. The effects of free fall distance and intermittent discharge and filling on segregation at filling as well as the effect of hopper angle on segregation at discharge were investigated. Furthermore, the influence of filling rate is discussed. Based on the results, side-to-side segregation with accumulation of fine particles to the silo walls clearly increases with increasing free fall distance. Segregation is also aggravated in situations where the silo is filled and discharged intermittently, because the shape of the powder bed’s surface changes when a portion of the silo contents is withdrawn. The effect of filling rate remains unclear and should be more deeply investigated in the future. The hopper angle determines the discharge flow pattern, i.e., funnel or mass flow, but the composition of the powder mixture towards the end of complete emptying is mainly determined by the material distribution at the levels of fill that are withdrawn last. The presented findings increase the understanding of the effect of process parameters and silo design on segregation, and can be used for mitigating the detrimental effects of segregation of bulk solids handled in silos.     

The dynamics of wet granular matter under a vertical vibration bed

This study investigates the dynamic properties of convection rolls in a 2D wet vibrated granular bed. A particle tracking method with the help of image-processing technology was used to measure the velocity fields, convection flow rate, and the granular temperatures in the wet vibrated granular bed. This study examines the dynamic behaviors of wet granular materials subjected to external vertical vibration. Different liquid contents, viscosities, and surface tensions were added to glass beads forming cohesive granular materials in the vibrated granular bed. This study presents a systematic investigation of the effects of the addition of liquid content, viscosity, and surface tension on dynamic properties of wet particulates. Results show that the convection flow rate and granular temperature decrease monotonically as the added liquid content and liquid viscosity increase. However, the effects of surface tension on the convection flow rate are more significant at the smaller liquid content than that at a higher liquid content. The convection flow rate also decreases in a power decay as the modified Bond number increases.     

Mixing of solids in different mixing devices

Mixing of powders is a common operation in any industry. Most powders are known to be cohesive, many agglomerate spontaneously when exposed to humid atmosphere or elevated storage temperature. Agitation of the powder (especially powders with different bulk densities) may result in migration of smaller particles downwards and of larger ones upwards. Another problem is segregation whose main cause is the difference in particle size, density shape and resilience. There are standard mixing devices, such as drum tumblers or Turbula mixers. Alternate device type used is the static mixer of Kenics type. Static mixers save energy, disable segregation and effect particle migration. In this paper, static mixers, as devices for powder mixing, are tested as well as Turbula and V-shaped drum mixer, since those devices are commonly used for powder blending in industry. Mixtures that were blended by means of those three devices were made out of the model material, quartz sand, in different component ratios (20:80 and 30:70). The results were statistically calculated and graphically presented. Cohesion indexes were measured with Powder Flow Analyser to see the effect of material flow on the mixture quality. The results obtained by those three devices, the particle size effect and cohesion indexes, bring us to the conclusion that static mixers could be used for mixing of powders, but their shape, number of mixing elements and the mixer length should be adapted for each mixture separately, experimentally and mathematically, through modelling of the system.