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.

Test particle simulations of resonant interactions between energetic electrons and discrete, multi-frequency artificial whistler waves in the plasmasphere

Modulated high frequency （HF） heating of the ionosphere provides a feasible means of artificially generating ex- tremely low frequency （ELF）/very low frequency （VLF） whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high energy electrons. Combining the ray tracing method and test particle simulations, we evaluate the effects of energetic electron resonant scattering driven by the discrete, multi-frequency arti- ficially generated ELF/VLF waves. The simulation results indicate a stochastic behavior of electrons and a linear profile of pitch angle and kinetic energy variations averaged over all test electrons. These features are similar to those associated with single-frequency waves. The computed local diffusion coefficients show that, although the momentum diffusion of relativistic electrons due to artificial ELF/VLF whistlers with a nominal amplitude of ~ 1 pT is minor, the pitch angle scattering can be notably efficient at low pitch angles near the loss cone, which supports the feasibility of artificial triggering of multi-frequency ELF/VLF whistler waves for the removal of high energy electrons from the magnetosphere. We also investigate the dependences of diffusion coefficients on the frequency interval （△f） of the discrete, multi-frequency waves. We find that there is a threshold value of Af for which the net diffusion coefficient of multi-frequency whistlers is inversely proportional to △f （proportional to the frequency components Nw） when △f is below the threshold value but it remains unchanged with increasing Af when △f is larger than the threshold value. This is explained as being due to the fact that the resonant scattering effect of broadband waves is the sum of the effects of each frequency in the ＇effective frequency band＇. Our results suggest that the modulation frequency of HF heating of the ionosphere can be appropriately selected with reasonable frequency intervals so that better performance of controlled precipitation of high energy electrons in the plasmasphere by artificial ELF/VLF whistler waves can be achieved.

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.

Validation of the current and pressure coupling schemes with nonlinear simulations of TAE and analysis on the linear stability of tearing mode in the presence of energetic particles

Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently.Numerical equivalences between these two coupling schemes are strictly verified under different approximations.First,when considering only the perturbed distribution function of energetic particles(EPs),the equivalence can be proved analytically.Second,when both the variations of the magnetic field and the EP distribution function are included,the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations.On this basis,the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n=2/1 tearing mode(TM)have been investigated(where m and n represent the poloidal and toroidal mode numbers,respectively).The results of scanningβh of EPs show that the co-passing and trapped EPs are found to stabilize the TM,while the counter-passing EPs tend to destabilize the TM.The behind(de)stabilization mechanisms of the TM by EPs are carefully analyzed.Furthermore,after exceeding critical EP betas,the same branch of the high-frequency mode is excited by co-/counterpassing and trapped EPs,which is identified as the m/n=2/1 energetic particle mode.

An efficient non-iterative smoothed particle hydrodynamics fluid simulation method with variable smoothing length

In classical smoothed particle hydrodynamics(SPH)fluid simulation approaches,the smoothing length of Lagrangian particles is typically constant.One major disadvantage is the lack of adaptiveness,which may compromise accuracy in fluid regions such as splashes and surfaces.Attempts to address this problem used variable smoothing lengths.Yet the existing methods are computationally complex and non-efficient,because the smoothing length is typically calculated using iterative optimization.Here,we propose an efficient non-iterative SPH fluid simulation method with variable smoothing length(VSLSPH).VSLSPH correlates the smoothing length to the density change,and adaptively adjusts the smoothing length of particles with high accuracy and low computational cost,enabling large time steps.Our experimental results demonstrate the advantages of the VSLSPH approach in terms of its simulation accuracy and efficiency.

Study of deep transportation and plugging performance of deformable gel particles in porous media

Deformable gel particles(DGPs) possess the capability of deep profile control and flooding. However, the deep migration behavior and plugging mechanism along their path remain unclear. Breakage, an inevitable phenomenon during particle migration, significantly impacts the deep plugging effect. Due to the complexity of the process, few studies have been conducted on this subject. In this paper, we conducted DGP flow experiments using a physical model of a multi-point sandpack under various injection rates and particle sizes. Particle size and concentration tests were performed at each measurement point to investigate the transportation behavior of particles in the deep part of the reservoir. The residual resistance coefficient and concentration changes along the porous media were combined to analyze the plugging performance of DGPs. Furthermore, the particle breakage along their path was revealed by analyzing the changes in particle size along the way. A mathematical model of breakage and concentration changes along the path was established. The results showed that the passage after breakage is a significant migration behavior of particles in porous media. The particles were reduced to less than half of their initial size at the front of the porous media. Breakage is an essential reason for the continuous decreases in particle concentration, size, and residual resistance coefficient. However, the particles can remain in porous media after breakage and play a significant role in deep plugging. Higher injection rates or larger particle sizes resulted in faster breakage along the injection direction, higher degrees of breakage, and faster decreases in residual resistance coefficient along the path. These conditions also led to a weaker deep plugging ability. Smaller particles were more evenly retained along the path, but more particles flowed out of the porous media, resulting in a poor deep plugging effect. The particle size is a function of particle size before injection, transport distance, and different injection parameters(injection rate or the diameter ratio of DGP to throat). Likewise, the particle concentration is a function of initial concentration, transport distance, and different injection parameters. These models can be utilized to optimize particle injection parameters, thereby achieving the goal of fine-tuning oil displacement.

Effect of Ellipsoidal Particle Shape on Tribological Properties of Lubricants Containing Nanoparticles

Adding nanoparticles can significantly improve the tribological properties of lubricants.However,there is a lack of understanding regarding the influence of nanoparticle shape on lubrication performance.In this work,the influence of diamond nanoparticles(DNPs)on the tribological properties of lubricants is investigated through friction experiments.Additionally,the friction characteristics of lubricants regarding ellipsoidal particle shape are investigated using molecular dynamics(MD)simulations.The results show that DNPs can drastically lower the lubricant's friction coefficientμfrom 0.21 to 0.117.The shearing process reveals that as the aspect ratio(α)of the nanoparticles approaches 1.0,the friction performance improves,and wear on the wall diminishes.At the same time,the shape of the nanoparticles tends to be spherical.When 0.85≤α≤1.0,rolling is ellipsoidal particles'main form of motion,and the friction force changes according to a periodic sinusoidal law.In the range of 0.80≤α<0.85,ellipsoidal particles primarily exhibit sliding as the dominant movement mode.Asαdecreases within this range,the friction force progressively increases.The friction coefficientμcalculated through MD simulation is 0.128,which is consistent with the experimental data.

Influence of syngas components and ash particles on the radiative heat transfer in a radiant syngas cooler

Radiant syngas cooler(RSC)is widely used as a waste heat recovery equipment in industrial gasification.In this work,an RSC with radiation screens is established and the impact of gaseous radiative property models,gas components,and ash particles on heat transfer is investigated by the numerical simulation method.Considering the syngas components and the pressure environment of the RSC,a modified weighted-sum-of-gray-gases model was developed.The modified model shows high accuracy in validation.In computational fluid dynamics simulation,the calculated steam production is only 0.63%in error with the industrial data.Compared with Smith's model,the temperature decay along the axial direction calculated by the modified model is faster.Syngas components are of great significance to heat recovery capacity,especially when the absorbing gas fraction is less than 10%.After considering the influence of particles,the outlet temperature and the proportion of radiative heat transfer are less affected,but the difference in steam output reaches 2.7 t·h^(-1).The particle deposition on the wall greatly reduces the heat recovery performance of an RSC.

Particle size spatial distribution in landslide dams

The particle composition and spatial distribution of landslide-induced dam bodies are critical geotechnical parameters for studying the hazards of dam-break floods.However,current research often neglects the influence of the initial particle composition and spatial distribution of the landslide on the particle composition and spatial distribution of the landslide dam.This study investigated the impact of initial particle size distribution,volume,and sliding length on the energy and velocity changes of characteristic particles during the sliding process and the spatial distribution of particle sizes in the landslide dam body.Numerical simulations and physical models were employed to examine the effects of sequential gradient arrangements(where particle sizes decrease from top to bottom)and four other different initial particle arrangements on the energy and velocity changes of particles and the spatial distribution of particle sizes in the dam body.The study reveals the characteristics of translational and rotational energy of different particles and the laws of mechanical energy conversion,obtaining the spatial distribution patterns of particle sizes in landslide-induced dams.The results show that under the sequential gradient arrangement,the energy dissipation of the landslide movement is lower,with larger particles mainly distributed at the distal end and smaller particles at the proximal end of the landslide dam.In contrast,under the reverse gradient arrangement,the energy dissipation of the landslide movement is higher,and the distribution pattern of the dam particles is opposite to that of the sequential gradient arrangement.For the other arrangement modes,the spatial distribution of dam particles falls between the aforementioned two.There is a positive correlation between particle size and translational kinetic energy within the particle flow during the landslide process,and rotational motion increases energy dissipation.Under constant slope conditions,sliding length does not affect the movement pattern of the particle flow or the spatial distribution of particles in the dam body.The findings of this study provide a scientific basis for the accurate simulation and prediction of dam-break flood processes.

Modeling analysis of cobalt-based Fischer-Tropsch catalyst particles

The influences of particle size,shape,and catalyst distribution on the reactivity and hydrocarbon product selectivity of a cobalt-based catalyst for Fischer-Tropsch synthesis were investigated in the present work.A self-consistent kinetic model for Fischer-Tropsch reaction proposed here was found to correlate experimental data well and hence was used to describe the consumption rates of reactants and formation rates of hydrocarbon products.The perturbed-chain statistical associating fluid theory equation of state was used to describe vapor-liquid equilibrium behavior associated with Fischer-Tropsch reaction.Local interaction between intraparticle diffusion and Fischer-Tropsch reaction was investigated in detail.Results showed that in order to avoid the adverse influence of intraparticle diffusional limitations on catalyst reactivity and product selectivity,the use of small particles is necessary.Large eggshell spherical particles are shown to keep the original catalyst reactivity and enhance the selectivity of heavy hydrocarbon products.The suitable layer thickness for a spherical particle with a diameter of 2 mm is nearly 0.15 mm.With the same outer diameter of 2 mm,the catalyst reactivity and heavy product selectivity of hollow cylindrical particles with a layer thickness of 0.25 mm are found to be larger than eggshell spherical particles.From the viewpoint of catalytic performance,hollow cylindrical particles are a better choice for industrial applications.

Location and Capacity Determination Method of Electric Vehicle Charging Station Based on Simulated Annealing Immune Particle Swarm Optimization

As the number of electric vehicles(EVs)continues to grow and the demand for charging infrastructure is also increasing,how to improve the charging infrastructure has become a bottleneck restricting the development of EVs.In other words,reasonably planning the location and capacity of charging stations is important for development of the EV industry and the safe and stable operation of the power system.Considering the construction and maintenance of the charging station,the distribution network loss of the charging station,and the economic loss on the user side of the EV,this paper takes the node and capacity of charging station planning as control variables and the minimum cost of system comprehensive planning as objective function,and thus proposes a location and capacity planning model for the EV charging station.Based on the problems of low efficiency and insufficient global optimization ability of the current algorithm,the simulated annealing immune particle swarm optimization algorithm(SA-IPSO)is adopted in this paper.The simulated annealing algorithm is used in the global update of the particle swarm optimization(PSO),and the immune mechanism is introduced to participate in the iterative update of the particles,so as to improve the speed and efficiency of PSO.Voronoi diagram is used to divide service area of the charging station,and a joint solution process of Voronoi diagram and SA-IPSO is proposed.By example analysis,the results show that the optimal solution corresponding to the optimisation method proposed in this paper has a low overall cost,while the average charging waiting time is only 1.8 min and the charging pile utilisation rate is 75.5%.The simulation comparison verifies that the improved algorithm improves the operational efficiency by 18.1%and basically does not fall into local convergence.

Refinement of Adaptive Dynamical Simulation of Quantum Mechanical Double Slit Interference Phenomenon

We applied adaptive dynamics to double slit interference phenomenon using particle model and obtained partial successful results in our previous report. The patterns qualitatively corresponded well with experiments. Several properties such as concave single slit pattern and large influence of slight displacement of the emission position were different from the experimental results. In this study we tried other slit conditions and obtained consistent patterns with experiments. We do not claim that the adaptive dynamics is the principle of quantum mechanics, but the present results support the probability of adaptive dynamics as the candidate of the basis of quantum mechanics. We discuss the advantages of the adaptive dynamical view for foundations of quantum mechanics.

Cascade refrigeration system synthesis based on hybrid simulated annealing and particle swarm optimization algorithm

Cascade refrigeration system(CRS)can meet a wider range of refrigeration temperature requirements and is more energy efficient than single-refrigerant refrigeration system,making it more widely used in low-temperature industry processes.The synthesis of a CRS with simultaneous consideration of heat integration between refrigerant and process streams is challenging but promising for significant cost saving and reduction of carbon emission.This study presented a stochastic optimization method for the synthesis of CRS.An MINLP model was formulated based on the superstructure developed for the CRS,and an optimization framework was proposed,where simulated annealing algorithm was used to evolve the numbers of pressure/temperature levels for all sub-refrigeration systems,and particle swarm optimization algorithm was employed to optimize the continuous variables.The effectiveness of the proposed methodology was verified by a case study of CRS optimization in an ethylene plant with 21.89%the total annual cost saving.

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）.