The paper records some of the results and observations from a pilot scale plane-flow silo with a variable geometry hopper and a fully width slot outlet. The original objectives were simply to study the shape of arches and their failure mechanisms under a range of conditions. However, the behaviour of arches did not conform to the conventional assumptions and neither did other silo behaviour. The paper contains a summary of the main findings of this work, but concentrates on the arches formed under mass-flow and non-mass-flow geometries for the filling condition.
Silos and bins fail with a frequency that is much higher than that of almost
any other industrial equipment. Sometimes the failure involves only
distortion or deformation that, while unsightly, does not pose a safety or
occupational hazard. In other cases, failure involves complete collapse of
the structure with accompanying loss of use and even loss of life.
Three major causes of silo failure are identified: design errors,
construction errors, and utilization errors. Numerous case histories are used
to illustrate common mistakes, limits of design, and lessons learned.
Stress distributions developing in granular materials in hoppers during the process of filling is fundamental for an understanding of the phenomena observed in hoppers. Predictions of such stress distributions are therefore essential. In this paper, based on a model which was created to simulate various filling procedures, an (ABAQUS) analysis has been carried out to investigate the development of stress distribution in the material and the loads on the hopper wall when the hopper is filled by the concentric-filling method. Calculations have been carried out either according to a procedure known as "switch-on" or according to the so-called layer-by-layer procedure. It was found that the maximum stress developed at the end of the filling, not at the bottom, but somewhere in the lower area of the hopper (layer 3). The stresses developed during layer-by-layer filling were greater than those developed during the switch-on filling in the lower area of the hopper, but were smaller in its upper area. Maxima of normal pressure along the wall were not at the outlet, even from the very beginning of filling. Instead, it was located at a position around 2/5 of the length of the wall from the outlet when the filling was finished. Various filling methods would have an effect on the stress distribution within the material and, consequently, affect the type and magnitude of loads on the hopper wall, and particularly at the hopper outlet.
A finite element analysis has been carried out to investigate flow patterns and loads on silos either with a ralatively steep hopper, or with a shallow hopper but in the presence of an insert. A Lagrangian-Eulerian approach was first adopted to simulate the material flow pattern, with the precondition that mass flow was obtained. It was then attempted to predict the loads exerted by granular materials on the walls of such silos. The load on the insert was also simulated. Techniques such as the adoption of adaptive meshes and filleting along sharp corners were applied in the analysis to overcome the difficulties usually encountered with large deformations in the FEM and the mathematic singularity presented by the abruptness of geometry. Filleting proved to be necessary to bring down the pressure peak at the transition level. The insert took over a significant part of the loads. Comparison with the classic theories have confirmed that the loads predicted on the wall agree quite well with the theoretical results in the silo's cylinder section, but that differences exist in the hopper section; the difference is greater when the hopper is shallower. It has also shown the limitations of predicting flow patterns of granular materials with the traditional elastic-plastic model; a more advanced model is needed.
While numerical methods have become an integral part of everyday work in
process engineering for fluid processes, there is a curious lack of such
methods in the field of solid handling. One of the reasons may be
the inability of the most often used CFD codes to handle bulk solids. In
the paper an attempt is made to show how the behaviour of bulk solids can be
modelled using a CFD code without a specific constitutive model for bulk
solids.
Another reason for not using numerical tools to handle bulk materials is
the difficulty of generating the necessary material parameters. Those material
models suitable for bulk solids that are available in commercial packages are
mostly derived from soil mechanics. Their parameters are determined using
a triaxial cell. This device is generally not available in the chemical
industries and most often not suitable for bulk solids, due to the high
stress levels applied in those tests. In the paper a method is presented
which allows the use of standard shear test data, supplemented by data from
a compression tests in a "lambda-meter", to determine the parameters of an
extended Drucker-Prager model with a compressive yield cap. Model
equations are given and parameters are determined for white polymer powder.
With these parameters a simulation of silo discharge has been performed
successfully using a CFD code.
To make CFD codes, which already have the much-needed multi-phase
capability, capable of handling bulk solid flow, significant work remains
to be done (e.g. shear stresses at rest and anisotropic stress tensors).
Common problems of industrial silo design can be solved with the use of the Jenike method. The Jenike method is an established procedure to investigate the critical outlet dimensions of a silo and the flow profile. However, in some cases the Jenike method is assumed to lead to overdesign, especially when silo design is calculated for highly dispersed bulk solids in the nano range or if the bulk solid contains moisture. Another way to determine the critical outlet dimension of a silo is a model test. We then have to consider the boundary conditions, i.e. the particle size, and a possible size reduction of the model silo, which is only possible in a centrifugal field using cohesive bulk solids. In this work, results of experiments in a silo centrifuge regarding scale-up are presented. The experiments have been performed to investigate the critical outlet dimension for a silo for very fine and moist bulk solids.
The paper contains a review of experiments with rape seed in a model silo with a semicircular flat bottom equipped with a low-height discharge device. Observations of flow patterns were made during filling and discharging through the transparent front wall of the model silo. Measurement of wall normal pressures and discharge flow rate were also made. A properly designed discharging device can eliminate a pressure peak which is usual for the transition point (dynamic overpressure) in mass flow silos. Experiments have shown that a low-height discharge device can be applied to reduce the pressure increase during discharging damaged silos.
Steady-state flow (ssf) of powders has been investigated using alternating strain paths, with precompacted powder samples sheared in alternating directions. The dependency of ssf on the level of precompaction is shown.
Over a period of about 12 years a research program on silo structures was going on in Germany, financed by the Deutsche Forschungsgemeinschaft. One of the subjects studied was the straining of silo structures in case of dust explosions, which often occur in silo plants. This was done by experiments and theoretical analysis. The first and third authors were engaged in this project. A few years later a very large silo structure was erected, where the third and second authors served as check engineers. A short report is given on the basic results obtained in the research and their application at the large silo plant, where in the meantime a dust explosion has occurred.
The paper deals with experimental and theoretical research of resonance effects during silo emptying. The influence of resonance effects on wall pressures in silos has been investigated with model tests and FE analyses. The model tests were carried out with a cylindrical and rectangular silo containing various cohesive and non-cohesive bulk solids. The onset of dynamic silo flow was simulated with controlled outlet velocity along the bottom in a plane strain model and large silo. The confined flow of dry sand in a silo with parallel walls during resonance was described with a finite element method based on a polar elasto-plastic constitutive law. It differs from the conventional theory of plasticity by the presence of Cosserat rotations and couple stresses using mean grain diameter as a characteristic length. In the FE calculations, the silo walls were taken into account.
This paper deals with the experimental investigation and numerical
simulation of silo discharge processes, including dynamic interactions
between silo filling and elastic silo walls.
The experiments have taken place in a large model silo with a height of 3m
and a rectangular base of 800 to 400mm. Optical measurement techniques
have been applied to investigate the flow profile, while load cells on the silo walls
have registered the stress' evolution, e.g. a stress peak (switch) move from the
outlet to the transition of hopper and shaft.
The measured data have been compared with simulation results of the Institute of
Applied Mechanics at the Technical University of Braunschweig. It has been
possible because the numerical simulation examples have been chosen to be similar
to the experimental test silo. The discharge process in the simulation is
described by a system of nonlinear differential equations. Via the Finite
Element Method (FEM) based on an Eulerian reference frame deformation
rate, velocity field, porosity and stress distribution can be
calculated without the need for re-meshing the FE grid.
The paper reviews the characteristics of pulsating or cyclic flow of bulk solids during gravity discharge in bins and silos. The dynamic load phenomenon is often referred to as "silo quaking" and is known to occur in silos of various geometrical shapes, operating under different flow patterns. Examples include mass-flow, funnel-flow, expanded-flow, multi-outlet bins and bins operating under intermediate-flow. While silo quaking is often associated with tall bins, depending on the flow pattern, the problem can also be experienced in bins of squat proportions. The period of pulsations during flow is influenced by various factors, such as, particle size and size distribution, silo wall material and wall roughness, internal friction, moisture content and discharge flow rate. Of particular relevance is the influence of slip-stick effects during shear flow, and velocity at critical sections in the silo during discharge. The paper presents an overview of silo quaking with case studies to illustrate the range of problems that can occur.
A simplified analysis of deformation and stress states in converging hoppers during filling and discharge of granular material is presented. In particular we discuss a method for solving the set of differential equations governing the flow of granular material in a plane wedge hopper. The equilibrium conditions and stress-strain relations are satisfied for the planar slice elements assuming the dependence of displacement and stress on the Cartesian coordinate z. The transient flow of an icompressible, cohesionless granular material in a two-dimensional converging hopper is considered. We assume the material to be in elastic or elasto-plastic states within the hopper satisfying the Coulomb yield condition and the non-associated flow rule. The paper presents a detailed analysis of the evolution of pressure acting on the hopper wall during the filling and emptying processes when the initial active state of pressure is transformed into a passive state. Analytical and numerical analyses are presented. It is shown that at the initial stage of the emptying process a considerable switch overpressure develops, exceeding the steady-state passive pressure several times.
The paper deals with numerical modelling of confined flow of granular materials in vertical bins. Quasi-static mass flow of non-cohesive sand with a controlled outlet velocity along the entire silo bottom was numerically studied using a finite element method taking into account an elasto-plastic constitutive law laid down within a Cosserat continuum. The influence of the initial density and the mean grain diameter of the solid, wall roughness, wall stiffness and imperfection, the initial stress state and the pressure level on the stress and deformation states in plane-strain vertical bins was investigated. The numerical results were compared with similar model tests performed with a rectangular vertical bin containing sand. The calculated results were in satisfactory agreement with the experimental ones. The advantages and limitations of the polar elasto-plastic approach to model granular silo flow were outlined.
The problems of flow of a granular material is the processes of silo discharge and filling are considered. Dynamic, two-dimensional problems are analyzed, both the plane and axisymmetric ones. The material point method is applied as an analytical tool, a variant of the finite element method capable of solving pertinent equations of motion on an arbitrary computational element mesh and tracing state variables at material points chosen independently of the mesh. The mechanical behaviour of a granular material is described with non-associative elastic-perfectly plastic and elastic-viscoplastic material models with the Drucker-Prager yield condition. The influence of friction between the flowing granular body and silo walls is taken into account. The material point method enables one to analyze silos of arbitrary shapes, including silos with inserts controlling the flow of the stored material. The mass and funnel types of flows are analyzed.
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