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.     

Quantitative estimation of volume changes of granular materials during silo flow using X-ray tomography

The aim of the paper is to show the potential of the X-ray tomography to quantitatively measure volume changes in granular materials during silo flow in a rectangular model bin. The experiments were carried out with initially dense sand. The bin walls were smooth or very rough. In the first step, continuous X-ray radiographs were conducted. The results of volume changes were presented in form of 1D cross-sectional plots and 2D images. They were directly compared with corresponding experimental results obtained with a Particle Image Velocimetry (PIV) method allowing for measuring displacements on the solid surface. Measurement errors in both methods were discussed.     

Silo music: Sound emission during the flow of granular materials through tubes

The present work deals with experiments and a model related to the emission of sound during the flow of granular materials through tubes. Experiments have been conducted using tubes fitted either with pistons or orifice plates at the ends. Earlier workers have observed that the height H of the granular material above the piston or orifice must exceed a critical value H_c for the music to occur. The critical height H_c was determined using the recorded sound signal for flow velocities in the range 0.4-1.8 mm/s (piston experiments) and 3-36.2 mm/s (orifice experiments).A simple model is constructed by treating the powder column as a spring and slider in series. The slider interacts with the tube wall via a rate and state variable friction law. The model predicts that the material either moves with a constant velocity (steady sliding) or in a jerky manner (stick-slip), depending on the parameter values used. As suggested by earlier workers, we postulate that the silo music is generated by the stick-slip motion of granular material. For H < H_c, it is postulated that steady sliding occurs, and this is shown to be consistent with the model predictions. For H > H_c, the model predicts that steady sliding is unstable with respect to small perturbations. The velocity of the slider exhibits sustained oscillations, which is the expected behavior of a system undergoing stick-slip motion. The model parameters have been estimated by fitting data on the variation of H_c with the flow velocity. The predicted acceleration of the slider is similar in some respects to the data of Muite et al. (Powder Technol. 145 (2004) 190-202) for the flow of glass beads in a tube fitted with an orifice. Muite et al. found that the dominant frequency of the sound was given by c_s / (4L_a), where c_s is speed of sound in air and L_a is the length of the air column above the granular material. This expression also fits the present data for the piston experiments.     

Application of particle image velocimetry (PIV) for deformation measurement during granular silo flow

The paper presents results of deformation measurements in dry cohesionless sand during free flow in small rectangular model silos using a non-invasive, indirect method called particle image velocimetry (PIV). It is an optical technique for measuring surface deformations from successive digital images. Laboratory model tests were performed with a mass and funnel flow silo to investigate the kinematics of the flowing sand. The measurements were carried out for granular flow in model silos without inserts and in a funnel flow silo equipped with three different types of inserts: cone-in-cone, inverted cone and double cone. The effect of the initial sand density and roughness of silo walls on the volumetric and deviatoric strain in sand was investigated. The accuracy of measurements was discussed. Advantages and disadvantages of PIV were outlined. The results were qualitatively compared with sand displacements obtained with colored sand layers and with the aid of X-rays (initially dense sand).     

Modeling of shear localization during confined granular flow in silos within non-local hypoplasticity

The paper deals with multiple shear zones in the interior of cohesionless granular bodies during plane strain quasi-static granular flow with controlled outlet velocity in experimental silos. The finite element calculations were carried out with a hypoplastic constitutive model enhanced by a characteristic length of micro-structure by means of a non-local theory to obtain mesh-independent results. The constitutive model can reproduce the essential features of granular materials during shear localization. FE analyses were performed with the help of an Arbitrary Lagrangian-Eulerian formulation using an explicit time integration approach for experimental silos containing initially dense dry cohesionless sand. Silo walls were assumed to be very rough or smooth. Emphasis was given to the propagation of multiple shear zones in the interior of flowing sand. The numerical results were compared with corresponding experimental tests.     

Investigation of fine granular material flow through a packed bed

Three different methods cut-off, time-of-flight, and Pulsed Field Gradient Nuclear Magnetic Resonance were used to study downstream flow of fine granular material through the fixed bed reactor. For describing the transport of solid particles within a fixed granular bed, a model has been developed. In time-of-flight and cut-off techniques the highest average velocity of filtration is observed at the lowest mass flow rate in all experimental traces, while upon the flow rate increase it tends to an asymptotic value. Experimental results obtained by pulsed field gradient nuclear magnetic resonance technique have revealed the bimodal character of particles velocities distribution. The average filtration velocity has a maximum at an intermediate mass flow rate close to the bed flooding, in contrast to the results obtained by cut-off and time-of-flight methods. The velocities measured using all three techniques were compared by converting them into dimensionless values. From the experimental results, the values of model parameters have been evaluated which allowed us to describe particle velocities within a bed.     

Couette grain flow experiments: The effects of the coefficient of restitution, global solid fraction, and materials

Granular flows are complex flows of solid granular material which are being studied in several industries. However, it has been a challenge to understand them because of their non-linear and multiphase behavior. The present experimental work investigates granular flows undergoing shear, by specifically studying the interaction between rough surfaces and granular flows when the global solid fraction and the material comprising the rough shearing surface are varied. A two-dimensional annular shear cell, with a stationary outer ring and inner driving wheel, and digital particle tracking velocimetry (DPTV) technique were used to obtain local granular flow properties such as velocity, local solid fraction, granular temperature, and slip. A customized particle drop test apparatus was built to experimentally determine the coefficient of restitution (COR) between the granular and surface materials using high-speed photography. Results showed that wheel surface materials that produce higher COR values exhibit higher velocity and granular temperature values near the wheel, and lower slip velocities. The local solid fraction appears inversely related to the COR values. The global solid fraction seemed to correspond with velocity and granular temperature, while displaying an inverse relationship to slip. Results also showed an initial decrease in the kinetic energy of the flow as the global solid fraction increased, due to the formation of a distinct contact region. This was followed by a rise in kinetic energy as the global solid fraction continued to increase, based on the increase of particles present in the kinetic region of the flow.     

Simulation of granular flow in 2-D hoppers using the Caram-Hong model

The Caram-Hong stochastic model for granular motion in hoppers or silos was applied, with minor modification, to describe the flow of particles in 2D batch hoppers. The predictions of the model were compared to experimental measurements, made by particle image velocimetry, on a laboratory hopper containing zinc particles. With respect to both the spatial variation of particle velocity and the rate of descent of the top surface of the bed, the model showed satisfactory agreement with the experimental data.     

The effect of solid concentration on the secondary air-jetting penetration in a bubbling fluidized bed

The introduction of secondary air (SA) in fluidized bed boilers is of important engineering significance. In the present work, an experimental study on the characteristics of SA penetration is carried out by operating a bubbling fluidized bed model. Floater, the ash formed from coal combustion, is used as experimental bed material. It has an average size of 0.83 mm and a low density of 620 kg/m³. Results indicate that the floater is more suitable to be operated in a spouted or a bubbling bed. Comparing with the conventional sand and FCC, the fluidizing characteristics of the floater are similar to those of Geldart Group D particles. From measurements of the solid concentration in the bed cross section at SA injection level by use of a solid concentration measuring thief probe of own design, the relation between SA jetting distance and SA velocity under different solid concentrations is obtained when the properties of bed material and SA ports are fixed. Furthermore, a dimensionless correlation is proposed for general cases. The results may provide a basis for further study.     

CFD study of solids concentration in a fluidised-bed coater with variation of atomisation air pressure

The solids volume fraction inside a tapered fluidised bed coater was simulated with the use of an Eulerian computational fluid dynamics (CFD) model with atomisation nozzle sub-model. The drag force, describing momentum transfer between the gas and solid phases was calculated using the drag model proposed by [1]. In order to account for the particle size distribution of the fluidised solid materials, a 4-phase Eulerian model was used. The model-predicted results for different atomisation air pressures were verified using published experimental data [2]. It was shown that the model proved to be highly sensitive to changes in the fluidisation air flow rate with regard to the model-predicted solids volume distribution.     

Numerical simulation of self-diffusion and mixing in a vibrated granular bed with the cohesive effect of liquid bridges

The discrete element method (DEM) is employed to study the self-diffusion motions and mixing of cohesive powders with the effect of liquid bridges in a two-dimensional vibrated granular bed. The dynamic liquid bridge forces are considered as the cohesive forces between particles, and three types of viscous liquids with different values of viscosity are used. A simplified model of dynamic bridge strength based on the superposition of lubrication and circular approximation is incorporated in the simulation model. It is found that the granular temperatures and the self-diffusion coefficients of cohesive powders are highly anisotropic with a greater component in the vertical direction. The diffusion coefficients for cohesive powders are larger than those of cohesionless powders and are related to the interstitial liquid volume. The mixing is strongly dependent on the self-diffusivity and is related to the magnitude of interstitial liquid volume. The variations of the self-diffusion coefficients and the mixing rate for three types of interstitial liquids show that the mixing rate constants are proportional to the diffusion coefficients.     

CFD–DEM simulation of the gas–solid flow in a cyclone separator

In this work, a numerical study of the gas–solid flow in a gas cyclone is carried out by use of the combined discrete element method (DEM) and computational fluid dynamics (CFD) model where the motion of discrete particles phase is obtained by DEM which applies Newton’s equations of motion to every individual particle and the flow of continuum fluid by the traditional CFD which solves the Navier–Stokes equations at a computational cell scale. The model successfully captures the key flow features in a gas cyclone, such as the strands flow pattern of particles, and the decrease of pressure drop and tangential velocity after loading solids. The effect of solid loading ratio is studied and analysed in terms of gas and solid flow structures, and the particle–gas, particle–particle and particle–wall interaction forces. It is found that the gas pressure drop increases first and then decreases when solids are loaded. The reaction force of particles on gas flow is mainly in the tangential direction and directs mainly upward in the axial direction. The reaction force in the tangential direction will decelerate gas phase and the upward axial force will prevent gas phase from flowing downward in the near wall region. The intensive particle–wall collision regions mainly locate in the wall opposite to the cyclone inlet and the cone wall. Moreover, as the solid loading ratio increases, number of turns travelled by solids in a cyclone decreases especially in the apex region of the cyclone while the width of solid strands increases, the pressure drop and tangential velocity decrease, the high axial velocity region moves upwards, and the radial flow of gas phase is significantly dampened.     

A model of the coagulation process with solid particles and flocs in a turbulent flow

A mathematical model was developed on the basis of population balances to predict the floc size distribution in a coagulating suspension. The coagulation process is performed in a stirred tank reactor with a turbulent flow field. In the population model the influence of the different local energy charges inside the reactor is taken into account. Moreover two sorts of particles are distinguished, i.e. the originally present and completely dispersed primary particles and the flocs. Contrary to the primary particles the flocs can be disrupted due to pressure and shear forces as they are mechanically not very stable. This different behaviour requires separate population balances for the two sorts of particles. The model parameters that are necessary are adapted to one single experiment.For the steady state the results represent different floc size distributions dependent on the solid concentration and the energy charge. Moreover it is shown that the assumption of an ideally mixed reactor that is often used cannot be maintained to be always true for the prediction of the resulting floc size distribution. The calculation results achieved are validated by image processing measurements of coagulating quartz particles in an aqueous suspension.     

Investigation of wall stress and outflow rate in a flat-bottomed bin: A comparison of the DEM model results with the experimental measurements

The present paper provides a discrete element method (DEM) analysis of the filling and discharge processes of granular material in a 3D flat-bottomed bin. A granular aggregate of nearly round particles (20,400 pea grains, 7.2-7.8 mm in diameter) is considered. The numerical results are compared with the experimental data. The DEM analysis provides an accurate prediction of wall stress distribution and the outflow rate of discharge throughout the bottom orifice. The stress distribution developed within the granular material after filling and during the discharge phase is considered, and the transition from the active to passive stress state is discussed. This analysis aims to quantitatively predict the flow parameters related to the careful identification of the material parameters. The investigation presented may be useful for the ongoing development of DEM.     

Assessment of flow and heat transfer characteristics for proposed solid density distributions in dilute laminar slurry upflows through a concentric annulus

A computational model is developed to predict the hydrodynamic and heat transfer characteristics of dilute liquid-solid laminar upflows through a concentric annulus. The dilute slurry is treated as a single phase Newtonian fluid of locally variable physical and thermal properties. Available experimental data of radial solid density distributions in dilute water-feldspar annular upflows is used in the model. Various important characteristics of laminar slurry flows were successfully predicted. It was also shown mathematically that in the limiting case of zero average solid loading, the solution reduces to that of the single phase. The radial location of maximum slurry density in the annular gap was found to be an important factor in determining both the flow and heat transfer behavior of the present system; also, the higher heat transfer enhancement ratios were predicted at the lower slurry Reynolds numbers.     

Electrolytic synthesis of succinic acid in a flow reactor with solid polymer electrolyte membrane

This paper describes the galvanostatic synthesis of succinic acid from maleic acid in an ion exchange membrane flow cell. The electrolysis was carried out at stainless steel, lead and copper cathodes under variable conditions of current density and substrate concentration. Depending upon the experimental conditions, the yield of succinic acid varied from 95 and 99% with a coulombic efficiency of 80–99%. The product was characterized by various physicochemical techniques, viz. ¹H-NMR, IR and UV–Visible spectroscopy and elemental analysis. The operational conditions giving maximum yield of product were identified. The mechanism of electrochemical reduction of maleic acid and advantages of using a catholyte without supporting electrolyte are discussed.     

CFB煤燃烧／热解双反应器立管内气固流动模型分析

在循环流化床（CFB）煤燃烧／热解双反应器冷态实验装置上,以硅胶和电厂锅炉灰为实验物料,考察了立管内的气固流动特性,其中立管的内径44mm、高3m。研究结果表明,立管内的气固流动形态为移动床流动,Leung的立管流动模型适合对该系统中立管内移动床流动的描述,经拟合分别得到了立管内气、同速率以及气同相对速率与固体速率之间的经验方程,对热态实验过程中判断立管内的气固流动型态以及料封的稳定性均具有一定的参考价值。     

Blend morphology development during melt flow: Correlation of a model concept based on dynamic phase volume with practical observations

An approach is first developed that can be used to identify the global morphology of an immiscible two‐phase polymer–polymer blend under shear flow. The basis for the modeling is the concept of a dynamic phase volume; this is based on relative abilities of the respective phases to flow when under stress, and determined by the actual phase volume fraction and the viscosity ratio between phases. One result of the modeling is a schematic diagram providing guidelines for morphology development during melt processing in a nonuniform stress field. Bisphenol A polycarbonate(PC)/ABS blends were studied as an immiscible system, using variations of component ratio and viscosity ratio at constant composition. Blend morphology was characterized by scanning electron microscopy and solid‐state dynamic mechanical spectroscopy. Model predictions correlate well with experimental observations of the frozen‐in solid‐state morphology following injection molding. Discussion also cover the utility of the model for blend design and limitations of the modeling approach. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 311–318, 1999