Analysis of particle porosity distribution in fixed beds using the discrete element method

This report discusses the use of the discrete element method (DEM) to the porosity distribution of spherical particles in narrow pipes as a function of the pipe-to-particle diameter ratio. It was found that the packing structure depends mainly on the pipe-to-particle ratio and the particle friction. The numerical results with respect to the radial porosity distribution are in agreement with experimental data from the literature. Radial porosity distributions were calculated using algorithms developed by Mueller. The packing structure of the particles shows channeling for small pipe to particle diameter ratios. The simulated height averaged porosity distribution agrees with models from the literature. Moreover, DEM provides the possibility to include particle properties which reflect on the porosity distribution.     

鼓泡床床层高度的细网格DEM模拟

气固流化床DEM的细网格模拟中,采用传统方法计算网格空隙率和局部空隙率会对模拟结果造成较大偏差,给出一个精确面积分数模型和一个完全依赖颗粒环境的局部空隙率模型,从而更加合理地计算网格空隙率和局部空隙率。采用二倍颗粒直径的细网格模拟了小规模鼓泡流化床,模拟的气泡形状和尺寸与实验结果接近。模拟结果表明：采用给出的面积分数模型和局部空隙率模型能较好地模拟鼓泡流化床床层高度随时间变化的波形。     

Analysis and evaluation of permeability techniques for characterizing fine particles Part I. Diffusion and flow through porous media

The specific surface area and particle size can be deduced with speed and simplicity from appropriate measurements and calculations of fluid flow and diffusion in porous media. The interdependence of these two processes is developed in a series of two articles.In Part I, models are presented for molecular and Knudsen diffusion during flow through aggregates of solid particles at both atmospheric and low pressure permeametric conditions. For a randomly packed bed of granular particles, a cell model is developed that takes into account the tortuosity and variations in the cross-sectional area. A new analytical expression for the Kozeny constant is derived in terms of the bed porosity and particle shape. The effect of porosity on surface area measurements using permeability methods is explained.     

基于CCDM的流态化制冰的多相流动与传热特性

流态化制冰是一种新型的直接接触式动态制冰方式,通过建立联合连续和离散模型的CCDM(combined continuum and discrete model)全耦合模型,采用一种非结构网格颗粒搜索法,计算了流态化制冰过程所涉及的颗粒-流体多相系统的流动和传热特性。结果表明:基于CCDM模型计算出的结果与实验数据有较好的一致性,模型的准确度高;冻结程度关键值的提出,简化了颗粒间碰撞模型的判断和颗粒相表面传热量的等效计算;颗粒间的碰撞、聚并对颗粒粒径的作用,会进一步影响颗粒的运动速度、停留时间以及轴向浓度分布的变化,难以忽略其对于流态化制冰过程的多相流动与换热特性的影响。     

A numerical investigation of the void structure of fibrous materials

The void structure of particulate solids has been studied with the aid of a numerical packing algorithm based on the minimisation of an energy potential. This algorithm has been used to form densely packed assemblies of spherical and fibrous particles. The void space within these materials has been characterised using an algorithm that finds chains of voids that pass through the assemblies. The tortuosity (as defined by Carman [P.C. Carman, Fluid flow through granular beds, Trans. Instn. Chem. Engrs., v15 pp 150-166, 1937.]) and mean diameter of these chains have been determined and examined as important parameters that are relevant to the permeability of these materials. Tortuosity was approximately constant in the spherical particle assemblies, while the void size varied with the particle size. In general, the spherical particle assemblies showed much smaller void sizes (relative to the particle diameter) and lower tortuosity than the fibrous materials. The tortuosity of the fibrous materials was found to be a function of both the aspect ratio of the fibres, and the packing efficiency of the assembly.     

Numerical investigation of particle shape and particle friction on limiting bulk friction in direct shear tests and comparison with experiments

In this study, the discrete element method (DEM) was used to investigate the influence of particle shape and interparticle friction on the bulk friction in a Jenike direct shear test. Spherical particle and non-spherical particles using two overlapping sphere giving particle aspect ratio of up to 2 and a full range of interparticle contact friction coefficient were studied numerically. These were compared with physical Jenike shear tests conducted on single glass beads and paired glass beads. To separate the influence of sample packing density from interparticle contact friction on the bulk shearing response, the same initial packing was used for each particle shape in the simulations. The interplay between contact friction and particle interlocking arising from geometric interaction between particles to produce the bulk granular friction in a direct shear test is explored and several key observations are reported. The results also show that particle interlocking has a greater effect than packing density on the bulk friction and for each particle shape; DEM can produce a good quantitative match of the limiting bulk friction as long as similar initial packing density is achieved.     

烯烃催化裂解反应器局部颗粒堆积结构的颗粒解析模拟

烯烃催化裂解固定床工艺中的反应过程对压力敏感,深入研究催化剂堆积颗粒结构中的流动及压力分布对优化固定床结构及操作参数有重要意义。颗粒解析模拟方法广泛用于固定床内堆积结构的模拟,可以准确描述堆积结构中的流体力学行为,但对于复杂堆积结构网格生成困难。采用基于多孔介质模型的浸入边界法(PMM-IBM)结合网格自适应,实现了对固定床堆积结构的颗粒解析模拟,既解决了网格划分困难的问题,又节省了计算资源。采用网格自适应技术后,与均匀网格相比,堆积结构的网格总数减少大约80%。通过与贴体网格法的单颗粒表面受力分析对比,确定了此浸入边界法的关键模拟参数。随后模拟预测了三种床层与颗粒直径比值条件下堆积结构的空隙率及其内部的压力及流动分布。研究表明,堆积结构空隙中的局部轴向速度的最大值可以达到入口速度的10倍以上,轴向平均速度的径向分布与轴向平均空隙率分布一致,均成震荡衰减趋势。除此之外,预测的床层压降与Reichelt经验关联式结果较为吻合。在此基础上,耦合单颗粒内扩散和烯烃裂解的主反应,预测了反应物随孔径和孔隙率的变化,为进一步考虑外流场的变化奠定了方法基础。     

Modelling the Effective Thermal Conductivity in Polydispersed Bed Systems: A Unified Approach using the Linear Packing Theory and Unit Cell Model

A comprehensive, unified approach, using the Linear Packing Theory and Unit Cell Model, is proposed for calculating of the effective thermal conductivity of polydispersed packed beds. In this new approach, the effect of packing density is incorporated by the use of (i) an initial porosity to take into account the packing of mono‐sized particles, and (ii) the packing size ratio as a measure of the particle‐particle interaction. The proposed approach was validated with the experimental measurements of binary and ternary beds. This new approach demonstrates that the effective thermal conductivity of beds composed of polydispersed particles can be simulated for any composition without the need to measure the in situ porosity.     

Predicting the effective thermal conductivity of polydispersed beds of softwood bark and softwood char

In this paper, the effective thermal conductivity (ETC) of softwood bark and softwood char particle beds which are highly polydispersed has been studied theoretically and experimentally. Use of the linear packing theory and unit cell model of heat conduction enabled to express ETC of polydisperded beds as a function of particle size distribution. Each of the softwood bark and softwood char samples were sieved into seven fractions. The initial porosity and binary packing size ratio of the particles have been characterized as a function of mean sieve size. ETC of polydispersed beds of bark and char has been predicted as a function of particle size distribution. Model predictions were in good agreement with the experimental measurements. The proposed approach can be used to predict the ETC of any size distribution of softwood bark and softwood char beds without measuring the in situ bed porosity.     

Flow of sphero-disc particles in rectangular hoppers—a DEM and experimental comparison in 3D

Flows of “sphero-disc” granular particles in a rectangular hopper are studied both experimentally using high-speed video recording and mathematically using the discrete element method (DEM). The flow behaviour of particles and their arching and discharging in the hopper are analysed and compared with the DEM results for three hopper openings. In general, good agreement is shown on particle static packing, the flow behaviour and hopper discharging rates and the arching effect when flow ceases due to an inadequate hopper outlet opening. Spherical particles with a similar volume to the disc-like particles are also tested and compared and a clear effect of particle shape on flow rates is shown. Although some minor discrepancies are shown, these are likely to be caused by the practical difficulties in matching the exact particle parameters between the simulations and the experiments. The DEM is shown to be a powerful tool to analyse the interactions between irregularly shaped particles and demonstrates a great potential in analysing detailed particle packing structure and flow patterns, which may lead to the elaboration of a novel method for hopper design. Further work will focus on developing DEM to model a wider range of particle shapes and hopper geometries, use of DEM for flow and structure analysis, and the development of more sophisticated measuring tools such as tomography to validate the DEM model.     

Critical review of the impact of tortuosity on diffusion

Most of the present formulations for the mass conservation of species do not correctly represent changes in the time scale of diffusion as a function of porosity in a system of porous media. In sediments, or in any porous system, the presence of solid particles causes the diffusion paths of species to deviate from straight lines. To represent the role of porosity on diffusion, the diffusion coefficient must be scaled with tortuosity. In this paper we present a review of the available formulations for the scaled diffusion coefficient with tortuosity, sensitivity tests with analytical solutions, and calibration of these formulations with respect to measured data.     

Particle Crowding Analysis of Slip Casting

The particle crowding index and interparticle spacing terms were calculated for seven alumina suspensions. The particle crowding index was used to interpret the casting rate for the tested alumina suspensions; the index was successfully correlated with the casting rate for cakes that produced the same modes of porosity. Unfortunately, this index could not be correlated with the casting rate for the particle system that produced varied porosity as a function of composition. The interparticle spacing term was correlated with viscosity for particle size distributions between 31 and 0.1 μm. For particle size distributions extended to 44 μm, the viscosity could not be correlated with interparticle spacing, because the quantity of fine particles, rather than the particle packing, controlled the viscosity.     

Evaluation of Particle Bounce in Various Collection Substrates to be Used as Vaporizer in Aerosol Mass Spectrometer

The determination of the collection efficiency (CE) of particles during transport, vaporization, and ionization in the aerosol mass spectrometer (AMS), which uses vaporizer to evaporate non-refractory particles with subsequent ionization, is important for accurately quantifying the concentrations of chemical constituents. Particle bounce in the vaporizer can be considered as one of the most important parameters influencing the CE of particles. Substrates with various shapes (flat, cylindrical, reverse-conical, cup, trapezoidal, and reverse-T), materials (stainless steel, copper, tungsten, and molybdenum), pores with average sizes of 0.2, 1, 5, 20, and 100 μm, and mesh with a size of 79 μm, which can be a possible candidate for the vaporizer in the AMS, were constructed. Bounce fractions of sub-micrometer particles (polystyrene latex, oleic acid, and dioctyl phthalate) were determined using the differential mobility analyzer (DMA)-impactor technique under a constant impact velocity. For the porous substrate, the particle bounce fraction significantly decreased with increasing pore size and porosity, but there was an upper limit for the pore size above which the particle bounce fraction no longer decreased significantly (i.e., the rebounded particles successfully escaped from the pores). The mesh substrate also had a lower particle bounce fraction than the flat substrate. Among the tested materials, the copper substrate having the lowest hardness and elasticity had the lowest particle bounce fraction. In addition, the reverse-T shape substrate having more available surfaces for particle entrapment led to the reduction of particle bounce fraction. In terms of phase, the liquid particles had lower particle bounce fractions than the solid particles. Our results suggest that the vaporizer in the AMS should provide traps for multiple collisions of the rebounding particles with an appropriate porosity or mesh and should be made of low-hardness materials to minimize particle bounce.

Copyright 2015 American Association for Aerosol Research     

Dynamic Trajectory and Capture of Fine Dust by Magnetic Mesh Filters Based on a Particle Velocity Model

The particle velocity model developed in this study described the dynamic motion of fine dust particles along the magnetized mesh wires in a low Stokes regime. The numerically evaluated velocity contour of the particles modeled the critical path lines indicating the threshold positions for magnetic collection. The velocity contour was determined using the parameters such as particle size, magnetic intensity, flow velocity, and mesh configuration including wire thickness and packing density. Particle size was one of the most significant parameters to determine the magnetic collection. The theoretical estimation matched well with the lab experiments, but the discrepancy increased for large particles with a fine filter. In consequence, application of magnetized mesh filters could contribute to the collection of the ferromagnetic dust or aerosols to a certain extent without any additional power or pressure resistance.

Copyright 2015 American Association for Aerosol Research     

Experimental validation of polyhedral discrete element model

The flow of polyhedral granular particles in a small 3D slice hopper is studied experimentally and computationally by applying the discrete element method (DEM). A high speed camera was used to obtain the experimental results. The experimental packing structure, flow behaviour, arching and discharging in the hopper are analysed and compared with the DEM results for three hopper half angles. Reasonable agreement is shown on the static packing, flow behaviour and hopper discharge rates. The critical orifice length at which flow ceases to be smooth is investigated and arching of the material around the orifice is demonstrated experimentally and computationally. Spherical particles of nearly identical volume and density to the average of the polyhedral particles are also tested and compared to the polyhedra. The DEM is shown to be reasonably adept at modelling the interactions between polyhedral particles in a system in which there are very many possible particle geometrical interactions. Further work should consider the cohesion between the particles and the particle and the wall. Simulations of a greater number of particles in different hopper geometries should also be explored.     

气体、溶液中的非电解质和电解质在多孔颗粒内扩散的对比研究

实验测量了气体、溶液中的非电解质以及电解质三类性质相差较大的体系在相同的多孔颗粒内(孔隙率0.234～0.632)的有效扩散系数,并计算出曲折因子.探讨了由D_(?)=D_oε/τ定义的曲折因子对孔隙结构和扩散组分特性的依赖关系.     

Investigation of particle packing in model pharmaceutical powders using X-ray microtomography and discrete element method

This paper outlines a novel technique, based on combination of modern desktop X-ray microtomography, quantitative image processing and computer simulation using the discrete element method (DEM), to investigate randomly packed particles in an attempt to model the process of pharmaceutical tablet manufacture by powder compaction. The systems studied include glass ballotini and spheroidal micronised cellulose (Celphere), all with typical particle sizes between 180 and 300 μm. We demonstrate that X-ray microtomography (XMT) and DEM can reproduce the structure of real packing systems in three-dimensions and have the potential for further investigation of pharmaceutical processes by both modelling and experimental study. This was achieved by generating packing systems using DEM simulations that are consistent with the structural measurements made by XMT on real packed powders via the comparison of their radial distribution functions (RDFs). These results have been validated by direct volume measurements, and scanning electron microscopy (SEM) observations in terms of particle morphologies and size distribution. The result is a significant step forward for the quantitative analysis of model systems for pharmaceutical powders.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.     

Measurement of coal particle size and shape with concentrated coal-water mixtures

The behavior of concentrated coal-water mixtures having narrow particle size ssfractions of coal was investigated. The pulverized coal was fractionated into six distinct particle size ranges, i.e. -70+80, -80+120, -120+140,-140+200, -200+400 and -400 mesh sizes by using a series of sieves. Settling rates were determined as functions of solids concentration for suspensions in water of coal particles to establish the measurement of particle size and shape factor and to assess concentration effect upon the observed hindered settling rates. The settling rates were modelled using the Richardson-Zaki model with the exponent n variable to account for the nonspherical shape of the coal particles. The data was also correlated with the Michaels-Bolger model which explicitly account for the excess water which is dragged down along with the particles undergoing sedimentation. In addition, coal particles and suspensions were characterized by coal analysis, heating value, solid heat capacity and thermal conductivity, densities, maximum packing concentrations and pore size distributions.     

Particle‐scale simulation of the flow and heat transfer behaviors in fluidized bed with immersed tube

A kind of new modified computational fluid dynamics‐discrete element method (CFD‐DEM) method was founded by combining CFD based on unstructured mesh and DEM. The turbulent dense gas–solid two phase flow and the heat transfer in the equipment with complex geometry can be simulated by the programs based on the new method when the k‐ε turbulence model and the multiway coupling heat transfer model among particles, walls and gas were employed. The new CFD‐DEM coupling method that combining k‐ε turbulence model and heat transfer model, was employed to simulate the flow and the heat transfer behaviors in the fluidized bed with an immersed tube. The microscale mechanism of heat transfer in the fluidized bed was explored by the simulation results and the critical factors that influence the heat transfer between the tube and the bed were discussed. The profiles of average solids fraction and heat transfer coefficient between gas‐tube and particle‐tube around the tube were obtained and the influences of fluidization parameters such as gas velocity and particle diameter on the transfer coefficient were explored by simulations. The computational results agree well with the experiment, which shows that the new CFD‐DEM method is feasible and accurate for the simulation of complex gas–solid flow with heat transfer. And this will improve the farther simulation study of the gas–solid two phase flow with chemical reactions in the fluidized bed. © 2009 American Institute of Chemical Engineers AIChE J, 2009