Silo Discharge Research Articles

Flow properties and arching behavior of biomass particulate solids

Abstract This paper addresses the problem of estimating solid biofuel flowability, with particular reference to arching phenomena in silo discharge. The flow properties and the tendency to arch formation over openings of three different biomass particulate solids, two cuts of sawdust and a dried ground olive husk, were studied. Shear testing experiments indicated that flow properties of particulate biomass could be measured by shear cells when the particle size is below 2 mm and that, however, particle elasticity or irregular shape could determine uncommon flow behavior. The pipe to arch transition was characterized for the biomass samples and a gypsum powder in a new tester, in which the critical opening size for arching was characterized as a function of the consolidation stress. This test allowed the ranking of material flowability which compared well with the ranking obtained according to the Jenike classification. A new procedure, derived from the Jenike's classical arch stability analysis, was proposed to evaluate the flow function of the materials from the critical orifice diameter for arching. An optimized procedure was suggested to obtain an estimate of material flow function from arching tests with a limited knowledge of other particulate biomass flow properties.

Buckling in Eccentrically Discharged Silos and the Assumed Pressure Distribution

Eccentric discharge in slender metal silos is known to be one of the most critical load conditions, responsible for many silo buckling disasters in the past. The high failure rate may be significantly attributed to difficulties in devising a suitable wall pressure representation for this condition. Where the flow of stored solids is eccentric and has partial contact with the wall in a slender silo, the solid exerts much lower pressures than the adjacent stationary solid. This pressure drop leads to very high local axial compression and causes buckling failure. Experimentally measured pressures indicate that a significant rise in pressure may occur just outside the flow channel, but its form and magnitude are not yet well understood because very detailed and expensive instrumentation is needed to obtain data that can define it. This paper explores the nonlinear structural behavior and buckling of a slender metal silo with and without specific inclusion of an adjacent rise in pressure, to determine whether it is a necessary part of any design pressure representation. To assist this investigation, the mechanics of the nonlinear behavior of a cylindrical silo under this load condition is explored using the analogy of a propped cantilever slice beam. Advantage is taken of a particular load condition that leads, by chance, to buckling at the same load factor for both linear and geometrically nonlinear analyses. This special case permits the detrimental effect of wall flattening and the beneficial effect of the changing prebuckling stress pattern to be explored to give a deeper insight into the behavior. The slice-beam analogy may also be generalized to describe the nonlinear behavior of any thin-walled cylindrical shell under meridional strip-like loads acting on part of the circumference.

Design and instrumentation of a mid-size test station for measuring static and dynamic pressures in silos under different conditions – Part II: Construction and validation

Using the design described in the first of this pair of articles, a full-size silo pressure test station was constructed. In this present article, the main characteristics of this station are described, together with the results obtained from the first validation tests. In addition, these results are compared with the European standard on silos.Very few experimental installations in the world have full-scale silos, and very few assays have been conducted on them. Consequently, many uncertainties remain which require further research in order to reliably predict the behaviour of material stored in this kind of structure.The results obtained demonstrate that the theoretical design of the test station is valid for measuring silo pressures and that the station offers multiple possibilities for future research.Although the principle aim of this article is to demonstrate that the previous theoretical design is valid, some novel conclusions can also be drawn from the tests performed. For example, observation of pressure patterns under static conditions inside the silo, and of overpressure surge patterns during silo discharge, has led us to conclude that the existence of asymmetrical pressures inside the silo is not a consequence of chaotic behaviour, but rather obeys certain physical laws which have still not been sufficiently studied.

Slender thin cylindrical shells under unsymmetrical strip loads

Modern procedures for the design of shell structures against buckling have their basis in analytical studies of axisymmetric shell geometries under the very simple load cases of uniform compression, external pressure and torsion. Studies of more complex but realistic stress states were based on prebuckling analyses using either membrane theory or linear bending theory because even these involved considerable mathematical complexity. As a result, only limited conclusions for practical design could be drawn and the effects of geometric nonlinearity could not be assessed. With recent advances in computing power and nonlinear finite element programs, it is now possible to undertake nonlinear analyses of complex load patterns that would have been very difficult to do only a decade or so ago.A number of practical load cases lead to a strip of pressure down one meridian, of which the best known ones are probably wind on tanks, eccentric discharge in silos, local thermal differentials, and partial fluid filling of a cylinder. This paper explores some of the rather unexpected stress patterns and modes of buckling that are predicted to develop in thin-walled cylindrical shells under such unsymmetrical strips of normal pressure. The results of a parametric study are presented to show the influence of the circumferential spread of the pressure strip on the structural behaviour. It is shown that the structural response to such loads may be very different, depending on whether the load acts inward or outward, and whether geometric nonlinearity and geometric imperfections are also included in the assessment.

ECT Image Analysis Methods for Shear Zone Measurements during Silo Discharging Process

The paper covers the electrical capacitance tomography (ECT) data analysis on shear zones formed during silo discharging process. This is due to the ECT aptitude for detection of slight changes of material concentration. On the basis of ECT visualisations, wall-adjacent shear zone profiles are analysed for different wall roughness parameters. The analysis on changes of material concentration, based on ECT images, enables the calculation for the characteristic parameters of shear zones—size and material concentration inside the shear zone in a dynamic process of silo discharging. In order to verify the methodology a series of experiments on gravitational flow of bulk solids under various conditions were conducted with different initial granular material packing densities and silo wall roughness. The investigation shows that the increase in container wall roughness is an effective method for reducing the dynamic effects during the material discharging, since these effects are resulted from the resonance between hopper construction and trembling material. Such effects will damage industrial equipment in practical applications and need further investigation.

Analysis of the bulk solid flow during gravitational silo emptying using X-ray and ECT tomography

This paper presents results of the solid concentration changes and shear zone analysis in cohesionless bulk solids during granular flow in a rectangular silo using X-ray technique during continuous exposure. The analysis of 1D cross-sectional plots and 2D images based on X-ray radiographs present the evolutions of solid concentrations and formation of shear zones in dry sand during silo discharge. Experiments were carried out with different initial packing densities of sand and silo wall roughness. The obtained 1D and 2D results carried out in the bin section of the silo were compared with the ones obtained on the same silo model using Electrical Capacitance Tomography. This comparison, besides the gravitational flow analysis, is an essential element of the research, which aims at a better interpretation of the measuring signal from ECT in the case of monitoring and diagnostic of solid flow.

Segregation of powder mixtures at filling and complete discharge of silos

This paper presents segregation of powder mixtures in silos of different scale on the basis of recent experimental findings with binary and ternary mixtures as well as commercial construction materials. Dimensional analysis is performed to reduce the number of variables and to bring forth dimensionless groups. Based on these experimental correlations (models) are proposed for describing the concentration of fine particles at the walls as a result of silo filling and segregation towards the end of complete discharge. Parameters of both models are fitted to experimental data using the method of least sum of squares. The filling model shows good agreement with experimental data and the description of segregation at discharge is in general agreement with experimental findings. Important variables for the distribution of particles at silo filling include the mass fraction of fines, particle size ratio (coarse/fine), particle solid density ratio (coarse/fine), free fall distance, silo diameter and inlet diameter. On the basis of the proposed model for silo filling, the concentration of fine particles at the silo walls increases with increasing fines content, size ratio and density ratio for the powder mixture, as well as the ratio for free fall distance and silo diameter and the ratio for silo diameter and inlet diameter. This result is in general agreement with the findings of other investigators, but the observation that segregation at silo discharge is, to a large extent, determined by the material distribution at filling is new and interesting. This confirms the qualitative conclusions of earlier work by the authors and shows that mass flow designs do not always entirely correct for side-to-side segregation patterns (induced during filling) at silo discharge. The findings of this paper should be of considerable interest to producers of construction materials and to other industries where segregation of powder mixtures in silos is a major concern.

Flow Channel Boundaries in Silos

AbstractThe critical slip planes at the silo filling state are compared with the flow channel boundary during silo discharge for semi‐mass flows. The static critical slip planes are determined by using the dynamic programming method based on the stress field of granular solids stored in silos at the filling state. The flow channel boundary is estimated through the finite element analysis of the silo discharge. The results indicate that the critical slip line lies above the flow channel boundary. This characteristic can be attributed to the changeover of major principal stress directions of granular solids from the silo filling to the silo discharge. The analysis demonstrates that the silo wall friction tends to lift up the critical slip plane and flow boundary. A simple correlation is developed between the positions of critical slip planes and flow boundaries and is experimentally verified.

Flowers in flour: Avalanches in cohesive granular matter

We report on the intermittent dynamics of the free surface of a cohesive granular material during a silo discharge. In absence of cohesion, one observes the formation and the growth of a conical crater whose angle is well defined and constant in time. When the cohesion is involved the free surface exhibits a complex dynamics and the crater, resulting from a series of individual avalanches, is no longer axisymmetric. However, in spite of the intermittent behavior of the free surface, the flow rate is observed to remain constant throughout the discharge.

Simulation for Silos Discharge with 2D DEM

In this paper, using the discrete element method (PFC2D)particle flow procedure to establish a model of cylindrical silo, in the warehouse filled with particles within the reach of static equilibrium state, then the record of its wall static lateral pressure measurement value, while monitoring the measured dynamic wall pressure during the silo discharging. It was shown that the static pressure as well as the dynamic pressure simulated with the numerical model is in good agreement with the experimental results. So the discrete element method can give a new way to study dynamic question of silos.

Outflow properties of silos: The effect of arching

Engineers working on the field of agriculture, food- or pharmaceutical industry or in the architecture frequently meet problems arising from the special properties of granular assemblies. Storing large amount of particulate raw materials is mostly made by using large containers, called silos. The design of such large silos is far not an easy problem. The outflow properties are one of the most important parameters of silo design. The constant discharge rate of silos differs from the discharge rate of containers filled with liquids. In case of fluids, the flowing velocity and discharge rate changes with fluid level. In case of granular materials, the velocity is constant (independent of the filling level of silo). There are methods used for the determination of silo discharge rate, but these are mostly experimental without physical explanation of the phenomenon. In this paper we demonstrate that the constant discharge rate is caused by the formation and collapse of arches in the bin. Based on this assumption, we derive an equation for determining the discharge rate. Using the same arching hypothesis we derive the equations describing the velocity distribution at silo outlets. The usability of our new approach is demonstrated by experimental investigations.

High-speed imaging of traveling waves in a granular material during silo discharge

We report experimental observations of sound waves in a granular material during resonant silo discharge called silo music. The grain motion was tracked by high-speed imaging while the resonance of the silo was detected by accelerometers and acoustic methods. The grains do not oscillate in phase at neighboring vertical locations, but information propagates upward in this system in the form of sound waves. We show that the wave velocity is not constant throughout the silo but considerably increases toward the lower end of the system, suggesting increased pressure in this region, where the flow changes from cylindrical to converging flow. In the upper part of the silo the wave velocity matches the sound velocity measured in the same material when standing (in the absence of flow). Grain oscillations show a stick-slip character only in the upper part of the silo.

Membrane theory treatment of eccentric flows in concentric hoppers

This paper presents an initial study of the effects of an accidental eccentric flow channel that sometimes develops in the conical hopper of a metal storage silo. A simple assumed pressure regime is adopted, based on studies of eccentric discharge in cylindrical silos, and the structural actions are analysed using shell membrane theory. The results are verified against a finite element analysis. A set of equations is derived which give the complete membrane stress state in the hopper under such an unsymmetrical pressure regime. Under symmetrical loading, silo hoppers are subject to biaxial tension, with failure normally governed by material rupture due to tensile meridional membrane stresses. It is found that the eccentric flow channel leads to dramatically increased meridional membrane stresses at the transition. Compressive membrane stresses are also found near the hopper outlet and at the sides of the flow channel near the transition. A reasonably close correlation is found between the derived membrane theory equations in a right circular conical hopper and linear elastic finite element predictions.

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)

Application of ECT to solid concentration measurements during granular flow in a rectangular model silo

The paper presents results of concentration changes in cohesionless sand during dynamic mass flow in a rectangular model silo composed of a bin and hopper. Electrical capacitance tomography (ECT) was used. Sensors were located outside the silo along both the periphery and height. Local horizontal one-dimensional and cross-sectional two-dimensional evolutions of solid concentrations in dry sand during silo discharge were determined. The first ones were estimated from the raw data and the latter were obtained with the aid of the reconstructed data using a Linear Back Projection algorithm (LBP) to solve an inverse problem. Experiments in a model silo were carried out with two different initial sand densities and wall roughness grades. The measured results with ECT were compared with corresponding ones obtained with a Particle Image Velocimetry (PIV) method.

Calibration of discrete element parameters and the modelling of silo discharge and bucket filling

The discrete element method (DEM) is a promising approach to model machine–granular material interaction. The accuracy of DEM models depends on the model parameters. In this study a calibration process is developed to determine the parameter values. Laboratory shear tests and compressions tests are used to determine the material internal friction angle and stiffness, respectively. These tests are repeated numerically using DEM models with different sets of particle friction coefficients and particle stiffness values. The shear test results are found to be dependent on both the particle friction coefficient and the particle stiffness. The compression test results show that it is only dependent on the particle stiffness. The combination of shear test and compression test results can be used to determine a unique set of particle friction and particle stiffness values. The calibration process is validated by modelling silo discharge and bucket filling. It is shown that DEM can accurately predict the silo discharge rate and flow patterns. It is also shown that DEM can predict bucket forces, fill rates and fill patterns.

A study of influence of gravity on bulk behaviour of particulate solid

This paper examines the influence of gravity on the bulk responses of a granular solid. The loading scenarios in this study include confined compression, rod penetration into a granular medium and discharging through an orifice. Similar loading and flow conditions are likely to be encountered in the stress and deformation regimes that regoliths are subjected to in extraterrestrial exploration activities including in situ resource utilisation processes. Both spherical and non-spherical particles were studied using the discrete element method (DEM). Whilst DEM is increasingly used to model granular solids, careful validations of the simulation outcomes are rather rare. Thus in addition to exploring the effect of gravity, this paper also compares DEM simulations with experiments under terrestrial condition to verify whether DEM can produce satisfactory predictions. The terrestrial experiments were conducted with great care and simulated closely using DEM. The key mechanical and geometrical properties for the particles were measured in laboratory tests for use in the DEM simulations. A series of DEM computations were then performed under reduced gravity to simulate these experiments under extraterrestrial environment. It was found that gravity has no noticeable effect on the force transmission in the confined compression case; the loading gradient in the rod penetration is linearly proportional to the gravity; the mass flow rate in silo discharge is proportional to square root of the gravity and the angle of repose increases with reducing gravity. These findings are in agreement with expectation and existing scientific evidence.

Arch-Free flow in aerated silo discharge of cohesive powders

Arching can occur during silo discharge of cohesive powders. In general this happens when the outlet size is not wide enough. Flow aid devices, such as aeration pads, are commonly used in the industry to achieve proper flow of cohesive materials. However, no design criteria are presently available for such kind of devices and, in particular, for the intensity of aeration to be used to avoid arching. Aim of this paper is the evaluation of the limiting aeration condition to produce the collapse of established arches and the minimum aeration rate necessary for no arching discharge flow. Experimental tests are carried out in an aerated flat bottom silo. The measured quantities are the aeration rate at arch collapse and the arch size. Powder permeability is characterized by fluidization experiments. A simplified model is proposed to assess on the prevailing physical phenomena and predictively evaluate the minimum aeration rate to determine no arching discharge flow.

Determination of bulk solid concentration changes during granular flow in a model silo with ECT sensors

Experiments in a cylindrical model silo were carried out with different initial densities of sand and silo wall roughness. Solid concentration changes during granular flow in the model silo were measured with electrical capacitance tomography (ECT) sensors. During silo flow, strong dynamic effects connected with booming sound occurred. Local one-dimensional (1D) and cross-sectional 2D evolutions of solid concentrations in dry sand during silo discharge were observed. The 1D phenomena were estimated from the raw data and the 2D phenomena were obtained from the reconstructed data by solving an inverse problem with a linear back projection algorithm.

Discrete modeling of granular flow with thermal transfer: Application to the discharge of silos

Heat transfer in particulate beds has an important impact for many industrial processes as well as for the storage of particulate material. This study is aimed at modeling the granular flow and heat transfer between particles during the discharge of a silo. A numerical model based on the detection of contacts and the evolution of heat transfers in particle flow has been developed by using discrete element method (DEM). Through this study, we model the heat flows generated by friction and its transfer by conductance. Influence of the friction coefficient and discharging velocity on the granular flow and heat transfer has been investigated through some numerical examples. This modeling enables to understand better the phenomena at the contact point between particles as well as the heat transfer for a great number of particles in motion from their intrinsic mechanical properties and contact conductance.