Granular Flow In Silos Research Articles

DEM modeling of the dilute-to-dense transition of granular flow in silos

The dilute-to-dense transition of granular flow in silo has been investigated by researchers, yet a detailed particle-scale description of this transition is still lacking. In this study, three-dimensional (3D) discrete element method (DEM) simulations are performed to investigate the dynamics of particles during this transition process through adjusting the inflow rate at the upper inlet. Based on Voronoi tessellation, the concept of caged particles is introduced to characterize the microscopic packing details of particles inside the silo. The analyses of probability density functions (PDFs) of vertical velocity and local packing fraction of particle in the proximity of outlet suggest that the dilute flow regime can be divided into two sub-stages (stage I and stage II). And the transition from stage I to stage II is manifested by the formation of persistent connection between the left and right clusters made of caged particles. It is found that for the dilute-to-dense transition process under fixed inflow rate condition, there exist two well defined critical packing heights that scale with the outlet size. Dynamic buildup and collapse of contact force network astride the whole outlet take place when the packing height of particle assembly at the centerline is in between these two critical heights. The simulation results thus suggest that the formation of a persistent contact force network spanning the whole outlet signals the transition of flow state from the dilute to dense.

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.

Effects of vibrations on tilted silo discharge

Introducing vibrations is a common way to improve the granular flow in silos to avoid clogging. In this study, a three-dimensional silo submitted to vertical vibration was built. The effect of vibration on the discharge of tilted silo was studied. The results showed that, the discharge rate did not depend on the particle depth but decreased with the increase of the outlet tilt angle, regardless if the silo was vibrated or not. Discharge rate showed non-monotonic relationship with vibration frequency at high amplitude, while increased with increasing frequency at low amplitude. The contour plots of the influence of vibration and tilt angle on the discharge were given. Based on the analysis of variance (ANOVA), the effect of the tilt angle on the discharge was higher than the vibration amplitude and frequency.

Micro-modelling of shear localization during quasi-static confined granular flow in silos using DEM

The paper deals with the quasi-static confined flow of cohesionless sand in a plane strain model silo with parallel walls and a slowly movable bottom. Numerical modelling was carried out by the discrete element method (DEM) using spheres with contact moments to approximately capture a non-uniform shape of sand particles. Different initial void ratios of sand and silo wall roughness grades were employed. Regular triangular grooves (asperities) with the same inclination and a different height were used to describe the varying wall surface topography. The emphasis was on the formation and evolution of both wall and internal shear zones during sand flow. DEM simulation outcomes were compared with corresponding model experiments and theoretical solutions. In addition, the particle displacements, particle rotations, normal contact forces, void ratios and wall stresses were evaluated. The numerical findings enhance the understanding of shear localization at the grain level during confined flow in silos and its strong impact on the magnitude, distribution and oscillation of wall stresses.

Modelling of shear zones during quasi-static granular silo flow using material point method (MPM)

The paper focuses on confined silo flow of cohesionless sand. The problem considered is a quasi-static flow in a plane strain model silo with parallel walls simulated with the material point method (MPM). The simulation used a non-local hypoplastic constitutive model. Initially, the paper validated the implemented numerical approach with basic element tests and a plane strain compression test. The subsequent MPM calculations for a model silo were performed with different initial void ratios of sand and silo wall roughness. The flow simulations took also into account the different both location and width of the outlet. The emphasis was on the evolution of both shear zones (wall and internal curvilinear shear zones) and their impact on wall stresses/forces during flow. The numerical findings enhance the understanding of shear localization in granular materials during confined controlled flow in silos and its immense effect on the magnitude and distribution of wall pressures.

Multifractal Intermittency in Granular Flow through Bottlenecks.

We experimentally analyze the intermittent nature of granular silo flow when the discharge is controlled by an extracting belt at the bottom. We discover the existence of four different scenarios. For low extraction rates, the system is characterized by an on-off intermittency. When the extraction rate is increased the structure functions of the grains velocity increments, calculated for different lag times, reveal the emergence of multifractal intermittency. Finally, for very high extraction rates that approach the purely gravitational discharge, we observe that the dynamics become dependent on the outlet size. For large orifices the behavior is monofractal, whereas for small ones, the fluctuations of the velocity increments deviate from Gaussianity even for very large time lags.

Modeling methods for gravity flow of granular solids in silos

Abstract This paper provides a review on the flow of free-flowing particles inside silos. We have previously reviewed in detail the experimental studies in this field. In the present work, the focus is placed on the theoretical approaches allowing numerical simulation and modeling of these systems. Modeling of granular flow in silos is very significant due to the advantages of modeling compared to experiments. The simulation methods are divided into four main groups: analytical methods, finite element method, discrete element method, and hybrid models. In each section, the most significant researches are reviewed. The drawbacks and advantages of each method are discussed, and the effects of different parameters are reviewed. Finally, the perspective of future work and the main challenges in this area are discussed.

Quantitative comparison of hydrodynamic and elastoplastic approaches for modeling granular flow in silo

Hydrodynamic and elastoplastic theories are two commonly used continuum approaches for modeling granular materials. Here, the elastoplastic approach is extended to incorporate the rheology of dense granular flow, which therefore allows a quantitative comparison with the hydrodynamic approach under the same setting of rheological laws, material parameters, and numerical method. The flow patterns yielded by two approaches are apparently similar and the discharge rates are close. Yet the elastoplastic approach creates a narrow dome‐like flow zone in contrast to the wide cone‐like flow zone generated by the hydrodynamic approach. The shear localization is also less prominent in elastoplastic modeling owing to the existence of elastic deformation. The stresses predicted by two approaches match well in flow zones but show significant differences in stagnant zones. The proposed elastoplastic approach incorporating flow rheology can be used generally in both solid and fluid states of granular materials. © 2019 American Institute of Chemical Engineers AIChE J, 65: e16533, 2019

Granular silo flow of inelastic dumbbells: Clogging and its reduction.

We study the discharge of inelastic, two-dimensional dumbbells through an orifice in the bottom wall of a silo using discrete element method (DEM) simulations. As with spherical particles, clogging may occur due to the formation of arches of particles around the orifice. The clogging probability decreases with increasing orifice width in both cases. For a given width, however, the clogging probability is much higher for the nonspherical particles due to their arbitrary orientations and the possibility of geometrical interlocking. We also examine the effect of placing a fixed, circular obstacle above the orifice. The clogging probability depends strongly on the vertical and lateral position of the obstacle, as well as its size. By suitably placing the obstacle the clogging probability can be significantly reduced compared to a system with no obstacle. We attempt to elucidate the clogging reduction mechanism by examining the packing fraction, granular temperature, and velocity distributions of the particles in the vicinity of the orifice.

Shape dependence of resistance force exerted on an obstacle placed in a gravity‐driven granular silo flow

Resistance force exerted on an obstacle in a gravity‐driven slow granular silo flow is studied by experiments and numerical simulations. In a two‐dimensional granular silo, an obstacle is placed just above the exit. Then, steady discharge flow is made and its flow rate can be controlled by the width of exit and the position of obstacle. During the discharge of particles, flow rate and resistance force exerting on the obstacle are measured. Using the obtained data, a dimensionless number characterizing the force balance in granular flow is defined by the relation between the discharge flow rate and resistance‐force decreasing rate. The dimensionless number is independent of flow rate. Rather, we find the weak shape dependence of the dimensionless number. This tendency is a unique feature for the resistance force in granular silo flow. It characterizes the effective flow width interacting with the obstacle in granular silo flow. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3849–3856, 2018

Study of granular flow in silo based on electrical capacitance tomography and optical imaging

This paper presents a comparison between optical images and two different modalities of electrical capacitance tomography (ECT), namely an off-the-shelf ECT system and a model one combining an inductance (L) - capacitance (C) - resistance (R) meter with a multiplexer. This comparison was performed to analyse the degree of measurement accuracy and to estimate the spatial resolution of the ECT systems. In this case, the detection of the position of flow boundaries during silo discharging and its translation when discharging changes from concentric to eccentric were investigated. A versatile rectangular silo model was used to generate different types of funnel flow of rice material, which was designated as the most adapted granular material to create both optical and electrical permittivity contrasts between stagnant and flowing zones. When a high temporal resolution is not requested, the model ECT system reduces the measurement error of flow boundary detection between 3% and 9% when compared with optical measurements. Moreover, the system is able to capture boundary translation of about 5% of the silo bin width, which is below the assumed spatial resolution of standard commercial ECT systems.

Obstacle-shape effect in a two-dimensional granular silo flow field

We conducted simple experiment and numerical simulation of two-dimensional granular discharge flow driven by gravity under the influence of an obstacle. According to the previous work (Zuriguel {\it et al.,\,Phys.\,Rev.\,Lett.}\,{\bf 107}: 278001, 2011), the clogging of granular discharge flow can be suppressed by putting a circular obstacle at a proper position. In order to investigate the details of obstacle effect in granular flow, we focused on particle dynamics in this study. From the experimental and numerical data, we found that the obstacle remarkably affects the horizontal-velocity distribution and packing fraction at the vicinity of the exit. In addition to the circular obstacle, we utilized triangular, inverted-triangular, and horizontal-bar obstacles to discuss the obstacle-shape effect in granular discharge flow. Based on the investigation of dynamical quantities such as velocity distributions, granular temperature, and volume fraction, we found that the triangular obstacle or horizontal bar could be very effective to prevent the clogging. From the obtained result, we consider that the detouring of particles around the obstacle and resultant low packing fraction at the exit region effectively prevent the clogging in a certain class of granular discharge flow.

STUDY OF DEGRADATION AND GRANULAR FLOW PROCESSES USING X-RAY IMAGING

This paper reviews the work that has been done in the past 10 years at the Lodz University of technology about the visualization and the quantification of phenomena related to degradation processes (i.e. stress corrosion cracking in stainless steel, fatigue crack in titanium alloys) in engineering materials as well as granular flow in silos using X-ray imaging (i.e. radiography and (micro)tomography). Besides presenting the experimental protocols, the paper also presents the image processing strategies that have been applied to enable the extraction of characteristic parameters from the volumetric images.

Testing the μ(I) granular rheology against experimental silo data

Industrial storage of granular material using silos is common, however, improved understanding of silo flow is needed. Various continuum models attempt to describe the velocity of dense granular flow in silos. Kinematic, and recently, stochastic models, based upon the diffusion of some quantity, perform well when there is a single orifice, and when the yield criterion is satisfied. However, if system stresses are insufficient to satisfy the yield criterion, or if there is a second orifice, these models fail to capture the entire flow behaviour. Advances in granular rheology have allowed a pressure dependent friction law to be defined which can capture the behaviour of granular silo flow including un-yielded zones, flow-rate independence of fill height, the Beverloo flow-rate, and various other phenomena. We performed silo discharge experiments in a flat bottomed planar silo with a single and two adjacent orifices, for two grain types. The velocity was measured using Particle Image Velocimetry. Results were compared to a mathematical model based on the μ (I) rheology which was shown to qualitatively capture the observed phenomena including plug-like zones where the yield criterion is not satisfied. These preliminary results strongly encourage future investigations into the effect of friction parameters and numerical boundary conditions.

Application of inserts for suppression of coupled dynamic–acoustic effects during confined granular flow in silos

The paper discusses methods to prevent coupled dynamic–acoustic effects during silo flow by means of inserts. Laboratory tests were carried out with a perspex and steel model silo with different inserts along the wall. As bulk solids, sand, polymer granulate and PET flakes were used. An effective method for a reduction of dynamic–acoustic phenomena during silo flow was elaborated. It was verified in large metal silos.

Confined granular flow in silos with inserts — Full-scale experiments

The paper describes results of experimental investigations of confined granular flow in a silo with different inserts. Over 100 experiments were carried out with dry cohesionless sand in a large metal silo with and without inserts at Tel-Tek, dept. POSTEC, in Norway. Wall pressures and flow patterns were measured during both silo filling and emptying. Three different insert types were used in the silo: double cone, cone-in-cone and inverted cone. Different positions of inserts were also investigated. Experimental results with inserts were compared with those without inserts. Some design recommendations for silos equipped with inserts were worked out.

Finite element methods for strongly‐coupled systems of fluid‐structure interaction with application to granular flow in silos

AbstractA monolithic approach to fluid‐structure interactions based on the space‐time finite element method is presented to investigate stress states in silos filled with granular material during discharge. The thin‐walled silo‐shell is discretized by continuum based, mixed‐hybrid finite elements, whereas the flowing granular material is described by an enhanced viscoplastic non‐Newtonian fluid model. To adapt the mesh nodes of the fluid domain to the structural deformations, a mesh‐moving scheme using a pseudo‐solid is applied. The level‐set‐method involving XFEM is used, including a 4D split algorithm for the space‐time finite elements, in order to describe free surfaces. The method is applied to 3D silo discharges. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulations of Granular Flow in Silos with Different Finite Element Programs: ANSYS vs. SILO

Great effort has been made to improve the knowledge about the behavior of granular material in silos. Nevertheless, many important aspects such as wall pressure, to which silo structures are subjected, still remain uncertain. Numerical simulations based on the finite element method have become a valuable tool to simulate the behavior of granular material in silos at rest and during their flow and to estimate the actions for which the structure has to be designed. However, great differences between various FE software packages have been observed. In this article, the results of two different FE software packages, the general-purpose software ANSYS and a special non-linear dynamic program called SILO, are compared, and the main problems of numerical simulations of granular flow in silos are discussed. Stresses of granular material are calculated during filling and discharge for two- and three-dimensional geometries, including different eccentricities of the outlet. Some numerical problems appear in both models when the bin is filled in several layers. Lateral pressures obtained with both models are similar for filling, but several differences may be observed during discharge. The ANSYS model presents some problems after short simulation discharge time, while the SILO model can simulate almost the entire process of discharge.

Experimental and theoretical investigations of silo music

This paper deals with strong dynamic effects connected with booming sound (called silo music) appearing during confined granular flow in silos. Novel experimental data have been gained through Electrical Capacitance Tomography (ECT) and an extraction of operational deflection shapes. A dynamic plane strain FE model of the granular material and oscillating wall was presented. The numerical results support the key role of dynamic coupling between silo wall oscillations and dynamics of the flowing material induced by a change of a flow direction at the transition zone between cylindrical and converging flow.

Modeling of shear localization during confined granular flow in silos within non-local hypoplasticity

The paper deals with multiple shear zones in the interior of cohesionless granular bodies during plane strain quasi-static granular flow with controlled outlet velocity in experimental silos. The finite element calculations were carried out with a hypoplastic constitutive model enhanced by a characteristic length of micro-structure by means of a non-local theory to obtain mesh-independent results. The constitutive model can reproduce the essential features of granular materials during shear localization. FE analyses were performed with the help of an Arbitrary Lagrangian–Eulerian formulation using an explicit time integration approach for experimental silos containing initially dense dry cohesionless sand. Silo walls were assumed to be very rough or smooth. Emphasis was given to the propagation of multiple shear zones in the interior of flowing sand. The numerical results were compared with corresponding experimental tests.