Random Packing Of Spherical Particles Research Articles

Pore network modelling of slender packed bed reactors

Packed bed reactors are common reactor types in chemical industries. In case of reactions with large heat effects, bundles of slender tubes are used. For such slender tubes, the column-to-particle diameter ratio, N, is small, which can give rise to significant flow channelling. This research uses two particle-scale numerical approaches, namely particle-resolved computational fluid dynamics (PR-CFD) and pore network model (PNM), to investigate the hydrodynamics of three packed beds containing random packings of spherical particles with 4.2⩽N⩽7.0. Global parameters of the PNM, such as shape and constriction factors, are optimized using the PR-CFD results. A comparison of computed PNM and PR-CFD results shows that the PNM captures local variations in the bed well. The low computational cost of PNM, as well as its ability to provide locally resolved data, makes the PNM a promising approach for the pore-scale modelling of slender packed bed reactors.

A quasi-physical method for random packing of spherical particles

In this work, a quasi-physical method for the random packing of spherical particles based on the equivalent spring structure and the principle of force equilibrium is proposed. The model is inspired by a meshing method “Distmesh”. For the purpose of generating a feasible packing, the proposed model calculates the displacements of each particle based on physical principles and disregards forces that may not help with convergence, thus offering a natural and possibly fast route towards the final packing configuration. The packing densities predicted by the proposed method are in good agreement with those predicted by other methods and the experimental results. Finally, the topological properties of the packing of particles with log-normal size distributions, binary mixtures and ternary mixtures are evaluated by radical tessellation. The results show that the particle size differences and the proportions of each kind of particles have significant effect on the packing properties of the mixture. • Proposing a new quasi-physical model for the random packing of particles. • The model is inspired by a meshing method, which can more easily form force grids. • The model offers a natural and possibly fast route towards the final packing. • The particle size and volume ratio have significant effect on the packing properties.

Full‐Field Modeling of Heat Transfer in Asteroid Regolith: 2. Effects of Porosity

AbstractThe thermal conductivity of granular planetary regolith is strongly dependent on the porosity, or packing density, of the regolith particles. However, existing models for regolith thermal conductivity predict different dependencies on porosity. Here, we use a full‐field model of planetary regolith to study the relationship between regolith radiative thermal conductivity, porosity, and the particle non‐isothermality. The model approximates regolith as regular and random packings of spherical particles in a 3D finite element mesh framework. Our model results, which are in good agreement with previous numerical and experimental datasets, show that random packings have a consistently higher radiative thermal conductivity than ordered packings. From our random packing results, we present a new empirical model relating regolith thermal conductivity, porosity, temperature, particle size, and the thermal conductivity of individual particles. This model shows that regolith particle size predictions from thermal inertia are largely independent of assumptions of regolith porosity, except for when the non‐isothermality effect is large, as is the case when the regolith is particularly coarse and/or is composed of low thermal conductivity material.

Structural Model of Two-Component Particulate Mixtures with Maximum Heterogeneous Contacts

Heterodiffusion processes or chemical reactions in heterogeneous media are initiated at contact points between dissimilar particles of the reagents. Therefore, the number of heterogeneous contacts in the starting mixture is assumed to determine the rate of these processes: in particular, the rate of mass transfer in self-propagating high-temperature synthesis. The conditions for obtaining structures with maximum heterogeneous contacts have not been clearly defined so far in the literature. The paper determines for the first time the optimal ratio of particle sizes for a two-component mixture. This ratio contributes to the starting mixture composition that involves the maximum number of dissimilar contacts at a given weight or volume content of the reagents. A model of two-component densely packed disordered biparticulate granular media is proposed. According to the model, the starting mixture is considered a random packing of spherical particles of two sizes. The particle size ratio has been established so that the number of heterogeneous contacts between the particles of different phases is the highest. The concept of an ideal reaction area, which is a biparticulate structure consisting of the maximum number of dissimilar particles, has been developed and the role of the starting particle size composition in the formation of such structure has been established. An algorithm is presented for calculating the characteristics of the starting mixture to promote the structure with ideal reaction areas.

The development and numerical modelling of a Representative Elemental Volume for packed sand

This article describes a comparison between a packed-sand geometric model derived from experimental digitization of a small volume of sand and from a mathematical model (Yet Another Development Engine, YADE) that produces a random packing of spherical particles. As the application of the model is towards smoldering combustion, the comparison focuses on the pressure drop and convective heat transfer at very low Reynolds numbers and a wide range of high temperatures. The comparison shows that the YADE geometric model gives results that are in good agreement with the digitized packed-sand model in the range of Reynolds numbers considered, which, given the cost and time saving of using a mathematical model, is an extremely useful result. The geometric model was also used to explore the influence of particle size variation and temperature dependence of air properties affects the flow and convective exchange at temperatures relevant to smouldering combustion. A correlation is presented to demonstrate how the heat transfer results can be put into a compact form for use in computations using a porous continuum approach.

A DNS study of flow and heat transfer through slender fixed-bed reactors randomly packed with spherical particles

A fully resolved direct numerical simulation of flow and heat transfer is presented for slender randomly packed bed reactors. The flow and temperature field are solved over a non-body fitted, non-conformal Cartesian computational domain. The coupling between fluid and solid (both spherical particles and cylindrical wall) is enforced by a second order accurate, sharp interface immersed boundary method (IBM). The present numerical technique neither requires any challenging volumetric mesh generation process nor demands manipulation of the geometry near the particle-particle and particle-wall contact points. Conjugate heat transfer has been considered where the temperature field is calculated both inside the solid particles and in the fluid. A discrete element method (DEM) is used to generate the random packings of spherical particles in the cylindrical column, and a methodology is proposed to calculate the radial porosity profile of the bed.The column-to-particle diameter ratio (N) is varied from 4 to 8, and two separate cases have been considered where N→∞. The particle Reynolds number (Red) is varied from 1 to 500. The numerically obtained pressure drop and overall wall-to-bed heat transfer coefficient for different simulation cases are critically compared with empirical correlations and a good agreement is reported. Moreover, based on the current numerical results, correlations are proposed for the pressure drop and the wall-to-bed heat transfer coefficient. The effect of the column-to-particle diameter ratio (N) on both the flow and heat transfer, as-well-as the effect of the solid to fluid thermal conductivity ratio on the conjugate heat transfer are discussed. Furthermore, the fully resolved accurate numerical simulations have helped to elucidate the detailed pore-scale flow and heat transfer feature in the packed beds.

The random packing density of nearly spherical particles.

Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials. By leveraging existing understanding of the random packing of spherical particles, we estimate the random packing density for all sufficiently spherical shapes. Our method uses the ensemble of random packing configurations of spheres as a reference point for a perturbative calculation, which we carry to linear order in the deformation. A fully analytic calculation shows that all sufficiently spherical shapes pack more densely than spheres. Additionally, we use simulation data for spheres to calculate numerical estimates for nonspherical particles and compare these estimates to simulations.

Optimized Dropping and Rolling (ODR) method for packing of poly-disperse spheres

Powder-based microstructures are traditionally modelled using densely packed spherical particles. In this letter, a new dropping and rolling packing algorithm is employed by means of analytical equations, to investigate the random packing of spherical particles. The three-dimensional randomly packed microstructures are quantified in terms of packing density and computational time.

Numerical Simulation of Random Packing of Spherical Particles for Powder-Based Additive Manufacturing

Powder-based additive manufacturing is an efficient and rapid manufacturing technique because it allows fabrication of complex parts that are often unobtainable by traditional manufacturing processes. A better understanding of the packing structure of the powder is urgently needed for the powder-based additive manufacturing. In this study, the sequential addition packing algorithm is employed to investigate the random packing of spherical particles with and without shaking effect. The 3D random packing structures are demonstrated by illustrative pictures and quantified in terms of pair distribution function, coordination number, and packing density. The results are presented and discussed aiming to produce the desirable packing structures for powder-based additive manufacturing.

A High-Fidelity CFD Model of Methane Steam Reforming in a Packed Bed Reactor

A novel high-fidelity CFD model is proposed for the process optimization and intensification of methane steam reforming in a packed bed reactor. The random packing of spherical particles is constituted by simulating a dumping of particles into the annular reactor by a commercial code based on discrete element method (DEM). The complex spatial geometry between hundreds of particles is created associated with a developed interparticle bridge method, which eliminates the interparticle and particle–wall contact regions by assuming that the small regions are stagnant and would not affect the reactor behavior. The conservation equations of mass, momentum, energy and chemical species are fully solved by employing a commercial CFD code based on finite volume method. A newly coded subroutine is incorporated into the CFD code to evaluate the reaction rates according to the species partial pressures and temperature on each surface cell covering the particles. The values of reaction, equilibrium and adsorption constants are specified based on the experiments in the literature. According to the reaction rates, the mass and heat sources are given to each fluid cell on the surface cell. It is verified that the developed CFD model is capable of predicting the distributions of species and temperature microscopically as well as macroscopically for methane steam reforming. The present DEM–CFD procedure enables one to investigate the behavior of packed bed reactor in detail once the catalyst is characterized in a conventional way. Therefore it would become a powerful tool to optimize and intensify any process in a packed bed reactor where the plug flow assumption is invalid.

Simulation of random packing of spherical particles with different size distributions

A numerical model for a loose packing process of spherical particles is presented. The simulation model starts with randomly choosing a sphere according to a pregenerated continuous particle-size distribution, and then dropping the sphere into a dimension-specified box, and obtaining its final position by using dropping and rolling rules which are derived from a similar physical process of spheres dropping in the gravitational field to minimize its gravity potential. Effects of three different particle-size distributions on the packing structure were investigated. Analysis on the physical background of the powder-based manufacturing process is additionally applied to produce optimal packing parameters of bimodal and Gaussian distributions to improve the quality of the fabricated parts. The results showed that higher packing density can be obtained using bimodal size distribution with a particle-size ratio from 1.5 to 2.0 and the mixture composition around n 2:n 1=6:4. For particle size with a Gaussian distribution, the particle radii should be limited in a narrow range around 0.67 to 1.5.

Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation

Randomly packed fixed-bed reactors are widely used in the chemical process industries. Their design is usually based on pseudo-homogeneous model equations with averaged semi-empirical parameters. However, this design concept fails for low tube-to-particle diameter ratios (=aspect ratios) where local phenomena dominate. The complete three-dimensional (3D) structure of the packing has therefore to be considered in order to resolve the local inhomogeneities. New numerical methods and the increase of computational power allow us to simulate in detail single phase reacting flows in such reactors, exclusively based on material properties and the 3D description of the geometry, thus without the use of semi-empirical data. The successive simulation steps (packing generation, fluid flow and species calculation) and their validation with experimental data are described in this paper. In order to synthetically generate realistic random packings of spherical particles, we apply a Monte-Carlo method. The subsequent numerical simulation of the 3D flow field and coupled mass transport of reacting species is done by means of lattice Boltzmann methods. The simulation results reveal that not only the local behaviour but also integral quantities like the pressure drop depend remarkably on the local structural properties of the packings, a feature which is neglected when using correlations with averaged values.

Investigation of the Density Characteristics of Three-Dimensional Stochastic Packs of Spherical Particles Using a Computer Model

A series of computer experiments were performed to model the random packing of spherical particles. Known algorithms for dense packing were modified to optimize density characteristics. The distribution of local density in random packs of spherical particles was investigated. The effect of boundary conditions on the density characteristics was determined, and the dimensions of the boundary distorted zone evaluated. Methods for controlling the integral density and local density distribution in packs of spherical particles were determined. These are based on the concept of density characteristics as functions of the ratio of particle sizes and numbers in a fraction, and in a mixture.

Dynamic simulation of random packing of spherical particles

Kicked rotor is a paradigmatic model for classical and quantum chaos in time-dependent Hamiltonian systems. More than fifty years since the introduction of this model, there is an increase in the number of works that use kicked rotor model as a fundamental template to study a variety of questions in nonlinear dynamics, quantum chaos, condensed matter physics and quantum information. This is aided by the experimental approaches that have implemented many variants of the quantum kicked rotor model. The problems addressed using kicked rotor and its variants include the basic phenomenology of classical and quantum chaos, transport and localization in one- and higher dimensional kicked systems, effects of disorder and interactions, resonant dynamics and the relation between quantum correlations and chaos. This would also include a range of applications such as for constructing ratchet dynamics and for atom-optics based interferometry. This article reviews the current status of theoretical and experimental research devoted to exploring these ideas using the framework of kicked rotor model.

Simulated effect of box size and wall on porosity of random packings of spherical particles

Effects of the size of the box which spherical particles are deposited into on the porosity of a resulting particle aggregate have been simulated and examined, particularly to find out if the extrapolation method often used by experimenters is certainly right; this method is based on the empirical fact that the porosity is inversely proportional to the box size. The simulation justified the inverse proportionality and demonstrated that the porosity obtained by the simulated extrapolation coincides with that by the simulation with use of conventional cyclic boundary conditions. This coincidence implies the extrapolation gives the right experimental results of porosities and also that the conventional cyclic boundary condition method is a really strong method to construct a random packing of “infinite” extent by simulation. An effect of the box wall has also been explored in view of area porosisties and cumulative distribution of diameters of circles appearing on aggregate cross-sections. Furthermore, slopes of the straight line of the porosity versus ratio of the particle diameter to the box size have been discussed in terms of two statistical geometry models.

Dynamic simulation of random packing of spherical particles

A computer simulation for evolution of random structures of spherical particles in two dimensions (2D) has been performed by the distinct element method (DEM). The forces among the particles considered were gravity, contact force, friction force, and van der Waals interaction (VDWI). The motions of the particles considered were translation and rotation. Two-hundred-forty mono-sized spherical particles were located without overlapping inside a rigid square box by generating the coordinates of centers of the particles with the help of a random number generator. Initial packing density was only 0.4712. The particles were allowed to settle under gravity. When the coefficient of friction among the particles and between the particle and the wall of the box was 0.364, the packing density was 0.8236, which is comparable to the density of dense random packing. If there was no friction, the density was 0.8696. For small particles, VDWI was considered in the simulation. It has been found that VDWI can reduce the packing density through formation of local clusters. To study rearrangement of particles, some trajectories of a few selected particles were traced. The average coordination number of dense random packing of this simulation is similar to German's results [R.M. German, Particle Packing Characteristics, Princeton, NJ, 1989]. With the comparison, it is concluded that the DEM and the present program are valid methods for research in the behavior of random packing spheres.

Computer Simulation to Evaluate Effective Elastic Moduli of Sintered Spherical Particles : Examination of Simulation Technique by 2D Model

A simulation method has been proposed to estimate the effective elastic moduli of a porous elastic body made of sintered spherical particles by analyzing the response of a random network of springs with 6 degrees of freedom to uniform deformations ; the spring network is constructed by computer simulation of a three-dimensional random packing of spherical particles, whereas the spring constants of a pair of sintered particles are estimated by the FEM. In order to verify the proposed method, its two-dimensional version has been applied to an estimation of the effective Young modulus, and the specific procedures of the proposed method have been examined in detail.

Statistical treatment of the sintering defect model and ceramic morphology development

A model is formulated to account for structural and collective reorganization effects in a random packing of spherical particles which, during sintering, is undergoing global densification as a consequence of reduction of the total free surface energy. This model is found to describe, both qualitatively and quantitatively, the rearrangement of the stacking in such a way that areas with high local coordination tend to contract at a relatively high rate and zones with low coordination densify at a reduced rate or even decrease their density. Statistical effects arising from peculiarities in the particle packing can also be analysed with the help of the mathematical description given. It is found that the rearrangement may also give rise to structural defects and ultimately lead to poor mechanical properties.

Computer Simulation to Evaluate Effective Elastic Moduli of Sintered Spherical Particles. Examination of Simulation Technique by 2D Model.

A simulation method has been proposed to estimate the effective elastic moduli of sintered spherical particles by analyzing the response of a random network of springs with 6 degrees of freedom to uniform deformation ; the network is constructed by computer simulation of a 3D random packing of spherical particles, while the spring constants of a pair of sintered particles are estimated by FEM. In order to verify the validity of the proposed method, its 2D version has been applied to an estimation of the effective Young modulus, and its specific procedures have been examined in detail.

A micro-mechanical connection between the single-particle strength and the bulk strength of random packings of spherical particles

With a view to obtaining a fundamental insight into the attrition taking place in packings of spherical particles, a so-called distinct element method has been used to simulate numerically the bulk behaviour of brittle granular material as a function of the single-particle properties. This ‘computational physics’ approach has been confirmed to give a good simulation of the mechanical behaviour of particle assemblies on a micro-level by local photo-elastic stress and strain measurements. For our purpose, the single-particle Side Crushing Strength (SCS) distribution of the spheres under investigation was connected with the so-called Bulk Crushing Strength (BCS) and Shear Resistance (ShR) of the material. The simulation results for both the BCS and the ShR tests show a good agreement with actual experiments. In the BCS test, the influence of the interparticle friction coefficient is not very outspoken due to the fact that the particles hardly move with respect to one another during compression. In the ShR simulations, the interparticle friction coefficient strongly influences the amount of breakage due to the large amount of particle movement. In both types of test, the influence of shape and position of the input SCS-distribution can be easily evaluated, and is found to be considerable. It is concluded that the distinct element approach is a valuable tool in coupling single-particle and bulk-particle tests.