Numerical simulation of particle motion in vibrated fluidized bed

The particle motion in vibrated fluidized bed was examined by using numerical simulation. A two-dimensional fluidized bed was used, and discrete element method (DEM) was used as for calculating the particle motion in vibrated fluidized bed. Geldart group B particle, which is regarded to have no effect of agglomerate, was used as the fluidizing particle. The vibration directions (vertical and horizontal) and vibration parameters (frequency and amplitude of vibration) were changed.In the case with vertical vibration, large bubbles caused by vibration gap (defined as the gap between particle bed and wall caused by vibration) appear in bed. When the vibration strength is high and the vibration frequency is low, it is difficult to fludize the particle bed in the case with horizontal vibration because the vibration gap acts like the channel. When the vibration frequency increases at the same vibration strength, the effect of vibration on the particle motion becomes small. The effect of vibration on the pressure loss in particle bed is large in the case with horizontal vibration.     

Mass transfer in shallow aerated vibrated powder beds

Mass transfer rates are reported for granular beds (depths = 24 and 1 mm) aerated by upward flow of nitrogen both in absence of vibration and also subjected to vibration at intensities affording maximum accelerations = two and four times gravity. Nitrogen flows were both below and above minimum gas-fluidizing velocities in absence of vibration.At both 24- and 1-mm bed depths, vibration at intensity four times gravity can enhance mass transfer by a factor between about 1.4 and 2. For mass transfer, bed depth is an important variable, with or without vibration. Without vibration, mass transfer at 1-mm depth can be ∼ 10 to 15 times greater than transfer in a 24-mm bed. A correlation is available that deals successfully with influence of bed depth in our data, both with and without vibration.Data reported herein at 1-mm depth bear upon performance of a chemical microreactor with cross-flow of gaseous reactants through particles in the coherent-expanded (CE) vibrated-bed state. The data suggest that a mass-transfer limitation need not ordinarily be taken into account in analysis of microreactor kinetic data for a chemical reaction for which a fluid bed reactor is an appropriate commercial choice.     

Favorable vibrated fluidization conditions for cohesive fine particles

The present study was performed to clarify the operational range for vibro-fluidization of fine cohesive particles (glass beads, d_p = 6 μm). Decreasing and increasing gas velocity methods were examined to clarify the favorable vibro-fluidization region. The upper limit of the gas velocity for intermittent channel breakage was higher in the case of the increasing gas velocity method than the decreasing gas velocity method. This was because the changes in the bed flow pattern from a favorable (intermittent channel breakage) to an unfavorable fluidization state (stable channels) were moderate in the case of the increasing gas velocity method. In the increasing gas velocity method, two kinds of cross-points were obtained from the relationship between the gas velocity and the bed pressure drop. At one of the gas velocities at these cross-points, the bed void fraction reached its maximum. In the present study, the above-mentioned gas velocity was defined as the upper limit of gas velocity for favorable vibro-fluidization, u_chu. A favorable vibro-fluidization region was determined by combining u_chu with u_chl, which is the lower limit of gas velocity for intermittent channel breakage obtained in a previous study. The value of u_chu was found to have a maximum corresponding to a certain vibration strength.     

Numerical simulation of cohesive particle motion in vibrated fluidized bed

The effect of vibration on the cohesive particle motion in the bed was examined by using discrete element method(DEM). The bed of dried fine particles was treated as the objective of calculation. The van der Waals force was used as the cohesive force because the van der Waals force was considered to be the main cohesive force in this case. Since the actual calculation time was too long, the fine cohesive particle was difficult to be treated. So a relatively large particle (1.0 mm in diameter) was used in calculation and the van der Waals force was assumed that the ratio of gravity force to van der Waals force of particle used in this calculation was equal to that of a fine particle (6.0 μm in diameter), to express the effect of van der Waals force significantly. The calculation results were compared with that case of cohesionless particle.In the case with vibration, the cohesive particle motion in the bed is observed, though no fluidization state appears in the case without vibration, and there is no bubble in the bed even the fluidization state. In the case of cohesive particle, the collision energy between particle and wall caused by vibration gap propagates from the bottom to top of bed, and the particle moves vigorously at the top of bed in the case with vibration. As the vibration gap increases, the effect of vibration on the cohesive particle motion becomes larger, i.e., the low vibration frequency at the same vibration strength or the large vibration strength at the same vibration frequency promotes the fluidization of the bed.     

Simulations of vibrated fine powders

During the past few decades, several studies have been conducted to understand the behaviour of powders in vibrated beds. This paper introduces a technique of incorporating the agglomeration and deagglomeration phenomena in the simulation of vibrated fine powders. Two-dimensional direct simulations are performed using 300 spheres 2.99 mm in diameter in a trapezoidal container vibrated vertically at an amplitude of 2.5 mm and 20 Hz frequency as preliminary conditions. Under non-cohesive conditions, the results are in agreement with those found in the literature. As a preliminary effort to predict the behaviour of cohesive fine powders under vibrated conditions, agglomeration and deagglomeration processes are modelled as the formation and destruction, respectively, of interparticle bonds during particle collisions. Two parameters used to model agglomeration and deagglomeration are the ease of cohesion and cohesivity of the powder. Dependencies of these parameters on certain physical properties of cohesive powders have been suggested. Simulation results reveal two aggregate populations, one with uniform size aggregates and another population with multi-sized aggregates. The former aggregates were more prevalent in weakly cohesive powders while the latter in highly cohesive powders. Interesting macroscopic bed behaviour such as alternating cycles of agglomeration and deagglomeration were also observed. Further work is needed in which the aerodynamic forces are taken into account and cohesion mechanisms at the particle surface are modelled.     

循环喷动流化床颗粒抛射高度的计算

通过对循环喷动流化床顶部封闭空间气体射流及气固运动的理论分析 ,得出了循环喷动流化床中颗粒出循环管后抛射高度的计算方法 ,所得计算结果与实测结果误差小于 8% ,为循环喷动流化床的设计提供理论依据     

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.     

Investigation into gas-solid heat transfer in a cryogenic vibrated fluidised bed

Experiments were carried out in a cryogenic vibrated fluidised bed to investigate the heat transfer between gas and rubber particles obtained from discarded tyres. The effects of parameters such as bed layer thickness and gas flow rate on the gas-solid heat transfer were investigated, and a heat transfer correlation obtained by regressing the experimental data. Theoretical analysis based on radial thermal conductivity indicated that higher heat transfer efficiency could be obtained by the use of a fluidised bed rather than a fixed bed or a moving bed, especially for rubber particles having low thermal conductivity under cryogenic conditions. A numerical modelling was developed, based on assumptions of the movement of the particles and the vibrating bed plate, using a unique method of regarding particles as the source term in the energy equation. Computational results from the modelling showed good agreement with the experimental data.     

Density-dependent separation of dry fine coal in a vibrated fluidized bed

The main purpose of coal separation is to reduce ash, sulfur, mercury and other mineral contaminants in the coal to increase the calorific value and benefit the environment. Dry coal beneficiation has obvious advantages over the wet process although the latter is currently the predominant method in use throughout the world. A vibrated fluidized bed was constructed for separating dry fine coal particles from unwanted gangue particles. An experimental investigation of vibrational energy transmission, and the interaction between vibration and gas flow, was performed. The motivation for these experiments was a theoretical development of the principles involved in forming a dense-media vibrated fluidized bed (DMVFB). The mechanism of bubble breaking by vibration is discussed. A formula for calculating the critical vibration frequency at which bubbles can be efficiently broken and bubble formation restrained is proposed. The experimental results demonstrate that the density of a dense-media vibrated fluidized bed is uniform, with a maximum relative error of 1.68% under optimal technological and operating conditions. The < 6 mm fine coal was efficiently separated with a probable error E value of 0.07 t/m³. A lower limit of separation of 0.5 mm was achieved. The DMVFB separation efficiency is higher than wet jig with E value of 0.11 t/m³.     

Spontaneous segregation behavior in a vibrated gas-fluidized bed for fine lignite dry cleaning

Fine lignite dry cleaning, which has the significant advantage of without process water, is becoming increasingly important due to global water shortage. Lignite particles of various compositions were experimentally studied in a vibrated gas-fluidized bed. This is the first report of the size-based segregation of fine particles in the vibrated gas-fluidized bed. Experimental results demonstrate that the –2 +0.5 mm lignite particles play an irreplaceable role in particle fluidization and segregation. To ensure good separation performance, the minimum content of –2 +0.5 mm lignite particles should be 13%. Separation results show that for –6 +0.5 mm lignite particles, the ash contents of clean coal and tailings are 23% and 45%, with the corresponding yields of 82% and 18%, respectively, which shows good separation performance.     

Development of a tribolelectric procedure for the measurement of mixing and drying in a vibrated fluidized bed

Fluidization of fine, pharmaceutical powders makes them easier to dry, coat and mix. Fine powders, however, are difficult to fluidize well with gas flow only. Vibration can often help achieve smooth fluidization at a lower gas flow. The objective of the present study was, thus, to develop reliable and quick experimental methods to characterize mixing and drying in vibrated fluidized beds of fine powders.Effective mixing is critical in many industrial applications and, in gas-solid fluidized beds, requires gas velocities greater than the minimum bubbling velocity (U_mb). There are a number of techniques available for determining U_mb. However, they often are impossible or impractical to use in an industrial application. A new measurement technique involving the use of triboelectric probes was developed. Signal characteristics obtained from sophisticated signal analysis were used to identify the minimum bubbling velocities. These predictions corresponded well with the values obtained from more traditional laboratory methods such as the bed pressure gradient.In a fluidized bed, particles hitting a metal probe will generate a small triboelectric current. Triboelectric probes are able to detect rapid changes in particle surface properties. Surface properties of the particles were modified by wetting the particles in a low shear mixer. This change was detected by triboelectric probes at various locations inserted throughout the bed. The water adsorbed on the particles will begin to evaporate when exposed to the gas stream and the surface properties of the particles will gradually return to their original dry state. The triboelectric probes were able to monitor this drying process. The effects of vibration amplitude on the mixing and drying rate of the bed were also determined.     

Mixing in a vibrated granular bed: Diffusive and convective effects

In this study, Discrete Elementary Method (DEM) is employed to simulate the motion and mixing behavior of granular materials in a three-dimensional vibrated bed, which is energized by vertical sinusoidal oscillations under different vibrating conditions. With frictional sidewalls, the convection flow is a very important phenomenon in the vibrated granular bed. The influence of vibrating conditions, including vibration acceleration and frequency, on the formation of symmetric convection flow is investigated in this study. In order to characterize the convective flow and the diffusive motion of granular materials, the dimensionless convection flow rate, J_conv, and the vertical self-diffusion coefficient, D_yy, are defined, respectively. Péclet number, Pe, is employed to characterize the ratio of the convective flow to the diffusive motion in vertical direction. The role of Pe in the formation of symmetric convection flow is discussed in detail. Moreover, the top-bottom initial loading pattern of two groups of glass beads with different colors is employed to investigate mixing behavior of granular materials. The well-known Lacey index is employed as the mixing degree, M, to quantify the mixing quality. The mixing rate is calculated from a least-square fit using the time evolution of M. The simulation results demonstrate that the mixing rates increase with increasing J_conv and D_yy in exponential relations.     

Flow patterns of solids in a two-dimensional spouted bed with draft plates: PIV measurement and DEM simulations

Particle flow behaviors in a two-dimensional spouted bed (2DSB) with draft plates were studied using both the particle image velocimetry (PIV) and the combined technique of discrete element method and fluid dynamic computation (DEM-CFD) while considering the gas turbulence effect. The bed consisted of a rectangular column, 152 mm wide and 15 mm deep, a conical section with an included 60° angle and two draft plates with a distance of 15 mm. Images of particle flow were recorded by a high speed CCD camera and analyzed using a self-developed PIV algorithm to obtain a time-averaged particle velocity field. Experiments predict that the addition of draft plates not only makes the streamline of particles in the annulus steeper, but the velocity magnitude is made smaller as well. DEM results predict well the longitudinal profile of the particle vertical velocity along the bed centerline, especially during the rapid acceleration stage at the lower part of the spout. Finally, the distributions of drag forces and net forces are introduced in this paper to explain the particle velocity profiles by PIV measurement.     

Particle dynamics in a dense vibrated fluidized bed as revealed by diffusing wave spectroscopy

We report granular temperature data and long-time dynamics of mono-disperse glass particles in a three-dimensional dense bed subject to vertical sinusoidal vibrations over a wide range of conditions. The granular temperature of the particles was found to scale with the square of the peak vibrational velocity. The mean time of flight between the collisions was found to scale with the inverse of the square of the peak vibrational velocity, whilst the mean free path of the particles was observed to scale with the inverse of this velocity. The movement of the particles throughout the bed, which was observed to be sub-diffusive over macroscopic timescales for all conditions considered here, appears to be governed by collective motion of particles between cavities defined by their neighbours.     

Experimental studies of particle flow dynamics in a two-dimensional spouted bed

In this paper, both time-averaged and fluctuating behaviors of granular solids in a two-dimensional spouted bed (2DSB) were investigated by particle image velocimetry (PIV). A self-developed algorithm for the high-gradient granular flow field was employed to measure particle velocity sequences together with power spectral density, mean particle velocity and granular temperature. The incoherent spout was characterized as an ‘X’ geometry marked with a periodic upwardly moving neck consisting of particle clusters. In the annulus, particles move periodically as a process of acceleration-deceleration-stagnation that has the same domain frequency as the pressure drop of 2DSB. The time-averaged downward velocities have a maximum at a certain position between the spout wall and conical wall. In the spout, the longitudinal profiles of vertical particle velocities along the axis exhibit a fast acceleration followed by a long flat peak, while the normalized lateral profiles at all bed levels tend to collapse into a third polynomial curve with an inflection point. A mushroom-like distribution of the granular temperature exists in 2DSB. The peaks of granular temperature occur not only near the spout-annulus interface, but also at the corner zone between the annulus and the fountain.     

Dry beneficiation of fine coal deploying multistage separation processes in a vibrated gas-fluidized bed

In this study, multistage separation processes were introduced into fine coal beneficiation in a vibrated gas-fluidized bed in order to improve the separation performance. The changes of coal properties, operational parameters, and density segregation characteristics during multistage separation were systematically studied. The results showed that with an increase in the separation stage, the range of density was narrowed down and the required input energy decreased. The results showed that with the same yield, the ash content of clean coal decreased from 12.53% for single separation stage to 8.91% for three separation stages, indicating a significant improvement on separation accuracy.     

Solid circulation rate in a circulating fluidized bed in the presence of fine powders

Fine powders (Geldart's group C) are added to a circulating fluidized bed (CFB) of coarse particles (Geldart's group A) and the solid circulation rate (SCR) is investigated with addition of fine powders of different sizes and different fractions (different hold-ups) to the bed. Experiments were carried out in a CFB of 2 m in height and 0.052 m in diameter, using FCC catalyst particles of as the coarse particles and cohesive aluminum hydroxide powders of 0.5- as the fine powders. The effects of hold-up of fine powders in the bed, fine powders size, and superficial gas velocity on the SCR were investigated.The SCR strongly depended on the hold-up of fine powders of 0.5- in size and noticeably decreased with increasing the hold-up of fine powders under constant gas velocity. This dependency disappeared when the size of fine powders was larger than . Thus, depending on the size of fine powders added to the CFB, two distinct regions for the changes of SCR could be clearly identified.     

Two-dimensional discrete element modeling of a spherical steel media in a vibrating bed

A discrete element model was developed to model granular flow in different vibratory beds and the results are compared with experimental measurements of bulk flow velocity and bed expansion. The sensitivity of the model predictions to the contact parameters was considered and the parameters were optimized with respect to the experimental results. The difference between the model predictions of the bulk flow velocity and the measurements was less than 10% at four locations in media beds of two depths. The average bulk density of the vibrating beds was also predicted to be within 10% of the measured values.     

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.     

Granular flow and segregation in a four-bladed mixer

In this study, we experimentally examine flow and segregation of granular material in a cylindrical mixer geometry agitated by four 45 pitched blades, which is representative of equipment such as high-shear granulators and filter-dryers. We observe that the free surface of the granular bed deforms, rising where the blades are present and falling between blades passes. Using particle image velocimetry (PIV), we measure the instantaneous, average, and fluctuating velocity fields at exposed surfaces (top surface and near the wall), for both near-monodisperse and polydisperse granular materials. The radial and axial point-velocity profiles indicate three-dimensional recirculation patterns indicative of avalanching and bed penetration. For polydisperse mixtures, we find that depending on the shear rate, different segregation mechanisms can take place. Under low shear, complex lobe and striation segregation patterns occur through stretching and folding due to surface avalanching. This leads to enhanced initial mixing rates in a manner consistent with spontaneous chaotic granular mixing. At high-shear rates, segregation is controlled by the rotation of the blades. As a result, coarse particles have a tendency to migrate both to the free surface and the outer wall independently of initial bed loading conditions.