Mass Flow Hoppers Research Articles

Maximum solids discharge rates from hoppers

A theoretical model based on bulk solids handling fundamentals has been developed for estimating the discharge rate of solids from mass flow and funnel flow hoppers. The model takes into account the bulk solid's unconfined yield strength, internal friction, compressibility, wall friction, and permeability. Permeability and compressibility in particular are important because these properties allow prediction of the adverse pressure gradient that develops when fine powders are discharged, which result in gas flowing counter to the solids. Calculated and experimental solids discharge rates from conical hoppers are compared.

Evaluation of pressures in slender silos varying hopper angle and silo slenderness

In this paper, we report the results for pressures in a full-scale silo obtained from assays performed on a test station using a free-flowing product. Six different types of silo geometry (slenderness and hopper angle) were tested by filling the silo to the height of interest and observing a static phase (10 min) followed by complete discharge. Our results show that discharge flow is not influenced by silo slenderness. The lateral pressure ratio and values obtained for vertical stress in the stored material at the transition were higher than those given in the Eurocode 1, part 4. In addition, the maximum frictional pressures in the cylinder showed peaks that exceeded the standard, as did the maximum normal pressure in the cylinder with maximum slenderness and mass flow (hopper β = 15°).

Shear Cell Test and Hopper Design

Relevance of the work. The Hopper and Bin design is the most commonly used technique of storing materials as it is a gravity fed system and is generally used for storing materials such as agricultural grains as well as mined minerals such as sand and coal. Mass flow, which is ideally the most desired flow type sees the bulk material travel uniformly with all particles in motion until all the material leaves the bin. The other types of flow generally occur with flat-bottomed bins with shallow hoppers are not seen as ideal as with this design problems such as arching and rat holing occur. The issue with the current design is that some of the material becomes stagnant in the bin, this can be costly as if the bulk material becomes stuck, degradation can occur over time. It can be observed for the Funnel and Expanded flow, the rat holing and arching occurring due to the stagnant material. Research Objective is to design a novel mass flow acrylic bin and hopper to store bulk quantities of sand without stagnation or degradation Methodology. Two separate experimental procedures were carried out including the measurement of the specific gravity of the sand, shear test and final hopper design. The data was then manipulated and plotted stress transformations and identified multiple key flow property constituents. Using values such as the yield loci and associative yield stresses the hopper half angle α and opening diameter B were tabulated. Results and Conclusions. The optimum opening diameter B for an uncompacted system is 2 mm and the hopper half angle α adjusted to 34.58o , this was tested and provided a successful mass flow hopper system. Overall, the techniques used with specific gravity and shear cell testing gave a sufficient insight into the appropriate procedure for designing efficient and accurate bin and hoppers. Then substituting the values gathered into the appropriate formulae provided a successful mass flow system for the intended bulk material which is sand.

New mass flow limiting lines based on segregation pattern and magnitude

Mass flow, by definition, means all of the mass in a hopper will move when some material is discharged from the outlet. Mass flow has been the recommended means to solve segregation issues. This generally works under conditions where the segregation pattern is radial and when the process operation is nearly steady state flow into and out of the hopper. If the segregation pattern is either axial or radial, but the mode of operation is to fill followed by completely emptying the bin, then segregation can easily be an issue – even in mass flow designs. Segregation prevention is all about velocity control, and matching the velocity to the segregation pattern and mode of operation.Ideally, one would like to estimate segregation using easily measured flow properties, segregation potential tests, and a description of the process geometry. This paper looks at a method of predicting segregation problems using flow properties like wall friction angle and effective internal friction angles coupled with the radial stress theory to compute the expected velocity profiles in a variety of process geometries. Using slope stability models, one can also relate the cascade behavior of cohesive material down a pile or slope. Imposing radial stress velocity profiles and cascade velocity profiles in a bin or hopper, then using particle tracking techniques, one can compute the time at which any particle in any portion of the bin might exit the system. Furthermore, imposing a measured segregation profile on the material initially placed in the bin, and then tracking groups of particles with an assigned segregation concentration through the bin, can help determine when and how segregated material might exit the bin. Doing enough of these calculations for a range of wall friction angles and hopper slope values, the velocity profile can be related to the segregation intensity exiting the bin as a function of these two variables. Since these two variables also determine the propensity for mass flow, this analysis can relate mass flow to segregation tendency for material subject to a filling and discharge mode of operation. Selection of an optimal mass flow design would then depend on the segregation pattern and the desired segregation intensity the process can live with.Applying this methodology to a conical hopper suggests that a material prone to segregation will segregate significantly in a funnel flow design. This is to be expected. However, this work also indicates that mass flow bins, when filled and then emptied completely, may experience significant segregation if the hopper walls are designed with traditional mass flow limits in mind. This work suggests that mass flow hoppers must be considerably steeper to mitigate segregation effects for a fill-then-empty mode of operation.

A modified flowability classification model for moist and cohesive bulk solids

The Jenike flowability classification is designed to indicate the handleability of bulk solids in material handling processes. However, for moist, cohesive bulk solids, it may fail to represent the true flowability/handleability at high consolidation stresses. The study presented in this paper introduces a modified flowability classification model aiming to improve the flowability/handleability prediction across a wide range of consolidation pressures. The evolution of the flow function of bulk materials under increasing moistures is initially discussed, based on which the Jenike flowability classification is reviewed. The modified flowability classification is then derived by considering the flow/no flow condition for mass flow hopper designs under both low and high consolidation stress states. The influence of the bulk material type and general operational conditions are also taken in account in deriving the modified classification method. A suite of bulk solids with a wide range of material properties are selected in an experimental program to validate the modified flowability classification. Results suggested the modified flowability classification is able to more accurately indicate the overall flowability/handleability of the bulk solids independent of the applied major consolidation stress.

Minimising the spread of residence-time distribution for flat and heaped powders in a wedge-shaped planar hopper

A wedge-shaped planar mass-flow hopper system was modelled using stress-field theory as found in the literature. The authors present governing equations for stress and velocity fields under a radial-flow assumption in a converging hopper. The velocity in the silo above the hopper is modelled as plug flow. Two set-ups are modelled, one where powder layers in the hopper are assumed to be flat, and the second in which the layers are heaped at some characteristic angle. The ejection times and residence-time distributions are calculated and presented for a range of heap angles. For realistic heap angles, the spread of the residence-time distribution decreases with increasing heap angle; in one case, the spread is halved to a well-defined limit. At this limit (the critical heap angle) the geometry of the hopper can be optimised to minimise the spread of the residence-time distribution, and hence to minimise predicted mixing in the system. We present examples of curves for a variety of parameters that minimise the predicted mixing in the hopper–silo system.

Ejection times from a conical mass flow hopper – Coulomb and conical model differences

The flow of a bulk solid powder through a mass flow hopper-silo system is modelled using stress field theory. Two common models are presented, the Coulomb and the conical model. The assumption is made that the velocity field is inversely proportional to the square of the radial coordinate. This simplification allows us to derive expressions for the stress and velocity fields in the system. The ejection times and residence time distributions for the two models are presented and the differences between the two models are shown. In particular, we find that the predictions of the two models differ greatly which has important implications for discharge and mixing as the powder flows through the system. A sensitivity analysis is also performed on some of the modelling parameters which affect the predicted differences between the Coulomb and conical models. Much of this work is based on Nedderman (1992).

Influence of protein concentration on the physical characteristics and flow properties of milk protein concentrate powders

This study investigated the physical characteristics and flow properties of seven milk protein concentrate (MPC) powders, ranging from 36.6 (MPC35) to 89.6 (MPC90) % (w/w) protein in dry-matter. MPC80, MPC85 and MPC90 had the smallest particle sizes (P<0.05) and significantly higher (P<0.05) specific surface areas, as measured using nitrogen adsorption. The bulk density of MPC powders decreased with increasing protein content, due to increased (P<0.05) levels of interstitial and occluded air. Flow testing indicated that high protein MPC powders were more compressible (P<0.05), had lower flow index values (P<0.05) and required larger (P<0.05) outlet diameters for optimal flow in mass-flow hoppers compared to lower protein MPC powders.

Experimental investigation of wall pressure and arching behavior under surcharge pressure in mass-flow hoppers

Based on Jenike's method, only the self-weight of each arch element is involved in the calculation of the arch thickness parameter which leads to the surcharge pressure not being taken into account in determining the critical outlet dimension of a bulk material storage bin. The aim of this study is to investigate the influence of surcharge pressure on wall pressure distribution and arching behavior in mass-flow structures. A method is introduced to measure the hopper wall pressure distribution. The measurements of the wall pressure and critical outlet dimension were conducted under different surcharge pressures and at various filling levels. The experimental results are compared with existing prevailing theories, where the theoretical outlet dimensions demonstrated significant overdesign in terms of low surcharge pressure and reasonable estimates corresponding to high surcharge. The peak wall pressures around the transition area of the bin are smaller than the calculated values, whereas the stresses close to the outlet are larger than the relative theoretical values.

Impact of flow-corrective insert on flow patterns in two-dimensional moving bed

This paper presents the study of the flow patterns inside a granular moving bed in a quasi-two-dimensional (2D) model of a granular moving bed filter (GMBF) vessel with vertical walls and a mass flow hopper. Fine quartz sand was chosen as the granular filter media in experiments. The related flow properties were measured by a Jenike Shear Tester. According to the flow properties of fine silica sand and Johanson's theory, a 2D moving-bed apparatus was built, with transparent walls and the flow-corrective insert to diminish the quasi-stagnant zones along the side walls. The flow patterns and velocity profiles of silica sand in the system with flow-corrective insert were studied experimentally, and the effect of the location of the flow-corrective insert on the internal flow patterns was investigated. The optimal placement of flow-corrective insert according to Johansson's theory was demonstrated to efficiently diminish the quasi-stagnant zones near the side walls. Little vertical shift of the flow-corrective insert from optimal position changed the stable and uniform mass flow pattern of moving bed into the funnel flow.

The Investigation of Arch Model Acting in Mass-Flow Hoppers

This paper presents the experimental results of mass-flow hopper arch geometry investigation, which was conducted using a variable geometry plane-flow bin. The cohesive arches formed under different critical outlet openings and hopper half-angles were measured using a 360° two-dimensional laser line scan system. This system was employed to obtain the complete surface profile of each arch across the width of the outlet by moving the rotating laser along the total length of the outlet. The test results were analyzed using Matlab, adopting stationary wavelet transformation de-noising to decrease the signal noise generated during the testing process. The geometric data for each single line scan was smoothed and combined to present a three-dimensional arch surface profile shown to be in good agreement with the observed experimental arch profiles. The angle η at the intersection of the arch with the hopper walls was then calculated by running a Matlab program and a new angle η' is introduced to the arch shape study. The detailed results are discussed in the paper. Arch geometry models, such as the parabolic arc and circular arc arch models developed, respectively, by Walker [ and Enstad [ are reviewed and their relevance is discussed based on the experimental results presented in this paper.

Review of mass-flow hopper design with respect to stress fields and surcharge loads

Current procedures for mass-flow hopper design are based on the radial stress theory developed by Jenike and involve the determination of the critical outlet dimensions for flow to be initiated. These procedures ignore the surcharge loads on the hopper and involve a study of the passive or arched stress field that exists under flow conditions. An alternative approach as applied to hopper wall load analysis is to employ the horizontal slice method. The arched stress field and horizontal slice methods of analysis are compared. The influence of surcharge loads in the determination of hopper geometry is investigated.

Investigation of flow properties of metal powders from narrow particle size distribution to polydisperse mixtures through an improved Hall-flowmeter

Initially, we critically examined the results provided by the improved Hall-flowmeter, based on bulk volume flow rate, with narrow particle size distribution metal powders (iron, aluminium and copper) of different sizes (fine to coarse) and shapes (nearly spherical to non-spherical). Binary and ternary mixtures of various combinations of fine (< 100 μm) and coarse (> 100 μm) metal powders at different size ratios and weight fractions were allowed to discharge from a mass flow hopper. The results show that the mass flow rate of polydisperse mixtures of metal powders is affected by four factors: the size ratio, the volume fraction of the smallest sieved fraction, the initial mass flow rate and the shape of metal powders.

Measurement of velocity and density profiles in discharging conical hoppers by NMR imaging

Nuclear magnetic resonance (NMR) imaging was used to measure velocity and density profiles in 3-D conical hoppers fed from an open vertical silo. Discharge of a 200 μm-diameter powder in both mass and plug flow was studied with hoppers of different half angles, of 10° and 80°, respectively. An analytical solution for compressible (variable density) mass flow in the 3-D axi-symmetric geometry was also developed following the procedure outlined in Tardos (1997) and Tardos and Mort (2005). The density variation and velocity profiles obtained experimentally were compared to predictions of this theory for dense, compressible granular flows. We found, from both theory and experiment, that the powder has to exhibit significant dilation (compressibility) as it is accelerated through the constriction in the hopper. The degree of compressibility was found, experimentally, to be lower than that predicted by the mass flow hopper theory. The powder unexpectedly exhibited a boundary layer with a fully-rough boundary condition in the mass flow hopper. In the funnel-flow hopper, the expected “dead zone” was found around the orifice and extended about one diameter length into the silo. The centerline velocity increased according to an exponential function.

Electrostatic charging during the flow of grains from a cylinder

Electrostatic charging is ubiquitous in granular processing, leading to problems of safety, jamming and unwanted material segregation. To better understand the mechanics of granular charging, we focus here on flow through a metal cylinder, where we can isolate charging regions near the cylinder walls from noncharging regions further away. We confirm that monodisperse grains charge in proportion to the area of contact between grains and the cylinder walls, and so in large cylinders, most particles remain almost uncharged. Those particles that do charge reach a plateau charge density after filling the cylinder and flowing past the walls a distance of less than one and a half centimeters. For bidisperse granular blends, the net charge produced by the mixture is dominated by the component that comes into contact with the walls of the apparatus. This is found to be caused by segregation effects as well as the coating of the larger particles by the smaller ones. We make use of these results to predict the charge generated in mass flow hoppers, and we test these predictions. Finally we examine the effect of grounding the experimental apparatus, and we find that paradoxically, grounding does not prevent charge accumulation.

Stresses in a bulk solid in a cylindrical silo, including an analysis of ratholes and an interpretation of rathole stability criteria

A two-dimensional model for stresses in a cohesive bulk solid in a vertical, cylindrical vessel has been developed, assuming a rotated, circular arc orientation of principal stresses, after Enstad [1995. On the theory of arching in mass flow hoppers. Chemical Engineering Science 30 (10), 1273–1283] and Li [1994. Mechanics of arching in a moving bed standpipe with interstitial gas flow. Powder Technology 78, 179–187]. The model assumes that principal stresses form a spherical dome surface within the vessel. At the wall, the surface makes a constant angle with the wall normal, necessitating a progression of arc centre up the vessel. An incremental element of upper and lower surfaces with vertical height δ x at the wall has variable thickness with arc angle ε measured from the vessel centre. Positions within the vessel are located by height at which the arc cuts the vessel wall x, and arc angle ε . Rotational symmetry is assumed through azimuthal angle θ . This gives 3 principal stresses: σ R ; σ ε ; σ θ . Static vertical and horizontal force balances yielded two partial differential equations, and a third was obtained by assuming a known ratio between effective stresses σ ε ′ and σ R ′ . These equations were integrated numerically to give stress surfaces in x – ε space. The model simulated variations in the state of stress across the arc surface, and in some conditions, this lead to large variations in stress between the wall and vessel centre. The model accurately predicted the minimum outlet radius required for flow of a cohesive bulk material. The presence of a vertical, co-axial rathole was modelled with minor geometrical modifications. The rathole was assumed to be an unconfined plane of principal stress where the radial stress, σ R , acted vertically downwards and its value increased linearly with bed depth, contrary to Jenike's [1964. Storage and flow of solids, Bull. 123, University of Utah, USA] assumption of a limiting stress in deep beds. Conventional stability criteria ( σ R < = f c for stability), suggest that only shallow ratholes can exist. However, a modified yield criterion, allowing for the curvature of the rathole, enabled deep, stable ratholes to exist. Results show that the stability of deep ratholes depends upon the rathole radius and the vessel radius.

Analysis of Dynamic Discharge Pressures in Cylindrical Slender Silos with a Flat Bottom or with a Hopper: Comparison with Eurocode 1

Few models simulate the discharge of flat-bottom silos by using finite elements. This paper presents a new dynamic model for silo discharge using the Drucker–Prager plasticity model. The model was used to study discharge in mixed flow and mass flow silos with rigid walls. Various silos were analysed, and pressures under different flow patterns were compared. Results were also compared with Eurocode 1—part 4 on actions in silos and tanks, which is the standard used in the European Union. Overpressure coefficients due to discharge were obtained in all cases. In the case of flat-bottom silos, overpressures occurred in the lower part of the silo. The values obtained for overpressures were lower than the values obtained in the case of mass flow hopper silos. The effects of wall friction and outlet radius were also analysed.

An Estimate of Hopper Outlet Size and Slope for Mass Flow from the Flowability Index

The opening size of the discharge outlet and the slope of a conical hopper can be determined using the well-known theoretical method of Jenike. This method enables designing the hopper almost so precisely as to permit mass flow powder discharge (without stagnant zone). On the other hand, a flowability index is customarily used as a measure of the ease of powder flow. From a practical point of view, it should be desirable to predict whether a given powder will form arches or bridges that will prevent its mass flow discharge from the hopper. In order to obtain such a predictive tool, we have studied the relationships, for 90 powders, between (1) the mass flow hopper outlet size and flowability index, and (2) the mass flow hopper slope and flowability index. In both cases, there is a considerable scattering of experimental data, but limiting functional relations have been obtained that allow practical determination of safety values for mass flow hopper outlet size and slope as a function of the flowability index.

Effects of the properties of bulk solids on the relative performance of polyethylene and stainless steel wall lining materials in mass flow hoppers and other applications

Reducing the friction between the walls of storage vessels and the bulk solids that they contain is widely known to be beneficial in obtaining more satisfactory flow patterns in such vessels, and to reduce flow problems. In particular, the advantages of low friction in promoting a mass flow discharge pattern are well understood; means of obtaining data to design a hopper for mass flow are also well established. In recent years a number of polyethylene materials have come on to the market, intended for use in lining silos and claimed by their manufacturers to offer low wall friction in comparison with other materials. In this paper, one particular commercial grade of ultra-high molecular weight polyethylene (UHMWPE) material has been tested alongside a commonly used type and finish of ferritic stainless steel. The wall friction has been measured for both materials, with a variety of bulk solid materials and conditions, and the hopper half-angles needed for mass flow computed for each combination. The results show that the UHMWPE material does not always offer a lower friction than the stainless steel; in some cases it offers much lower friction and hence much greater scope for obtaining mass flow discharge. However, in other cases it gives significantly higher friction and is a bad choice for promoting flow. The principal conclusion is that, under certain circumstances, UHMWPE offers substantial advantages over other wall materials. However, this advantage is by no means universal and, if it is to be considered for employment in a hopper design, then a wall friction test should be undertaken. This test should use a sample of the bulk solid to be handled against both the UHMWPE material and other possible materials.

DETERMINATION OF PHASE VELOCITIES IN MULTI-PHASE FLOWS IN HOPPERS USING DUAL PHOTON GAMMA-RAY TOMOGRAPHY

The temporal and spatial variations of the relative fluxes in a binary mixture flow consisting of particles of different size but almost equal density are investigated using a dual photon gamma-ray transmission technique. Experiments are carried out using the dual photon gamma-ray technique in a mass flow hopper containing a binary mixture of 20% per weight turnip seeds (fine phase) and 80% per weight ABS particles coarse phase of size ratio 2.11:1 and of nearly equal densities. Measurements are taken in a ‘snap-shot’mode to identify the solids fraction of the individual components in the mixture and a statistical analysis is applied to the solids fraction values to calculate self-diffusion velocities for each of the individual components of the mixture. Significant phase separation is observed within zones of high bulk shear gradients such as close to the hopper walls and close to the hopper outlet. Large interstitial voidage changes observed during the initial transient stage of flow are also found to give rise to significant self-diffusion velocities.