Mathematical modeling and simulations of stress mitigation by coating polycrystalline particles in lithium-ion batteries

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCo_(z)O_(2)(x≥0.8)(NMC)particles with poly(3,4-ethylenedioxythiophene)(PEDOT).The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion,and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport,promoting the lithium distribution across the secondary particles more homogeneously.Besides,the lower stiffness,higher ionic conductivity,and larger thickness of the coating layer improve the stress mitigation.This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels.

Numerical simulation of the sedimentation of cylindrical pollutant particles in fluid

The sedimentation of cylindrical pollutant particles which fall through a fluid is investigated. Differing from previous research work, particle oscillation and effect of particle on the fluid are considered, and the torque exerted on a particle when viscous fluid flow around a particle is got through experiment and included in the numerical simulation. The computational results showed that the sedimentation velocities of particle increase slowly with the increase of particle aspect ratio . For disk like particle, when the motion direction of particle is parallel to axis of particle, particle falls more slowly than the case of perpendicular to axis of particle; while for rod like particle, it is inverse. For sedimentation of a crowd of high frequency oscillating cylindrical particles with arbitrary initial orientation, both vertical velocity and horizontal velocity oscillate dramatically, the degree of oscillation of the former is stronger than the later. A crowd of particles fall more quickly than an isolated particle. Particles tend to strongly align in the direction of gravity. The computational results agreed well with the experimental ones and helpful for controlling of pollutant particles.

Numerical Simulation of Particle Concentration in a Gas Cyclone Separator

The particle concentration inside a cyclone separator at different operation parameters was simulated with the FLUENT software. The Advanced Reynolds Stress Model （ARSM） was used in gas phase turbulence modeling. Stochastic Particle Tracking Model （SPTM） and the Particle-Source-In-Cell （PSIC） method were adopted for particles computing. The interaction between particles and the gas phase was also taken into account. The numerical simulation results were in agreement with the experimental data. The simulation revealed that an unsteady spiral dust strand appeared near the cyclone wall and a non-axi-symmetrical dust ring appeared in the annular space and under the cover plate of the cyclone. There were two regions in the radial particle concentration distribution, in which particle concentration was low in the inner region （r/R≤0.75） and increased greatly in the outer region （r/R〉0.75）. Large particles generally had higher concentration in the near-wall region and small particles had higher concentration in the inner swirling flow region. The axial distribution of particle concentration in the inner swirling flow （r/R≤0.3） region showed that there existed serious fine particle entrainment within the height of 0.SD above the dust discharge port and a short-cut flow at a distance of about 0.25D below the entrance of the vortex finder. The dimensionless concentration in the high-concentration region increased obviously in the upper part of the cyclone separation space when inlet particle loading was large. With increasing gas temperature, the particle separation ability of the cyclone was obviously weakened.

Physical Simulation and Experimental Examination of ε-Cu Particles Dissolution Evolution During Welding of Copper Precipitation Strengthening Steel

The kinetics of ε-Cu particles dissolution in the matrix during welding of a copper-precipitation strengthening steel was determined by a combination of GleebleTM physical simulation, TEM examination and hardness meas urement. The ε-Cu particles underwent a coarsening and part dissolution and then complete dissolution reaction as the peak temperature increased from 750 to 1 000℃, which resulted in the decrease in the number density of ε-Cu particles and hardness in the heat affected zone （HAZ）. The results can be used to understand the evolution of this transformation and a softening behavior of the HAZ during welding of this type of steel.

Simulation of solute transportation within porous particles during the bioleaching process

A mathematical model, accounting for the sulfuric acid and ferric ions diffusion and the copper sulfide mineral leaching process, was developed for an ore particle by considering its porous structure. It was simulated with the simulation tool COMSOL Multiphysics. The simulation results show that the highest acid and ferric concentrations near the particle surface are apparent, while the concentrations in the central particle increase slightly as the less-porous ore core with low permeability prevents the oxidation from penetrating. The extraction of the mineral near the particle surface is the maximum, mainly because of ample sulfuric acid, ferric ions, bacteria, and oxygen available for the leaching process. Because of low oxidation concentration in the central part of the particle, the reaction rate and copper sulphide conversion are small. The simulation shows good agreement with the experimental results.

Numerical Simulation of Viscous Flow Through Spherical Particle Assemblage with the Modified Cell Model

The cell model developed since 1950s is a useful tool forexploring the behavior of particle assemblages, but it demandsfurther careful development of the outer boundary conditions so thatinteraction in a particle swarm is better represented. In this paper,the cell model and its development were reviewed, and themodifications of outer cell boundary conditions were suggested. Atthe cell outer boundary, the restriction of uniform liquid flow wasremoved in our simulation conducted in the reference frame fixed withthe particle.

Numerical Simulation of Gas Holdup Distribution in a Standard Rushton Stirred Tank Using Discrete Particle Method

The discrete particle method was used to simulate the distribution of gas holdup in a gas-liquid standard Rushton stirred tank. The gas phase was treated as a large number of bubbles and their trajectories were tracked with the results of motion equations. The two-way approach was performed to couple the interphase momentum exchange. The turbulent dispersion of bubbles with a size distribution was modeled using a stochastic tracking model, and the added mass force was involved to account for the effect of bubble acceleration on the surrounding fluid. The predicted gas holdup distribution showed that this method could give reasonable prediction comparable to the reported experimental data when the effect of turbulence was took into account in modification for drag coefficient.

Numerical simulation of predicting and reducing solid particle erosion of solid-liquid two-phase flow in a choke

Chokes are one of the most important components of downhole flow-control equipment. The particle erosion mathematical model, which considers particle-particle interaction, was established and used to simulate solid particle movement as well as particle erosion characteristics of the solid-liquid two-phase flow in a choke. The corresponding erosion reduction approach by setting ribs on the inner wall of the choke was advanced. This mathematical model includes three parts： the flow field simulation of the continuous carrier fluid by an Eulerian approach, the particle interaction simulation using the discrete particle hard sphere model by a Lagrangian approach and calculation of erosion rate using semiempirical correlations. The results show that particles accumulated in a narrow region from inlet to outlet of the choke and the dominating factor affecting particle motion is the fluid drag force. As a result, the optimization of rib geometrical parameters indicates that good anti-erosion performance can be achieved by four ribs, each of them with a height （H） of 3 mm and a width （B） of 5 mm equaling the interval between ribs （L）.

Numerical simulation of profile control by clay particles after polymer flooding

A three-dimensional,two-phase,five-component mathematical model has been developed to describe flow characteristics of clay particles and flocs in the profile control process,in which the clay particle suspension is injected into the formation to react with residual polymer.This model considers the reaction of clay particles with residual polymer,apparent viscosity of the mixture,retention of clay particles and flocs,as well as the decline in porosity and permeability caused by the retention of clay particles and flocs.A finite difference method is used to discretize the equation for each component in the model.The Runge-Kutta method is used to solve the polymer flow equation,and operator splitting algorithms are used to split the flow equation for clay particles into a hyperbolic equation for convection and a parabolic equation for diffusion,which effectively ensures excellent precision,high speed and good stability.The numerical simulation had been applied successfully in the 4-P1920 unit of the Lamadian Oilfield to forecast the blocking capacity of clay particle suspension and to optimize the injection parameters.

DEM simulation of particle flow on a single deck banana screen

A mathematical study of particle flow on a banana screen deck using the discrete element method (DEM) was presented in this paper. The motion characteristics and penetrating mechanisms of particles on the screen deck were studied. Effects of geometric parameters of screen deck on banana screening process were also investigated. The results show that when the values of inclination of discharge and increment of screen deck inclination are 10° and 5° respectively, the banana screening process get a good screening performance in the simulation. The relationship between screen deck length and screening efficiency was further confirmed. The conclusion that the screening efficiency will not significantly increase when the deck length L≥430 mm (L/B ≥ 3.5) was obtained, which can provide theoretical basis for the optimization of banana screen.

Direct Numerical Simulation of Particle Dispersion in Gas-Solid Compressible Turbulent Jets

A numerical method was developed to directly simulate the compressible, particle-laden turbulent jets.The fourth order compact finite difference schemes were used to discretize the space derivatives. The Lagrangian method was adopted to simulate the particle motion based on one-way coupling. It is found that the turbulent intensity profiles attain self-similar status in the jet downstream regions. At the Stokes number of 1, particles are concentrated largely in the outer boundaries of the large-scale vortex structures with the most uneven distribution and the widest dispersion in the lateral direction. Particles at the much smaller Stokes numbers are distributed evenly in the flow field, and the lateral dispersion is also considerable. Distribution of particles at much larger Stokes numbers is more uniform and the lateral dispersion becomes small. In addition, the inflow conditions have different effects on the particle dispersion. The direct numerical simulation (DNS) results accord with the previous experiments and numerical studies.

NUMERICAL SIMULATION OF THE TUBE EROSION RESULTED FROM PARTICLES IMPACTS

In this paper,a tube erosion caused by the turbulent flow of a dilute particle-laden gas isstudied numerically.Eulerian equations are used to describe the gas-phase motion with the turbulenceviscosity evaluated from a k-ε model of turbulence.The effect of the turbulence with a stochasticdispersion model has been taken into account for the prediction of impact particle velocity and itstrajectory,The particle impact and rebound model and the erosion model of ductile alloys obtainedby Tabakoff et al.are used to predict the particle rebound phenomena and the erosion suffered bythe tubes.The results obtained in this study include the distributions of particle collision frequencyand erosion of tube surface.

Effects of loading waveforms on rock damage using particle simulation method

The particle simulation method is used to study the effects of loading waveforms （i.e. square, sinusoidal and triangle waveforms） on rock damage at mesoscopic scale. Then some influencing factors on rock damage at the mesoscopic scale, such as loading frequency, stress amplitude, mean stress, confining pressure and loading sequence, are also investigated with sinusoidal waveform in detail. The related numerical results have demonstrated that： 1） the loading waveform has a certain effect on rock failure processes. The square waveform has the most damage within these waveforms, while the triangle waveform has less damage than sinusoidal waveform. In each cycle, the number of microscopic cracks increases in the loading stage, while it keeps nearly constant in the unloading stage. 2） The loading frequency, stress amplitude, mean stress, confining pressure and loading sequence have considerable effects on rock damage subjected to cyclic loading. The higher the loading frequency, stress amplitude and mean stress, the greater the damage the rock accumulated; in contrast, the lower the confining pressure, the greater the damage the rock has accumulated. 3） There is a threshold value of mean stress and stress amplitude, below which no further damage accumulated after the first few cycle loadings. 4） The high-to-low loading sequence has more damage than the low-to-high loading sequence, suggesting that the rock damage is loading-path dependent.

Pyrolysis of single large biomass particle: Simulation and experiments

Pyrolysis and heat transfer characteristics of single large biomass particle were investigated using threedimensional unsteady heat transfer model coupled with chemical reactions.The consumption of biomass and the production of products were simulated.Some experiments were designed to provide model parameters for simulation calculations.The simulation was verified by pyrolysis experiments of large biomass particle in a vertical tube furnace.The simulation results show the internal heat and mass transfer law during the pyrolysis of large biomass particle.When the biomass particle diameter is between 10 and 30 mm,for every 5 mm increase in particle diameter,the time required for complete pyrolysis will increase on average by about 50 s.When the pyrolysis temperature is between 673 K and 873 K,a slight decrease in the pyrolysis temperature will cause the time required for the biomass to fully pyrolyze to rise significantly.And the phenomenon is more obvious in the low temperature range.The results indicate that the numerical simulation agrees well with the experimental results.

Magnetic Field Improvement in End Region of Rectangular Planar DC Magnetron Based on Particle Simulation

For a rectangular planar direct current （DC） magnetron, anomalous target erosion may occur in the curve-out region and inner side of the curved region. One key factor is that the magnetic field in the end region is weaker than that in the straight region, and another important factor may be that there is a circumferential component of the magnetic field in the curved region. Through a calculation of three-dimensional magnetic field for the rectangular magnetron, a magnet structure shimmed by permanent magnet bars and ferromagnetic bars is proposed to solve the above problems. Through a three-dimensional non-self-consistent particle simulation and the Yamamura/Tawara formula, the target erosion profile could be predicted. The simulation results show that for an improved uniformity in magnetic field, the entire target utilization could be much enhanced.

Numerical simulation of the blocking process of gelled particles in porous media with remaining polymers

Gelled particles can be transferred deeply inside oil reservoirs to block water channels due to their physicochemical characteristics, including swelling, deformation, and synergetic effect （reacting with polymers）, and then the injection profiles are significantly modified. At present, research on gelled particles is mainly focused on laboratory studies of drive mechanisms, and rarely on mathematical models describing the blocking process of gelled particles. In this paper, the blocking process of gelled particles is divided into two sub-processes： deposition and desorption due to particle deformation. A mathematical model based on filtration theory is proposed considering the effect of characteristics of gelled particles on the blocking process. Blocking laws were simulated and researched using the mathematical model. Results of the simulation of the blocking of gelled particles are quite consistent with the experimental results, which confirms the reliability of the mathematical model developed.

NUMERICAL SIMULATION OF THREE DIMENSIONAL GAS-PARTICLE FLOW IN A SPIRAL CYCLONE

The three-dimension gas-particle flow in a spiral cyclone is simulated nu- merically in this paper. The gas flow field was obtained by solving the three-dimension Navier-Stokes equations with Reynolds Stress Model （RSM）. It is shown that there are two regions in the cyclone, the steadily tangential flow in the spiral channel and the combined vortex flow in the centre. Numerical results for particles trajectories show that the initial position of the particle at the inlet plane substantially affects its trajectory in the cyclone. The particle collection efficiency curves at different inlet velocities were obtained and the effects of inlet flow rate On the performance of the spiral cyclone were presented. Numerical results also show that the increase of flow rate leads to the increase of particles collection efficiency, but the pressure drop increases sharply.

Sample size adaptive strategy for time-dependent Monte Carlo particle transport simulation

When multiphysics coupling calculations contain time-dependent Monte Carlo particle transport simulations, these simulations often account for the largest part of the calculation time, which is insufferable in certain important cases. This study proposes an adaptive strategy for automatically adjusting the sample size to fulfil more reasonable simulations. This is realized based on an extension of the Shannon entropy concept and is essentially different from the popular methods in timeindependent Monte Carlo particle transport simulations, such as controlling the sample size according to the relative error of a target tally or by experience. The results of the two models show that this strategy can yield almost similar results while significantly reducing the calculation time. Considering the efficiency, the sample size should not be increased blindly if the efficiency cannot be enhanced further. The strategy proposed herein satisfies this requirement.

Computational modeling of free-surface slurry flow problems using particle simulation method

The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles.Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods,the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained.The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system.For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems,three examples involving slurry flow on three different types of river beds have been considered.The related particle simulation results obtained from these three examples have demonstrated that:1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields;2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed.

Dynamic Simulation of Shear-induced Particle Migration in a Two-dimensional Circular Couette Device

The shear-induced migration of neutrally-buoyant non-colloidal circular particles in a two-dimensional circular Couette flow is investigated numerically with a distributed Lagrange multiplier based fictitious domain method.The effects of inertia and volume fraction on the particle migration are examined.The results indicate that inertia has a negative effect on the particle migration.In consistence with the experimental observations,the rapid migration of particles near the inner cylinder at the early stage is observed in the simulation,which is believed to be related to the chain-like clustering of particles.The migration of circular particles in a plane Poiseuille flow is also examined in order to further confirm the effect of such clustering on the particle migration at early stage.There is tendency for the particles in the vicinity of outer cylinder in the Couette device to pack into concentric rings at late stage in case of high particle concentration.