Predicting the flow mode from hoppers using the discrete element method

In this work, the discrete element method (DEM) is used to assess powder flow from hoppers and the results are compared to widely-used hopper design charts. These design charts delineate mass-flow and funnel-flow behavior based on the hopper wall angle and a given set of material properties. The modeled system consists of hoppers with various wall angles and frictional, non-cohesive, spherical particles. The performance is assessed by measuring the particle residence times, particle velocities, and the extent of segregation during discharge. A Mass Flow Index (MFI) based on the velocity profile data is used to quantitatively characterize the nature of the flow pattern as mass-flow, funnel-flow, or some intermediate. The DEM predictions are generally in very good agreement with the Jenike design charts. The level of agreement shown here indicates that DEM cannot only reproduce the current estimates of hopper performance, but also provide additional insight into the flow-such as the internal granular structure-that may be difficult to obtain otherwise.     

Stresses in bulk solids in wedge hoppers: A flexible formulation of the co-ordinate specific, Lame-Maxwell equations for circular arc, principal stress systems

A 2-D model of stress distribution within bulk solids, with circular arc principal stress orientation, in a wedge hopper was developed in a previous paper [Matchett, O'Neill, & Shaw, Stress distributions in 2-dimensional, wedge hoppers with circular arc stress orientation — a co-ordinate-specific Lamé-Maxwell model, Powder Technology, 187(2008) 298-306]. This model worked in an orthogonal, curvilinear co-ordinate system co-incident with the principal stress trajectories: (x − ψ_o) space.This paper presents an equivalent model in (x − ε) space. This allows backward numerical integration of the force balance equations, enabling surface and wall boundary conditions to be modelled. This was not possible in the original model.The equations are first-order, and boundary conditions can only be specified at single surfaces. Thus, if a stable, cohesive arch is proposed, the surface overpressure is determined by the model. Calculated overpressures have reasonable physical values.The present model was integrated backwards from the surface downwards and it was found that the integration was very sensitive to the surface overpressure stresses.Likewise, wall boundary conditions were specified with backwards integration in ε.The minimum outlet for flow was calculated from the model and compared with the experimental data of Berry et al. Wall normal stresses in a wedge hopper from Schulze and Schwedes were also compared to model predictions. In both cases there was reasonable agreement between measurements and model predictions.     

Stress distributions in 2-dimensional, wedge hoppers with circular arc stress orientation — A co-ordinate-specific Lamé-Maxwell model

A 2-dimensional model of stress distribution in a wedge hopper has been developed. This is a co-ordinate-specific version of the Lamé-Maxwell equations in a space frame dictated by the assumption of circular arc, principal stress orientation.A set of orthogonal, independent variables has been defined as x-ψ_o space. x is the vertical height of intersection of the circular principal stress arc with the wedge wall and the radius of the circular arc is proportional to x. ψ_o is the angle that the radius makes to the vertical at the lower arc in the system — lower boundary condition. The second principal stress follows ψ-lines through the vessel from ψ_o at the lower boundary, eventually passing through the vessel wall and leaving the system.The model has been used to integrate the stress equations along lines of principal stress using numerical techniques. An analytical solution has been found at ψ_o = 0 of the same mathematical form as the Enstad/Walker/Walters equations.The model can be used to predict the location of the stable, cohesive arch and to predict unviable stress states in terms of the Mohr-Coulomb yield criterion.There is a requirement for experimental data of internal stress distributions within bulk solids in hoppers and silos to validate this and other models.     

料仓及重力场的粉粒体流动

在水泥的连续生产过程中，散体物料的储存与供给是必不可少的环节，因此在水泥厂中广泛应用着各种各样的料仓，如生料磨、水泥磨、煤磨的磨头仓，各种原料的中间储仓，还有存放大容量粉体物料的生料库、水泥库等。但在粉粒体物料储存过程中会发生各种问题，即常常发生结皮和结拱、偏析和不均匀排出、细粉物料的喷流等。然而刮目前为止，说明这些现象的定量理论还很少，并且欠缺完全可靠的处理方法，因此料仓故障仍然是需要研究的问题。本文拟就重力场的粉体压及静态壁压理论的研究现状、料仓常见故障及解决对策、散体物料流动性及结拱的关系等作一论述。     

Dust explosions in vented silos: Simulations and comparisons with current standards

Dust explosions represent a serious hazard to personnel and equipment in industries and silo facilities that handle combustible materials. Venting devices are the most common protective systems employed in silos, although their use may pose problems in large and low-strength silos. The main aim of the present work was to simulate dust explosions in silos using a commercial CFD program, the DESC code, to determine the pressures developed in vented explosions with vent areas of different sizes. Dust cloud characteristics were taken from studies carried out by the FSA (Research Centre for Applied System Safety and Industrial Medicine, Germany) in a 12 m³ silo with a mechanical feeding system. The pressures and associated vent areas in these simulations were compared to those contemplated in two venting standards. The simulated explosion pressures showed the expected trends for the associated vent areas and agreed reasonably well with the values contemplated in NFPA 68 (2007) [5]. However, when the reduced explosion overpressure was low, the vent area contemplated in EN 14491 (2006) [4] was much larger than in the present simulations.     

Numerical study on the behavior of funnel flow silos with and without inserts through a continuum hydrodynamic approach

In this paper the results from simulations performed using a hydrodynamic model proposed by Artoni et al. [Chem. Eng. Sci. 64 (2009a) 4040–4050] have been compared with published data of an extensive experimental investigation carried out at the Tel-Tek Research Institute in Porsgrunn, Norway. The experiments collected several data and observations on the wall stresses and the flow patterns observed during discharge of a full-scale funnel flow silo with and without inserts. The comparison between simulation and experiments showed the ability of the model to capture quantitatively the main features of both the flow and of the wall stress profiles when flow corrective inserts are put in the hopper of the silo in order to convert the discharge regime to a mass flow regime. Moreover information such as the stresses on the internals, which are difficult or impossible to get experimentally, have been collected from the simulations and discussed.     

Optical technique DPIV in measurements of granular material flows, Part 1 of 3—plane hoppers

The aim of this paper is to present the evolution of plug flow developing in three densely packed granular materials in the model of a hopper made of Plexiglas. For this purpose, the digital particle image velocimetry (DPIV) technique is applied to analyse the flow field of the granular material. When discharge starts, a plug flow zone in the flowing material expands upward. This zone changes its width reaching the upper surface of the material. The plug flow evolution as a function of time is described using DPIV. This technique yields the velocity profiles of flowing granular materials, velocity magnitude contours, vector fields, velocity distributions on certain levels in the model and traces of the selected particles. The results obtained for the evolution of the vertical velocity, height and width of the plug flow zone as a function of time, measured at the symmetry axis of the model for the amarantus seed are compared to the results obtained by Waters and Drescher. Measurements of the stagnant boundary as a function of time are compared to the results available in the literature.     

Effect of screw design on hopper drawdown of spherical particles in a horizontal screw feeder

Screw feeders are used to remove material from hoppers and bins at a controlled rate. The evenness of the flow in the bin depends on the drawdown pattern, which in turn depends on the screw and hopper design, shape of the particles and wall friction effects. A key design requirement is to ensure that a progressive increase in the screws volumetric capacity is achieved along the entire length of the hopper's opening so as to produce even drawdown. If this is not achieved then compositional variations in the outgoing stream and other operational problems (such as caking) can be created. Screw designs to date have been generally based on analytical models and at times the predicted flow pattern is not achieved. In this study, the Discrete Element Method (DEM) is used to predict particle transport in a horizontal screw feeder system for a range of conventional screw designs including a variable screw pitch, variable screw flight outside diameters and variable core diameters. The influence of screw choice on the particle mass flow rate, the evenness of particle drawdown from the hopper, power consumption, screw wear and wall friction variations are all investigated. Important features captured by DEM that are not accounted for by the analytic model and which vary strongly between competing screw designs, include the particle circulation in the hopper, shearing of the particle bed in the trough just outside the screw and the spatially varying particle force along the hopper which leads to non-uniform drawdown and to the existence of large stagnant or slow moving zones. The screw design and consequent flow patterns also strongly affect the power draw with variations up to a factor of three and screw wear with large changes in their distribution and magnitude. Finally, the surface frictional properties of the screw are shown to strongly influence the rate of bed compaction within and along the screw leading to strong variation in mass flow rate, uniformity of drawdown and power draw.     

Flow regime transition in a trickle bed with structured packing examined with conductimetric probes

Methods for identifying flow regime transitions in a trickle bed with structured packing based on the response of conductimetric probes are proposed. Time series of conductance measurements, obtained with an array of eight probes flushed to the reactor wall, are analyzed using tools borrowed from the theory of non-linear dynamics and symbolic dynamics. For the same range of gas and liquid velocities, the local hydrodynamics is inspected within a channel of the structured packing in a non-intrusive manner with a set of conductimetric probes imprinted on one of the corrugated plastic sheets that conforms a packing element. The local hydrodynamics within the channel is explored to interpret the trends of characteristic numbers calculated from the time series measured at the wall. The gas-liquid pattern shows a slugging behavior within the channel that is reflected in the analysis of the flushed probes response.     

低质量流速下四头内螺纹管内汽-水两相流摩擦压降特性试验研究

在压力为11.3-21.5MPa、质量流速为250～1 200kg/(m2·s)和工质干度为0～1的工况范围内,对结构为Φ28.6mm×5.8mm的四头内螺纹管中汽水两相流体在水平绝热条件下的摩擦压降特性进行了试验研究.研究结果表明,内螺纹管内两相流体摩擦压降大于同等条件下光管;两相摩擦倍率随工质干度的增大,在高干度时...     

The effect of sparger geometry on gas holdup and regime transition points in a bubble column equipped with perforated plate spargers

This paper investigates the effect of sparger geometry on flow regime of a bubble column. The experiments presented in this study were performed under atmospheric pressure with water/air in a cylindrical Plexiglas^® column of 33.0 cm i.d. and 3.0 m height. Three different perforated plate spargers were employed. Hole diameter was varied in the range of 1–3 mm, while the free area was 1.0%.The theory of linear stability is used for the prediction of regime transitions in the bubble column and a comparison has been presented between the predictions and the experimental observations. A good agreement between the predictions and the experimental values of transition gas holdup has been obtained.In addition, the data from the literature has been analyzed. Experimental values of transition gas holdups and predictions by the theory of linear stability have been compared with those of literature.A correlation based on dimensionless numbers (Archimedes, Froude, Eötvös and Weber) and the group (d_o/D_C) for the prediction of gas holdup in homogeneous regime is proposed. The average error between the correlation predictions and experimental values remains under ±10%.The proposed correlation is compared with the published data and found to be in fairly good agreement.     

不等极孔纤维缠绕球形压力容器的结构设计与性能

本文概要介绍了不等极孔纤维缠绕形压力容器的结构形式，受力状态及纤维铺层设计方法，提出了纤维强度发挥系数与在球体位置关系的函数概念，通过改变特征点的强度发挥系数，可以方便地进行球形容器的结构优化设计。     

Modern concept of acoustic emission (AE) coupled with electrochemical measurements for monitoring the elastomer-coated carbon steel damage in phosphoric acid medium

Elastomer coatings (rubber) are industrially used to protect phosphoric acid storage tanks against corrosion. Rubber constitutes a barrier against the penetration of H₃PO₄ to metallic surface. Coatings damage induces both acid infiltration and steel corrosion. In this concept, acoustic emission (AE) monitoring technique could be used for the detection of coatings damage as well as for steel corrosion under the coating. In the present work AE was coupled to electrochemical measurements (EM) for rubber damage evaluation and steel corrosion on three types of steels (XC48, E20 and A60) at room temperature in concentrated phosphoric acid (30% P₂O₅) contaminated by Cl⁻, F⁻, SO₄²⁻. Electrochemical behaviour of steels was studied and characterized by potentiodynamic curves and polarization resistance measurement. A good correlation between acoustic emission and polarization resistance or corrosion potential measurements was found during stages of coatings damage and steels corrosion. The majority of AE activity recorded during experiments is related to hydrogen bubbles release. The release of hydrogen bubbles gives rise to two populations of signals: one impulsive and another one resonant.     

液压胀贴与灌铅工艺的结合在大型高中压反应釜设计制造中的应用

本文通过一台6．0MPa10000L高中压反应釜的实例，阐述了液压胀贴与灌铅工艺的结合在大型高中压反应釜设计制造中的应用。