Silo Discharge Research Articles

A new GPU-based DEM simulator for polydispersed granular systems with wide size distribution and its application in the silo discharge

While discrete element method (DEM) has been successfully established in many studies, serious problems have limited its industrial-scale applications. Considerably long runtime is one of the most critical bottlenecks of the DEM simulation applicability. Despite extensive efforts on the parallelization of DEM on the CPU or GPU, DEM runtime on the current generation of computers is so long that further improvements are demanded. Moreover, while many real-world granular systems consist of polydispersed particles with a relatively wide size distribution, the majority of DEM simulation studies have assumed monodispersed particle assemblies. Few have studied the parallelization of polydispersed systems, and fewer have developed GPU-based codes for these systems. The main purpose of this study is to provide a novel solver, NP-DEM, which is optimized for GPU-based simulation of polydispersed particle systems with a wide size distribution. Silo discharge is chosen as the case study to examine the applicability of the code.

Multi-level arch characteristics and flow enhancement regulation of nano powders discharged from silo

Nanoparticles have broad application prospects, but their poor flowability poses a challenge to the handling and transportation. Here, we experimentally demonstrate that modulated pulsed aeration can destroy the consolidation of nano powder and achieve a breakthrough in silo discharge from clogging to flow. We confirm the multi-level arch structure in the silo discharge of nano powders: free-fall arch and cohesive arch. And the location of multi-level arch can be determined by the yield stress of material. Furthermore, the method of combined pulsed aeration was proposed to enhance the discharge flow. Specifically, the influence of modulation of pulsed airflow including frequency and duty cycle and aeration location configuration on nanoparticles silo discharge flow was explored. And the optimal combination method of double pulsed aeration was determined to eliminate the cohesive arch and greatly increase the discharge rate, which is close to the hypothesis liquid-like flow rate.

Neural network prediction of residence time distribution for quasi-2D pebble flow

An important parameter in silo discharging is residence time distribution (RTD), which describes the time each pebble stays within the bed. RTD can be applied as a key indicator to estimate reaction processes, and a key analytical metric to assess the inherent safety of reactors. However, due to the difficulty in obtaining pebble trajectories, few studies on discharging processes have been carried out. In this research, a pilot experimental study is conducted to get quantitative data and prediction model on RTD with precise predictions. The feasibility of applying neural network methods to RTD prediction is also checked. The accuracy of neural network prediction is confirmed by comparing the error between predicted and experimental results. It is discovered that RTD isoline changes in different regions and characterized by intuitive physical models. Compared to DEM, the neural network has a significant advantage in computing speed while retaining acceptable prediction accuracy.

Subdiffusion model for granular discharge in a submerged silo.

Silo discharge has been extensively studied for decades although questions remain regarding the nature of the velocity field, particularly for submerged systems. In this work, fluid-driven granular drainage was performed in a quasi-two-dimensional silo with grains submerged in fluid. While the observed Gaussian velocity profiles were generally consistent with current diffusion models, the diffusion length was found to significantly decrease with height in contrast to the increases previously seen in dry silos. We propose a phenomenological anomalous diffusion model for the spreading of the flow upwards in the cell, with the fluid-driven flows we study here falling in the category of subdiffusive behavior. As the viscous characteristics of the system were amplified, the diffusion length increased and the shape of the flowing zone in the silo changed, deviating further from the parabolic form predicted by traditional normal diffusion models, in effect becoming more subdiffusive as quantified by a decreasing diffusion exponent.

Continuum simulation of non-local effects in a granular silo discharge flow using a regularized μ(I) rheology model

The effect of non-local momentum transport on a silo discharge process is numerically investigated using a continuum simulation with the μ(I) rheology model in which the gradient expansion model is adopted to account for the non-local effects due to the non-uniform field of inertial number I [Bouzid et al., Phys. Rev. Lett. 111, 238301 (2013)]. The singularity for I = 0 is handled with a regularization scheme [Lin and Yang, J. Comput. Phys. 420, 109708 (2020)]. Compared to the discharge dynamics predicted with the local μ(I) rheology model, the non-local effect enhances the velocity field to increase the volume discharge flow rate Q, especially when the silo orifice L is narrower. Both the local and non-local flow simulations conform to the Beverloo relation Q=Cρg(L−kd)3/2, where d is the intrinsic grain diameter but the non-local effects appear to lessen the orifice reduction effect coefficient k. The difference between the local and the non-local flow rates ΔQ¯, made dimensionless by ρgd3/2, grew monotonically with decreasing L/d with a slight enhancement if the silo height-to-width aspect ratio deviates from unity. Finally, we evaluated the ratio of the shear strain rate to the instantaneous maximum value to define a high-shear zone when the ratio is above a threshold and studied its evolution from the onset to the end of the discharge process. Interestingly, non-local momentum transport helped to reduce the size of the high-shear zone to give a more uniformly fluidized central zone above the orifice.

Experimental analysis of wheat-wall friction and grain flow in a steel silo with corrugated walls

Frictional behaviour of wheat on corrugated steel walls, pressure distribution, and grain flow were investigated using a silo model with a square cross section. Corrugated steel sheets were attached to both side walls of the model silo, while clear polymethyl methacrylate was used for the front and rear walls to allow observation of the flow. In addition, a truncated steel pyramid was used for the hopper and a square outlet with sides varying from 0.02 m to 0.06 m. A test panel was placed at one of the side walls in the place of a cut off fragment of the wall to measure lateral and frictional wall forces. The tests were conducted using winter wheat, and two filling methods (central and distributed) were considered to analyse their possible influence on bulk density or shear behaviour during silo discharge. It was found for the distributed filling that the grain-wall friction coefficient during discharge was nearly 20% larger than that for the central filling. This coefficient was found to increase slightly with the increasing size of the outlet, a trend that was not observed for the central filling. The experimentally determined pressures and coefficient of wheat-wall friction were compared with the recommendations of Eurocode standard EN 1991-4. Differences between the experimental and theoretical results demonstrate that the formulae proposed by the Eurocode do not take into account some important issues associated with friction between the grain and the corrugated silo wall. • A silo with corrugated steel walls was constructed. • A test panel was placed at the side wall to measure lateral and vertical forces. • A side length of an square outlet in truncated pyramid hopper was varied. • No effect of the filling method on the mass flow rate of material was found. • Larger wheat-wall friction coefficient for distributed filling was obtained.

Comment on Maraveas, C. Concrete Silos: Failures, Design Issues and Repair/Strengthening Methods. Appl. Sci. 2020, 10, 3938

Current silo analysis and design methods developed from Janssen’s theory focus mainly on the flow of the granules inside the silo by assuming that the overall silo structure is infinitely rigid. A silo structure during discharge is technically a time varying mass dynamic problem, where the properties of the overall silo structure and the discharge rate and material properties also contribute to the development of the load. The physics of a silo system requires equilibrium between the granules inside the silo, the silo structure as a whole and the surrounding air. The established scientific principles and experimental data require fulfilling such equilibrium to accurately predict the dynamic loads during discharge. This correspondence explains how the equilibrium between the granules inside the silo, the silo structure as a whole and the surrounding air can be achieved to better predict and control the dynamic loads generated by the silo discharge process.

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.

Flow in an hourglass: particle friction and stiffness matter

Granular flow out of a silo is studied experimentally and numerically. The time evolution of the discharge rate as well as the normal force (apparent weight) at the bottom of the container is monitored. We show that particle stiffness has a strong effect on the qualitative features of silo discharge. For deformable grains with a Young modulus of about Y m ≈ 40 kPa in a silo with basal pressure of the order of 4 kPa, lowering the friction coefficient leads to a gradual change in the discharge curve: the flow rate becomes filling height dependent, it decreases during the discharge process. For hard grains with a Young modulus of about Y m ≈ 500 MPa the flow rate is much less sensitive to the value of the friction coefficient. Using DEM data combined with a coarse-graining methodology allows us to compute all the relevant macroscopic fields, namely, linear momentum, density and stress tensors. The observed difference in the discharge in the low friction limit is connected to a strong difference in the pressure field: while for hard grains Janssen-screening is effective, leading to high vertical stress near the silo wall and small pressure above the orifice region, for deformable grains the pressure above the orifice is larger and gradually decreases during the discharge process. We have analyzed the momentum balance in the region of the orifice (near the location of the outlet) for the case of soft particles with low friction coefficient, and proposed a phenomenological formulation that predicts the linear decrease of the flow rate with decreasing filling height.

Silo discharge: influence of the particle shape on the velocity profiles

Experiments on the discharge of a silo with an inclined outlet are performed using flattened seeds in order to evaluate the validity of a previous theoretical formulation developed in our work group [1]. In that description, funnel flow regime is assumed to be based on a free fall parabolic arc. The shape of this arc is described with a parameter which is the only one involved in the flow rate formulation. An experimental analysis of the behavior of this parameter is carried out based on the geometry and shape of the grains within the silo. Also, video analysis of the silo discharge is performed in order to investigate the velocity profiles at the outlet of the hopper for these non-spherical particles. Experiments are contrasted with analytical predictions derived from the proposed formulation in order to assess and discuss its validity for the case of flattened particles.

Granular size segregation in silos with and without inserts.

The storage of granular materials is a critical process in industry, which has driven research into flow in silos. Varying material properties, such as particle size, can cause segregation of mixtures. This work seeks to elucidate the effects of size differences and determine how using a flow-correcting insert mitigates segregation during silo discharge. A rotating table was used to collect mustard seeds discharged from a three-dimensional (3D)-printed silo. This was loaded with bidisperse mixtures of varying proportions. A 3D-printed biconical insert was suspended near the hopper exit to assess its effect on the flow. Samples were analysed to determine the mass fractions of small particle species. The experiments without the insert resulted in patterns consistent with segregation. Introducing the insert into the silo eliminated the observed segregation during discharge. Discrete element method simulations of silo discharge were performed with and without the insert. These results mirrored the physical experiment and, when complimented with coarse graining analysis, explained the effect of the insert. Most of the segregation occurs at the grain-air free surface and is driven by large velocity gradients. In the silo with an insert, the velocity gradient at the free surface is greatly reduced, hence, so is the degree of segregation.

The performance of the µ(I)-rheology model on flat bottom silos discharge

The aim of this work is to explore the capability of the µ(I)-rheology model and its numerical implementation in addressing a silo discharge problem by computational simulation. In order to do so, the model was implemented in the general structure of an Eulerian multiphase solver based on the Volume-Of-Fluid (VOF) method of the OpenFOAM(R) suite. First, the implementation is validated against the results of another Lagrangian and Eulerian codes in a two-dimensional discharge problem. After that, the model is tested against the experimental results of a lab-scale and industrial-scale discharge problem. While the results of the first one were satisfactory in terms of discharge rate, for the latter one, the model exhibits disagreements in the flow patterns inside the silo. The study shows the limits of applicability of the standard formulation of the model for real scale silos and sets the ground for further discussion and improvements.

The effect of cohesion on the discharge of a granular material through the orifice of a silo

We present the results of both experimental and numerical investigations of the silo discharge for a cohesive granular material. In our study, thanks to a cohesion-controlled granular material (CCGM) we propose to investigate the effect of the cohesive length lc, on the discharge of a silo for two different configurations, one axisymmetrical, and one quasi-2D rectangular silo. In both configurations, an adjustable bottom is used to control the size of the orifice. As observed for cohesionless granular material by previous studies, the mass flow rate and the density through an orifice are mostly controlled by the diameter of the orifice D. The experimental results of the quasi-2D silo are compared with continuum numerical simulations.

Silo discharge of mixtures of soft and rigid grains.

We study the outflow dynamics and clogging phenomena of mixtures of soft, elastic low-friction spherical grains and hard frictional spheres of similar size in a quasi-two-dimensional (2D) silo with narrow orifice at the bottom. Previous work has demonstrated the crucial influence of elasticity and friction on silo discharge. We show that the addition of small amounts, even as low as 5%, of hard grains to an ensemble of soft, low-friction grains already has significant consequences. The mixtures allow a direct comparison of the probabilities of the different types of particles to clog the orifice. We analyze these probabilities for the hard, frictional and the soft, slippery grains on the basis of their participation in the blocking arches, and compare outflow velocities and durations of non-permanent clogs for different compositions of the mixtures. Experimental results are compared with numerical simulations. The latter strongly suggest a significant influence of the inter-species particle friction.

Experimental investigation on air bubble dynamics during fine powder discharge in a silo

An unstable discharge rate occurs during dry fine powder discharge from a silo due to significant two–phase solid/gas interactions that occur in powder flows. In addition, the air bubble phenomenon may occur in a silo during fine powder discharge. The bubble dynamics seriously influence the fine powder discharge stability in the silo. Therefore, for some industrial applications with silo discharge of fine material, it is important to understand it. In this study, we experimentally investigate the effect of air bubbles on fine powder discharge behavior, including the discharge mass flow rate and variation in pressure inside the silo. An initial collapse of the powder bed in the silo is observed at the beginning of the discharge process, causing the pressure to change rapidly. Moreover, the dependence of the bubble size, bubble rising velocity, number of bubbles, and frequency of bubble generation on the size of the fine powder are analyzed in detail. The air–loss index for different particle sizes is calculated to investigate the proportion of the air flowing into the silo that disperses into the voids between the powders and does not become part of a bubble. The bubble properties in the experimental cases that use different particle sizes are consistent with the Geldart particle classification of the used powders. The results of this study successfully illustrate the bubble dynamics and the discharge behavior of fine powder.

An experimental investigation on jamming and critical orifice size in the discharge of a two-dimensional silo with curved hopper

During the silo discharging progress, if the orifice size is not large enough, the orifice of the silo would be jammed by granules due to the formation of an arch. The silo with a curved hopper can effectively prevent jamming because the contraction rate is constant. To clarify the critical orifice size of the curved hopper which does not affect the outpouring of cohesionless granules,the jamming at different orifice sizes was analyzed. It was found that the change in jamming probability is similar at different contraction rates. Moreover, the relationship between the structure of the arch and the critical orifice size was clarified. Later on, a prediction model for the critical orifice size of the curved hopper was proposed. Finally, the effectiveness of the model was verified by experiments. Overall, the results are useful for understanding the jamming during discharging andfurther providing guidelines for the appropriate design of curved hoppers.

Numerical Modeling of Wall Pressure in Silo with and Without Insert

Abstract This paper presents a methodology based on the finite element method to simulate the flow of granular materials. Moreover, it allows proper estimation of dynamic pressure during silo discharge since this subject is still under discussion, especially for designing silos with an insert (an input element). A 2-D simulation of the discharge process of a cylindrical silo with cone and a central discharging orifice was performed. Two cases were studied, with and without using insert in silo. Numerical analysis was carried out with the help of the uncoupled arbitrary Lagrangian–Eulerian (ALE) approach. The resulting dynamic pressure distribution on the silo wall for each of the two cases was inferred numerically. The resulting values of pressure were compared with the results of the experimental study on a cylindrical metal silo to demonstrate the accuracy of the numerical model in determining the dynamic wall pressure, especially in the case of using an insert in silo during discharge.

Application of a new method for experimental validation of polydispersed DEM simulation of silo discharge

There are numerous experimentally validated simulations for mono-dispersed systems in the literature based on discrete element method (DEM). In practice, however, most of granular systems consist of polydispersed assemblies of particles. Few studies have considered the effect of polydispersity, and yet fewer have experimentally validated the results. In this study, application of a new experimental method for granular flow analysis is presented, capable of validating the results of an in-house developed GPU-based DEM solver in both monodispersed and polydispersed assemblies. Silo discharge is chosen as the case study in which discharge time, flow pattern and more importantly, the outlet composition variation with time (for polydispersed configurations) have been experimentally evaluated and validated with numerical results. The outlet composition, which is the ratio of fine to coarse particles in the outlet stream, is an essential measure of segregation in polydispersed silos, and its numerical prediction can be correct only if the interactions between fine and coarse particles within the silo are modelled precisely. Measuring this parameter is not possible using conventional experimental methods established in silo discharge studies such as high speed photographing or high-frequency weight measurement of the bed. A new apparatus has been developed which can measure this parameter. The device is a compartmented wheel rotating with a motor which gathers the outlet stream of the silo into different compartments. Due to practical limitations, design and function of the apparatus are not ideal. Forward mixing, distribution of particles with the same resident time in different compartments, is the most critical problem. Non-idealities must be compensated by means of post-processing codes so that comparable results are obtained from experiment and simulation.

Eulerian modelling of the powder discharge of a silo: Attempting to shed some light on the origin of jet expansion

Powder discharging from a silo provokes an emission of dust. To understand and prevent this source of danger, 3D simulations of a silo discharge were performed using an Euler-Euler approach. The impact of the coupling between the flow inside the silo and the granular jet in free-fall is analyzed. Results show that the solid mass flow rate is correctly predicted and that gas back-flowing at the hopper exhaust appears responsible for the formation of a fluctuating and radially expanding jet. However, the radial expansion of the free-falling jet is underestimated. Stochastic fluctuations of the particles velocity at the hopper exhaust are introduced to evaluate their effect on the downstream development of the free-falling jet. These fluctuations are found capable of generating a development of the jet similar to that observed experimentally. This suggests that the granular flow conditions at the hopper exhaust are responsible for the further dispersion of powder.

Multi-scale experimental study on filling and discharge of squat silos with aboveground conveying channels

Filling and discharge tests of reduced-scale and full-scale squat silos with aboveground conveying channels are carried out to investigate the pressure distribution and the overpressure evolution on the wall and the channel. The filling tests imply that the pressure distribution on the wall bottom is significantly influenced by the channel. Rankine’s active earth pressure equation gives accurate prediction of the lateral pressure on the wall, which is overestimated by the Jaky’s equation. The filling pressure on the channel wall is related to the stored material heights caused by the repose cone. The arch effect of the channel and the equilibrium effect of the wall friction in the squat silos should not be overrated. The shallow buried theory gives more reasonable prediction of filling pressure on the wall and the channel in the squat silos. The discharge tests show the overpressure coefficient does not increase with the increase of the discharge eccentricity. Meanwhile, the aspect ratio has a great influence on the overpressure coefficient. An overpressure on the top wall and the side wall of the channel is observed in multi-scale discharge tests. It is suggested that the overpressure coefficient of the channel should be considered when calculating the discharge load.