A numerical study of particle wall-deposition in a turbulent square duct flow

The deposition of dense solid particles in a downward, fully developed turbulent square duct flow at Re_τ = 360, based on the mean friction velocity and the duct width, is studied using large eddy simulations of the fluid flow. The fluid and the particulate phases are treated using Eulerian and Lagrangian approaches, respectively. A finite-volume based, second-order accurate fractional step scheme is used to integrate the incompressible form of the unsteady, three-dimensional, filtered Navier-Stokes equations on an 80 × 80 × 128 grid. A dynamic subgrid kinetic energy model is used to account for the unresolved scales. The Lagrangian particle equation of motion includes the drag, lift, and gravity forces and is integrated using the fourth-order accurate Runge-Kutta scheme. Two values of particle to fluid density ratio (ρ_p/ρ_f = 1000 and 8900) and five values of dimensionless particle diameter (d_p/δ × 10⁶ = 100, 250, 500, 1000 and 2000, δ is the duct width) are studied. Two particle number densities, consisting of 10⁵ and 1.5 × 10⁶ particles initially in the domain, are examined.Variations in the probability distribution function (PDF) of the particle deposition location with dimensionless particle response time, i.e. Stokes number, are presented. The deposition is seen to occur with greater probability near the center of the duct walls, than at the corners. The average streamwise and wall-normal deposition velocities of the particles increase with Stokes number, with their maxima occurring near the center of the duct wall. The computed deposition rates are compared to previously reported results for a circular pipe flow. It is observed that the deposition rates in a square duct are greater than those in a pipe flow, especially for the low Stokes number particles. Also, wall-deposition of the low Stokes number particles increases significantly by including the subgrid velocity fluctuations in computing the fluid forces on the particles. Two-way coupling and, to a greater extent, four-way coupling are seen to increase the deposition rates.     

Ammonium phosphate slurry rheology and particle properties—The influence of Fe(III) and Al(III) impurities, solid concentration and degree of neutralization

Ammonium phosphate slurries are produced from impure phosphoric acid that contains Fe(III), Al(III) and Mg(II) ions. The insolubility of these metal ions and the onset of solid formation determined as a function of pH or mole ratio (MR) of ammonia to phosphoric acid were consistent with the trend for the pH of formation of the first hydrolysis product that decreases in the following order: Fe(III)<Al(III)<Mg(II). The hydrolysis products of Fe(III) formed at pH>2.0 or MR>0.5 initiate ammonium phosphate crystallization, reduce the size of particles formed and generate attractive interparticle forces. Similarly, the Al(III) hydrolysis products formed later at pH>2.6 MR>0.7), will also initiate further crystallization, adsorb on particles and produce attractive forces. The attractive forces and the high number concentration of particle—particle interactions are responsible for the increased viscosity and non-Newtonian flow behavior displayed at increasing Fe(III) and Al(III) concentration. Mg(II) ions are not hydrolyzed at MR<1.0 so its effect on rheology is negligible and its effect at MR<1.0 is also small as its concentration is much smaller than that of Fe(III) and Al(III) ions. The change in slurry viscosity with the degree of neutralization is also explained in terms of particle size distribution, solubility and solids concentration variations.     

Production of finely ground natural graphite particles with high electrical conductivity by controlling the grinding atmosphere

Natural graphite particles with high crystallinity sieved to obtain a particle size range of under 63 μm were ground with a ball mill, under various well-controlled grinding atmospheres such as N₂, O₂, He, H₂, and vacuum. The ratio, X_dif50/X_st50, i.e. between the 50 wt.% Stokes diameter and the 50 wt.% laser diffraction diameter, of the ground particles, was used as an index of the flakiness of the particles. The specific resistance of films composed of the ground graphite particles was systematically measured. The rate of reduction in the size of the particles by grinding was slow under an O₂-rich atmosphere such as 100% O₂ and dry air. On the other hand, it was relatively fast in vacuum, or under an N₂ or He atmosphere, and a gas mixture of 99% N₂ and 1% O₂. The rate of size reduction by grinding under a H₂ atmosphere was intermediate. In our experimental conditions, the flakiness of the ground particles increased with the decrease in the particles’ sizes. The electrical conductivity of the ground particles, however, tended to decrease with the decrease in their sizes. Under the condition that the Stokes diameter of the ground particles remains constant, the electrical conductivity of films made from the ground particles increases with the increase in the flakiness of the particles. It was finally determined from our systematic grinding experiments that small flaky particles, which had a size, X_st of ∼1 μm, with a high electrical conductivity can be produced by grinding in a gas mixture of 99% N₂ and 1% O₂. In this case, the flaky shape of the ground particles was visually confirmed by scanning electron microscopy.     

Nanocoating individual cohesive boron nitride particles in a fluidized bed by ALD

Experiments are conducted with alumina (Al₂O₃) deposition on a wide size range of hexagonal boron nitride (BN) platelet-like particles. Successful deposition of alumina films on these particles, with film thickness controllable at the Angstrom level, is observed based upon TEM imaging, ICP-AES, particle size distributions, and surface area analysis. While fluidizing, fine BN particles aggregate in the bed. The aggregates are the entities fluidizing, not the primary particles. However, individual particles are coated using Atomic Layer Deposition (ALD), not aggregates. Since ALD is a surface chemistry phenomenon, the films grow uniformly on every primary particle. BN particles are small platelets with different functional groups on the basal planes and edge planes. A small exposure to reagents [2.5×10⁶ Langmuir (L) per reagent per cycle], will only coat the edge planes of uncoated BN particles. A larger dose of 1×10⁸ L will coat the entire uncoated BN particle (edge and basal planes). After 10 ALD cycles of the 1×10⁸ L dose, the exposures can be reduced to 1×10⁶ L as the film is then growing on alumina and not BN. Peel strength data indicate that adhesion between the coated particles and a cured epoxy in a filled composite is ∼25% stronger than that of uncoated particles and the epoxy. The overall thermal conductivity drops ∼17% for an identical filler loading as expected due to the additional thermal resistance added by the film. However, the viscosity of an epoxy resin loaded with coated BN is as much as five times lower than that of the resin loaded with the same amount of uncoated BN. These results indicate that the loading of Al₂O₃ nanocoated BN particles in an epoxy matrix can be substantially increased relative to that of uncoated particles. The thermal conductivity of the more highly filled composite will be increased without adversely impacting filled resin viscosity or the peel strength of the cured material. This is the first reported study indicating that cohesive primary particles that fluidize as aggregates in a fluidized bed can be individually coated with a nano-thick ceramic film using ALD.     

Experimental investigation of particle contact time at the wall of gas fluidized beds

The contact time of particles at the walls of gas fluidized beds has been studied using a radioactive particle tracking technique to monitor the position of a radioactive tracer. The solids used were sand or FCC particles fluidized by air at room temperature and atmospheric pressure at various superficial velocities, covering both bubbling and turbulent regimes of fluidization. Based on the analysis of tracer positions, the motion of individual particles near the walls of the fluidized bed was studied. The contact time, contact distance and contact frequency of the particles at the wall were evaluated from these experimental data. It was found that in a bed of sand particles, the mean wall contact time of the fluidized bed of sand particles decreases by increasing the gas velocity in the bubbling and increases in the turbulent fluidization. In other words, the particle-wall contact time is minimum at the onset of turbulent fluidization in the bed of sand particles. However, the mean wall contact time is almost constant in both regimes of fluidization in the bed of FCC particles. All the existing models in the literature predict a decreasing contact time when the gas velocity in the bed is increased. It was also shown that the contact distance increases monotonously by increasing the gas velocity in the bed of sand particles, while it is almost constant for the bed of FCC particles. Contact frequency has a trend similar to that of the contact time for both sand and FCC particles.     

Computationally efficient solution of population balance models incorporating nucleation, growth and coagulation: application to emulsion polymerization

A computationally efficient solution technique is presented for population balance models accounting for nucleation, growth and coagulation (aggregation) (with extensions for breakage). In contrast to earlier techniques, this technique is not based on approximating the population balance equation, but is based on employing individual rates of nucleation, growth and coagulation to update the PSD in a hierarchical framework. The method is comprised of two steps. The first step is the calculation of the rates of nucleation, growth and coagulation by solving an appropriate system of equations. This information is then used in the second step to update the PSD. The method effectively decomposes the fast and the slow kinetics, thereby eliminating the stiffness in the solution. In solving the coagulation kernel, a semi-analytical solution strategy is adapted, which substantially reduces the computational requirement, but also ensures the consistency of properties such as the number and mass of particles.     

Numerical analysis of particle mixing in a rotating fluidized bed

This paper describes the numerical analysis of particle mixing in a rotating fluidized bed (RFB). A two-dimensional discrete element method (DEM) and computational fluid dynamics (CFD) coupling model were proposed to analyze the radial particle mixing in the RFB. Spherical polyethylene particles (Geldart group B particles) were used as model particles under the assumptions that they were cohesionless and mono-disperse with their diameter of 0.5 mm.The validity of the proposed model was confirmed by the comparison between the calculated degree of particle mixing and the experimental one, which was obtained by measuring the lightness of the recorded image taken by a high-speed video camera. Effects of the operating parameters (gas velocity, centrifugal acceleration, particle bed height, and vessel radius) on the radial particle mixing rate were numerically analyzed. The radial particle mixing rate was found to be strongly affected by the bubble characteristics, especially by the bubble size. The mathematical model for the rate coefficient of particle mixing as functions of operating parameters was empirically proposed. The radial particle mixing rate in a RFB could be well correlated by the three dimensionless numbers: dimensionless acceleration (Ac), bubble Froude number (Fr_b), and dimensionless radius on the surface of particle bed (β_s).     

Atomization of metal fluorides for enhanced flow characteristics of a multicomponent powder

The National Aeronautics and Space Administration's (NASA's) PS304 coating is a plasma spray deposited tribological coating with feedstock composed of NiCr, Cr₂O₃, Ag and BaF₂-CaF₂ powders. The effects of rounded BaF₂-CaF₂ particles on the gravity-fed flow characteristics of PS304 feedstock have been investigated. The BaF₂-CaF₂ powder was fabricated by water atomization using four sets of process parameters. Each of these powders was then characterized by microscopy and classified by screening to obtain 45-106 μm particles and added incrementally from 0-10 wt.% to the other constituents of the PS304 feedstock, namely nichrome, chromia and silver powders. The relationship between feedstock flow rate, measured with the Hall flowmeter, and concentration of fluorides was found to be linear in each case. The slopes of the lines were between those of the linear relationships previously reported using angular and spherical fluorides and were closer to the relationship predicted using the rule of mixtures. The results offer a fluoride fabrication technique potentially more cost-effective than gas atomization processes or traditional comminution processes.     

一种信息点多样性的粒子群优化算法

针对PSO在寻优后期尤其在高维搜索空间中无法得到满意结果,提出了一种信息点多样性的改进粒子群优化算法。粒子个体最优位置及全局粒子最优位置是两个有用的精确的信息点,而PSO的信息交互方式正依赖于这两个信息点,从多样性方面考虑,将该有用的信息点增加为粒子个体最优位置附近随机的一点。实验仿真结果表明,新算法的全局搜索能力、收敛速度、精度和稳定性均有了显著提高。     

桁架结构形状优化的粒子群优化算法

为解决有应力约束、几何约束以及局部稳定性约束的桁架结构的形状优化设计,将粒子群优化(PSO)算法应用于桁架结构的形状优化设计.首先详细介绍了原始PSO算法的基本原理,然后引入压缩因子改进了原始的PSO算法,并提出了合理的参数设置值.优化计算过程中,综合考虑了节点坐标和截面面积等两类不同性质的设计变量.最后对几个经典问题进行了求解,并与传统的优化算法进行了比较.数值结果表明,改进的PSO算法具有良好的收敛性和稳定性,可以有效地进行桁架结构的形状优化设计.