Hopper Wall Research Articles

Analysis of the active stress field in hoppers

Slice element methods are widely used for calculation of stresses in silos. However, more accurate means are available, since large computer capacities facilitate numerical calculation procedures. The active state of stress in plane-strain silos prevailing after initial filling of a silo is investigated by the method of characteristics with special emphasis on the stress pattern in the hopper section. Considering boundary conditions derived from the Mohr stress circle limits the solution of the active state of failure, i.e. plastic equilibrium, to certain combinations of the parameters internal friction, wall friction and hopper wall inclination. Other combinations of these parameters will only permit an elastic solution of the active stress field. If, however, the active state of stress does exist, then the vertical stresses prevailing in the hopper are very high and have to be considered for design of feeders and internals.

Einfluß der Wandreibung auf die Dimensionierung von Bunkern — Verfahrenstechnische und statische Gesichtspunkte

AbstractInfluence of wall friction on the design of silos – Aspects of process technology and statics. Mass flow and funnel flow are distinguished when considering the discharge of stored bulk solids. In order to cause mass flow to occur, i. e. the complete bunker filling is in motion, hopper walls need to be steep. Conditions close to the outlet are decisive, a large value of wall friction requiring steep hopper walls. For a safe design of bunker walls with respect to mechanical strength, DIN 1055, part 6 is commonly applied; it is currently being revised. From this regulation a strong influence of the angle of wall friction can be inferred, small values of the angle being associated with high horizontal pressures. In case the angle of wall friction depends on pressure and other parameters and safety factors are included there may be a considerable difference between the angle used by a process engineer and by a civil engineer.

Macromechanism of powder deformation in the incoherent zone during rolling

Observation of the deformation of a free-flowing material through transparent hopper walls is a technique yielding a great deal of useful information and enabling the deformation behavior of powders to be studied in the lag zone (breaks in the velocity field, formation of arch structures, and the like). A binding link between the geometric and physical parameters of the powder rolling process is the initial powder compressibility. An increase in the intensity of the shear deformation of powders before the commencement of their irreversible densification suggests that impeded deformation zones may not be able to form above the angle of rolling.

セルフアンローディング船の船倉におけるホッパー傾針角

In order to estimate the main hopper side slope in the cargo holds of self-unloading ships, a triangular, rigid, powder block was assumed at the transition of the walls of the cargo hold. When a given size of the powder block just slid off the hopper walls, the critical hopper slope was calculated from the force balance on the powder block.The calculated critical hopper slope increased with a decrease in the size of the powder block, and a maximum value was obtained when the powder block became infinitely small. For the desigh of the cargo hold, this maximum value was taken as a lower bound of the main hopper side slope.When assuming that the cargo hold is for carrying coal, the calculated hopper slope was 40°against an ulrta high molecular weight polyethylene plate, and was 51°against a steel plate. These calculated results were slightly large in comparison with the main hopper side slope adopted in the cargo holds of existing self-unloading ships. Consequenty, a low hopper slope required both a low frictional coefficient and a low adhesive force between the powder and the wall material of the hopper.

An investigation of the flow boundary during steady-state discharge from a funnel-flow bunker

The shape and size of the stagnant zones have been observed during steady-state discharge of coarse granular media ( d p ⩾ 1.0 mm) from flat-bottomed bins and shallow convergent hoppers. The effects of hopper geometry, wall friction and mean particle size on the observed flow fields and discharge rates are discussed. A comparison between the experimental results and the predictions of previous stress-based models shows that none of these models can predict the significant change in the flow boundary with varying particle size observed in practice. The kinematic flow model proposed previously by the authors is used to determine flow fields corresponding to different particle sizes. Good agreement with experiment is found in all cases.

Gravity flow of coarse cohesionless granular materials in conical hoppers

This paper is concerned with the flow of cohesionless granular materials in conical hoppers. The granules are considered to be coarse such that the effects of interstitial fluid can be neglected. Two analytical approaches based upon the method of integral relations are presented. In the first the detailed variations of shear and normal stresses over the cross-section of the hopper are considered. The second is a very simple analysis which makes use of a mean normal stress averaged over the cross-section. The two analyses yield predictions for the flow rate which are almost identical. After the inclusion of an empirical correction factor to account for non-uniform exit velocity profiles and bulk density reductions near the outlet, the flow rate predictions and their variations with internal and wall friction angles and with hopper wall slope are found to agree well with experimental measurements.

Factors affecting charge metering in the rolling of electrode strips from powders

The dependence of the key parameters of strip rolled from a powder on the latter's rate of flow is demonstrated. A method is described for studying the effect of a number of factors on the rate of flow of a powder issuing from the metering hopper of a rolling mill, and the results of such an investigation are presented. A description is given of a new laboratory apparatus designed at the Brovary Powder Metallurgy Factory for determining the rates of flow of powders from a metering hopper. It is shown that in the rolling of strip from a powder the rate of flow of the powder can be controlled by varying the cross section of issue of the powder from the metering device, apparent density and particle size distribution of the powder, the latter's degree of wetting, angle of inclination of the metering hopper walls, height of the powder column in the metering hopper, and roughness of the working surfaces of the mill rolls. Some recommendations are made for the design of metering devices for powder rolling mills.

Reducing hopper wall friction by mechanical vibration

Reduction of the effective wall friction in hoppers allows shallow core-flow hoppers to exhibit mass-flow characteristics. This paper presents theoretical and experimental evidence which indicates that a significant reduction in wall friction can be achieved by the proper use of applied vibrations. Some practical implications and applications of this reduced wall friction are discussed.

Internal pressures in flowing granular materials from mass flow hoppers

Internal pressures in flowing granular materials are of practical importance, since they lead to pressures on the hopper walls. Two granular materials (0.5 mm and 1.0 mm nominal diameter glass spheres) are chosen and their flow from two axial-symmetrical and one plane-strain experimental perspex mass flow hoppers is studied. Static and dynamic pressures are measured using a radiopill receiving system, when the pill is placed in the vertical and two horizontal orthogonal directions and at various radial positions and depths.Typical pressure traces of 220 experimental runs are analysed. The effects of stop/start operation and compaction of the fill material prior to the initiation of flow on dynamic pressures are also studied.Utilising the data on flow paths and velocity changes, the internal pressure—time traces are interpreted in terms of the pressure changes with distance from the hopper outlet for positions near the wall in the convergent sections of the hoppers. The results are compared with the Jenike-Johanson theory.

A further contribution to the evaluation of the Jenike method for design of mass flow hoppers

A critical comparison has been carried out between values for the minimum outlet slot width and the minimum hopper wall slope for mass flow predicted by the Jenike method, and values obtained from experiments on a full-scale silo with symmetrical wedge-shaped hopper. The data for the minimum slot width were obtained for a fine SiC powder whilst a coarser, free-flowing powder of the same material was used to determine the critical slope of the hopper walls. It was found that the Jenike method overdesigned the critical hopper slope by 8 - 10°. It was further found that the slot width was overdesigned by from 0 to over 100% depending on the way in which the failure loci were extrapolated into the range of small normal stresses.

Wall stresses in mass-flow bunkers

The paper discusses the various solutions that have been proposed for the stress conditions near the transition corner (i.e. the corner between the vertical bin walls and the convergent hopper walls) of a plane mass flow bunker. Stress conditions local to the transition are then examined in detail for bunkers with gently inclined (shallow) hopper sections and for bunkers with steep hopper sections. It is found that at least two stress solutions exist for each case, one continuous and one discontinuous and solutions are presented for the four cases. The analysis is then compared with experimental data of the flow of dense sand in various small mass flow bunkers which are instrumented with load cells and observed by radiography. The observed stress jumps at the transition corner are compared with the predicted stress jumps; the comparison is awkward because of the difficulty of establishing accurate values of the mobilised angles of internal friction and wall friction. The analysis and the experimental observations suggests a criterion to indicate whether flow will occur at the transition corner of a bunker, a necessary condition for mass flow.

Pressure on a hopper wall at a stress discontinuity during mass flow

Under some circumstances during mass flow from a bunker a stress discontinuity may occur giving a higher pressure on the wall than that predicted by Jenike's or Walker's theories. A formula and a graphical construction are derived for finding this pressure. For comparison with the pressures predicted by other theories, diagrams have been prepared to cover a range of values of angles of wall slope, wall friction and internal friction.

An approximate theory for pressures and arching in hoppers

A simple theory is developed which yields the approximate stresses within a granular material or powder flowing in hopper systems and gives the critical factors which ensure continued gravity flow. The stress fields during mass flow have been derived by consideration of the forces acting on elemental slices which are simultaneously yielding within themselves and along the hopper walls. Like Jenike, who has given an exact stress solution for hopper outlets only, when considering arching it is assumed that the powder strength is a function only of the local stresses that prevailed during the preceeding flow. Allowance has now been made, however, for the effect of the limited vertical shear stress that can be developed near a steep smooth wall on potential arch span. Consequently, the ideal hopper, designed from the material strength—stress characteristics is likely to have steep smooth walls which get steeper towards the outlet.