A fast algorithm for mass transfer on an unstructured grid formed by DEM particles

The Discrete Element Method (DEM) was used to generate a particle packing and transient mass transfer in the particle layer was simulated using a novel algorithm for determining the mass fluxes between DEM particles. This method is intended for simulating diffusion phenomena occurring during the dissolution of swelling polymers as the DEM particles can change size and distort the grid, whilst maintaining sharp boundaries between mesh elements. In this work, the robustness and accuracy of the algorithm was tested by solving a diffusion problem over the DEM mesh and comparing it to an accurate solution obtained by a finite difference (FD) approximation, whose discretisation was 10 times finer than that of the unstructured grid. Parametric studies were conducted where the random packing and the size distribution of the DEM particles were altered and the differences in concentration profiles were compared with the FD reference solution through the use of the mean squared error. Both steady state and transient cases were compared. Two methods to improve the accuracy of the DEM unstructured grid were devised and tested using porosity and tortuosity data. In one case the porosity and tortuosity were obtained from the steady-state simulations and in the other case, local convex hulls were used to calculate porosity. Although both these methods decreased the mean squared error up to a factor of two, they also resulted into increased complexity of the simulation. It was concluded that the use of an effective packing algorithm and a narrow particle size distribution are key to maintaining the accuracy of the DEM-generated unstructured grid method.     

The effect of air on the packing structure of fine particles

A numerical study of the effect of air on the packing structure of fine particles has been performed by a combined continuum and discrete numerical model. The forces considered are gravity, contact force, drag force, and van der Waals forces. The results are analyzed in terms of particle rearrangement, local porosity, coordination number, radial distribution function, and the distribution of contact forces. The results indicate the degree to which drag and van der Waals forces promote mean porosity increases and mean coordination number decreases. Drag forces allow contacts of particles reaching a state of rest in a packing to be closer to the Coulomb failure criterion for shear displacement when van der Waals forces are small. Increasing van der Waals forces imposes contact conditions that are far away from the Coulomb failure criterion. Increased drag and van der Waals forces tends to lead to more heterogeneous structure. It is demonstrated that average normal contact force is related to the ratio of van der Waals forces to particle weight.     

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.     

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.     

管式固定床反应器柱状颗粒床层流体流动模拟与实验研究

针对管式固定床反应器内管束数量多、规模大等特点,选取单个管束作为特征结构。对装填不同直径柱状颗粒的管束,采用程序坐标定位的方法,建立柱状颗粒床层的物理模型。采用DEM与CFD联合数值仿真方法,探究反应管内径与柱状颗粒的等比表面积球当量直径之比(管径比Di/dp)对柱状颗粒床层流体流动的影响,并建立单管固定床反应器试验台,采用差压测试方法进行实验研究。结果表明,当Di/dp由5.37增至12.75时,床层空隙率和流体分布均匀性均得到改善,壁面效应的影响由床层中心减弱到管壁。基于数值模拟及实验结果对Di/dp=12.75的柱状颗粒床层进行床层压降Ergun公式常系数修正,CFD模拟计算的结果与拟合公式吻合较好。研究结果能为固定床反应器压降预测提供参考。     

Further observations on the rheological behaviour of dense suspensions

The literature and recent WSL results on suspensions of spherical particles are surveyed and summarised. It is concluded that the steady shear properties of a dense suspension is not characterised by an unique viscosity or flow curve, but rather it is described by a wide viscosity distribution or a shear stress - shear rate flow band whose mean and standard deviation are functions of solids concentration, particle size distribution and viscometric geometry and dimensions. The standard deviation (or data spread) increases with solids concentration and with decreasing viscometer gap to particle diameter ratio. This property is due to poor sample reproducibility in respect of solids concentration and particle size distribution and the inherent two-phase nature of suspension which gives rise to particle migration and consequently non-uniform packing density or structure in a sample. Because a dense suspension is increasingly sensitive to these factors as concentration is increased, the standard deviation can be very large. Because the details of packing structure vary with flow, the viscosity distribution or flow band depends on viscometric flow geometry and measuring element dimensions. The implications of this conclusion on the study and characterisation of dense suspension property and the prediction of its behaviour in industrial handling and process equipment are discussed.     

Simulation study of the effect of wall roughness on the dynamics of granular flows in rotating semicylindrical chutes

A discrete element model (DEM) is used to investigate the behavior of spherical particles flowing down a semicylindrical rotating chute. The DEM simulations are validated by comparing with particle tracking velocimetry results of spherical glass particles flowing through a smooth semicylindrical chute at different rotation rates of the chute. The DEM model predictions agree well with experimental results of surface velocity and particle bed height evolution. The validated DEM model is used to investigate the influence of chute roughness on the flow behavior of monodisperse granular particles in rotating chutes. To emulate different base roughnesses, a rough base is constructed out of a square close packing of fixed spherical particles with a diameter equal to, smaller, or larger than the flowing particles. Finally, the DEM model is used to study segregation in a binary density mixture for different degrees of roughness of the chute. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2117–2135, 2015     

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.     

小管径-粒径比颗粒无序堆积通道内壁面效应数值研究

采用DEM-CFD方法对小管径-粒径比颗粒无序堆积通道内壁面效应进行了数值研究。针对D/d_p=5.0圆球无序堆积通道构建了光滑壁面和波节壁面两种通道壁面结构,分析了不同壁面结构堆积通道内孔隙率分布、流动和温度场分布及其流动换热性能。结果表明：小管径-粒径比光滑壁面颗粒无序堆积通道内壁面效应显著,壁面附近平均流速明显高于堆积中心区域,而平均温度要低于堆积中心区域,壁面附近0.5d_p区域内通过的流体质量流量比例为46%;波节壁面结构抑制了通道壁面附近漏流,可小幅提高堆积通道的换热能力,但堆积通道内的流动阻力也随之增大,其综合换热性能较光滑壁面堆积通道有所下降。     

Porosity Calculation of Binary Mixtures of Nonspherical Particles

An investigation has been made of the packing of binary mixtures of either spherical or nonspherical particles. It is shown that this binary packing system can satisfactorily be described by the Westman equation. By use of the concept of "equivalent packing diameter," nonspherical particle packing may be related to spherical particle packing. The porosity of binary mixtures of nonspherical particles can then be predicted by means of a model developed for spherical particles. This approach is verified by the good agreement between the calculated and experimental results.     

Microdynamic analysis of particle flow in a horizontal rotating drum

The flow of particles in a horizontal rotating drum is studied based on the results generated by Distinct Element Method (DEM). The simulation conditions are comparable to those measured by means of Positron Emission Particle Tracking (PEPT), with a drum being 100 mm in diameter, 35% filled by spheres of 3 mm diameter, and rotating at a speed from 10 to 65 rpm. The simulation method is validated from its good agreement with the PEPT measurement in terms of the dynamic angle of repose and spatial velocity fields. The dependence of flow behaviour on rotation speed is then analysed based on the DEM results, aiming to establish the spatial and statistical distributions of microdynamic variables related to flow structure such as porosity and coordination number, and force structure such as particle interaction forces, relative collision velocity and collision frequency. An attempt has also been made to explain the effect of rotation speed on agglomeration based on the present findings.     

Study on molding process of UHMWPE microporous filter materials

A method called loose sintering was first introduced to prepare ultrahigh‐molecular weight polyethylene (UHMWPE) microporous materials. The pore size was predicted by the face‐centered cubic structure model while considering the particles' arrangement and melt. The results showed that the experimental pore diameter was close to that calculated by the present model. The effects of UHMWPE molecular weight, particle diameter, packing density, sintering temperature, and sintering time on pore size, compressive strength, pore diameter distribution, and density were presented. The morphology of micropore and the uniformity of pore distribution were analyzed by scanning electron microscopy and fractal geometry. The results showed that average pore diameter and porosity both increased with the UHMWPE particle diameter while decreased with compressive strength and bulk density. Sintering temperature and sintering time determined whether the heat was redundant to melt the particles. They also determined the pore size and the uniformity. UHMWPE microporous materials could be successfully prepared with suitable processing conditions. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

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.     

Packing of multi-sized mixtures of wet coarse spheres

The effect of water addition on the packing of multi-sized coarse spheres has been experimentally investigated under standard poured packing conditions. The results indicate that porosity is strongly affected by particle characteristics such as particle sizes and their distribution, in addition to water content. The packing features in the relationship between porosity and moisture content for wet multi-sized spheres are found to be similar to those for wet mono-sized spheres, implying that the same governing mechanisms apply. The comparison between the dry and wet packing systems confirms that there is a similarity between them, suggesting that the packing of wet particles can be predicted within the framework of a packing model developed for dry coarse particles. Future work in this direction is also discussed.     

A particle packing algorithm for pellet design with a predetermined size distribution

In this paper a particle packing algorithm is proposed which is to be used to predict the behaviour of pellets in the blast furnace on a first principal basis. Pellets consist of particles of various mineralogical composition and the structure in which they pack together to form a pellet is dependant on the size distribution of the particles and the pellet porosity. This packing structure can result in isolated volumes within the pellet where the local composition deviates from the overall average composition. This can result in, for example, melt formation at lower temperatures than expected, which will have a detrimental effect on the pellet strength. These local compositions result from the contacts between particles of different minerals and can thus be quantified by the coordination number of the particles. By using a validated coordination number model, which is unique for a particle packing algorithm, virtual pellets were created for a range of particle size distributions and porosities. The algorithm used the Monte Carlo method combined with the simulated annealing minimisation algorithm to solve the pellet simulations. The objective function is a combination of two functions, one describing the deviation from the target coordination number of the particles and the other the average fraction of overlapping volume of the particles per contact. In this way a realistic pellet structure was maintained while at the same time controlling the coordination number of the particles.     

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.     

Computer simulation of granule microstructure formation

The diagenesis (porous microstructure evolution) of granules formed by a layering growth mechanism in a wet granulation process has been modelled. The model includes the packing of primary particles with a given size and shape distribution, and the deposition, spreading, and solidification of binder droplets within the growing granule. The dependence of granule porosity on the binder/solids ratio, primary particle size and morphology, and the rates of binder spreading and solidification has been investigated. The results are presented in the form of structure maps relating volume-averaged microstructure parameters with dimensionless groups including the ratio of droplet spreading and solidification times and the mean time between particle collisions. These graphs can guide the selection of process operating conditions or formulation ingredient properties required to obtain a particular granule microstructure.     

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.     

基于体视学的SAP混凝土气孔结构分析与研究

为了研究混凝土在添加高吸水性树脂后其内部气孔结构的变化规律,以及内部气孔结构的变化对混凝土试样抗压强度的影响,基于定量体视学的电子显微图像分析方法,对添加SAP混凝土的内部气孔结构特征展开了相关试验研究.采用干拌的方法拌和SAP混凝土,对不同配合比和不同SAP掺量的混凝土进行分批试验,测定出各组试样的气孔结构参数和抗压强度等,以深层次的剖析SAP对混凝土强度和内部气孔结构的影响.研究结果表明:混凝土内部气孔的平均孔径与间距系数随着SAP含量和水灰比的增加而增大,而混凝土抗压强度则呈现出相反的变化趋势.在配合比相同的情况下,小粒径SAP颗粒对混凝土气孔率的提高效果更为明显,而大粒径SAP颗粒对混凝土气孔平均孔径的提高效果更为明显;水灰比对气孔平均间距系数影响显著,而SAP粒径对混凝土内部气孔平均间距系数的影响不明显.     

Characterization of packing structure of tape cast with non-spherical natural graphite particles

A three-dimensional microstructure of green and pressed tapes cast with graphite particles of non-spherical shape were examined quantitatively on the basis of the distribution of void sizes among the packed particles. The distributions measured over the cross-sections of the tape in three directions were expressed by the theoretical ones deduced for non-spherical particles. Particle shape was characterized by shape indices defined by Fourier analysis of particle outlines measured over the corresponding cross-sections of the green tape. The relationships were totally established between the limiting packing density, characterizing the void size distribution at the same section voidage, and the shape index of particle over the section. As a result, the normalized median void diameter as well as the limiting packing density of the pressed tape was found to increase with the particle shape index, corresponding to wider void size distribution. Therefore, based on developed correlations, the optimization of packing microstructure of the cast tape can be expected to result in high performance battery by using shape-modified graphite particles.