Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures

A new computational fluid-dynamic (CFD) model with a separate granular temperature (2/3 random particle kinetic energy per unit of mass) equation for each phase or particle size was developed using constitutive equations derived earlier by Huilin, Gidaspow and Manger. In agreement with the experiment and model of Mathiesen, Solberg and Hjertager the new model computes the observed core-annular flow regime. It predicts the trends of the observed radial and axial particle diameter distributions. For elastic particles the computed particle velocity distributions are parabolic. They are close to the laminar type approximate analytical solution for flow in a pipe, where the mean velocity equals the inlet flux divided by the particle density and volume fraction. The computed turbulent intensity is lower for large particles than for small particles, as measured. This is in agreement with an approximate analytical solution for the granular temperature in the developed flow region of a riser for elastic particles. Computations show that for sufficiently inelastic particles the granular temperature in the center can be lower than near the wall resembling the measured particle fluctuating velocity distribution.     

Contact of a spherical particle with a droplet

The collection of particles by liquid drops is profoundly influenced by the contact angle of the particles with the drops and the surface tension of the drops. The present investigation was undertaken to establish an equation with reference to the force which acts on a particle by surface tension after contact of a particle with a drop, and to simplify its solution. Moreover, the approximate equations obtained can be applied as regards the arbitrary contact angle of a particle with a drop and the arbitrary ratio of the radius of the drop to the particle. The agreement between theoretical and experimental values could be verified by this experiment.It is considered from these results that the approximate equations can be utilized when it is necessary to know the behaviour of a particle after contact with a liquid drop.     

Experimental equation on intensity of transmitted light through particle suspension of higher concentration

For a given medium and wave and path lengths of incident light, the relationship was experimentally investigated among the intensity of transmitted light, the suspension concentration of particles and the median size on particle volume basis. The numerical correlations were examined and an approximate equation was proposed over a wider range of concentrations up to about 3 vol.%. This expression was found to be valid not only for uniformly sized particles but also for mixtures of different particle sizes as compared with the previous equations for low concentration of particles of uniform size.     

Phenomenological theory of depth membrane filtration

A phenomenological theory of depth membrane filtration (DMF), in which outside-in hollow fiber membranes are used as collectors of colloidal particles, is developed to study the performance of a hollow fiber membrane filter with two product streams, permeate (clarified liquid that passed through semipermeable membrane) and filtrate (clarified liquid due to the collection of suspended particles on the external surface of hollow fibers). The theory is based on the general phenomenological expression for the rate of particle deposition on the membrane surface, in which the deposition rate is proportional to the product of the particle deposition coefficient and the concentration of suspended particles, with the deposition coefficient being an arbitrary function of the mass of deposited particles and permeate velocity. The system of governing equations is solved by the generalized Crank-Nicholson finite-difference method and the approximate method using the averaging of the permeate velocity in the mass conservation equation. The effect of membrane permeability on the filter productivity is studied. It is shown that the approximate solution can be used as a relatively simple and accurate tool to study and design hollow fiber filters for DMF.     

PTFE胶乳粒子与 Fe2O3粒子共凝聚过程的研究

以共凝聚体系Zeta电位为主要表征量,研究无凝聚剂存在时,几种因素对PTFE胶乳粒子与Fe2O3粒子共凝聚过程的影响。结果表明,两种粒子电荷相反．Zeta电位绝对值相近是较好的共凝聚条件,两种粒子的粒径比等于7．54时可形成形态规则的以PTFE为壳、Fe2O3为核的核壳型的粒子。     

Toughening of Ceramics by Circumferential Microcracking

An approximate analysis is presented of the toughening induced by the incorporation of second-phase particles subject to microcrack-ing. It is demonstrated that the toughening becomes appreciable for a narrow size distribution of particles of appropriate size. The magnitude of the toughening is determined by the mismatch strain (due to thermal contraction incompatibility) and the microfracture resistance of the particle/matrix interface. Implications for designing optimally tough ceramics are presented.     

考虑颗粒凝并情况下充分发展圆管湍流场中的纳米颗粒的迁移(英文)

Numerical simulations of nanoparticle migration in a fully developed turbulent pipe flow are performed.The evolution of particle number concentration,total particle mass,polydispersity,particle diameter and geometric standard deviation is obtained by using a moment method to approximate the particle general dynamic equation.The effects of Schmidt number and Damkhler number on the evolution of the particle parameters are analyzed.The results show that nanoparticles move to the pipe center.The particle number concentration and total particle mass are distributed non-uniformly along the radial direction.In an initially monodisperse particle field,the particle clusters with various sizes will be produced because of coagulation.As time progresses,the particle cluster diameter grows from an initial value at different rates depending on the radial position.The largest particle clusters are found in the pipe center.The particle cluster number concentration and total particle mass decrease with the increase of Schmidt number in the region near the pipe center,and the particles with lower Schmidt number are of many dif-ferent sizes,i.e.more polydispersity.The particle cluster diameter and geometric standard deviation increase with the increase of Damkhler number at the same radial position.The migration properties for nano-sized particles are different from that for micro-sized particles.     

Modeling of the scattering and radiative properties of nonspherical dust-like aerosols

The optical and radiative properties of dust particles in solar and thermal infrared regions are investigated. Dust particles are assumed to be spheres and spheroids for a comparison aimed at understanding the nonsphericity effect of these particles on the radiation at the top of a dusty atmosphere. The classical Lorenz–Mie theory is employed to compute the optical properties of spherical dust particles. To compute the single-scattering properties of spheroidal dust particles, a combination of the T-matrix method and an approximate method is used in the present study. In the approximate method, applicable to large particles, the geometric optics method is applied to the computation of the scattering phase matrix. A combination of the solution from the geometric optics method and the contribution of the so-called edge effect is used to compute the extinction efficiency of a spheroidal particle whose absorption efficiency is computed by adding the so-called above- and below-edge effect (a term from the well-known complex angular momentum theory) to the geometric optics result. Numerical results show that the results from the T-matrix method and the present approximate approach converge at a size parameter of 50 for computing the integrated scattering properties (i.e., the extinction efficiency, single-scattering albedo, and asymmetry factor). Additionally, the phase functions computed from the two methods are quite similar for size parameters larger than 40 although some considerable differences may still be noticed for other phase matrix elements. Furthermore, the effect of surface roughness on the single-scattering properties of spheroidal particles is discussed. The present radiative transfer simulations illustrate the nonsphericity effect of dust particles is significant at short wavelengths, however, not at the thermal infrared wavelengths.     

Probabilistic model of dispersed turbulent flow in channels with rough walls

Abstract

An equation for the probability density function (PDF) for particle velocity and coordinates in a gas turbulent flow is derived. The system of equations for the first and second moments of particle velocity fluctuations is obtained. Using a method similar to Grad’s method, an approximate solution of the PDF equation was found. Based on this approximate solution, the system of equations for the averaged concentration, velocity, and second moments of particle velocity fluctuations was closed. Also, using an approximate solution, the boundary conditions on the rough wall of the channel were obtained. The boundary conditions self-consistently take into account the direction of the velocity vector of particles colliding with the surface, as well as the direction of the normal to a random plane that simulates the roughness. The fundamental difference between the mechanisms of generation of random motion of particles in channels with smooth and rough walls is shown.

Copyright © 2020 American Association for Aerosol Research     

Prediction of the Size of Aluminum-Oxide Particles in Exhaust Plumes of Solid Rocket Motors

The processes of coagulation and aerodynamic fragmentation of liquid particles of aluminum oxide in an accelerating gas flow in the Laval nozzle are analyzed. A formula obtained by an approximate analytical solution of equations of a two-phase flow is proposed to calculate the characteristic particle diameter at the nozzle exit. The limiting particle diameter in the nozzle throat calculated theoretically is close to the mean-mass diameter obtained by numerical simulation of polydisperse two-phase flows with particle coagulation and fragmentation. The formula proposed is in agreement with Hermsen's correlation dependences and is confirmed by numerous published data on measurement of the mean-mass diameter of aluminum-oxide particles in exhaust plumes of small-, medium-, and large-scale solid rocket motors. The formula contains physical parameters whose values are readily calculated and prescribed. The formula is tested by all the parameters that enter into it. Based on a comparison of theoretical calculations and numerous experimental data, the formula is recommended for prediction of the size of aluminum-oxide particles in exhaust plumes of various types of solid rocket motors. Key words: rocket motor, two-phase flow, aluminum oxide, fragmentation of drops.     

Controlled Generation of Solid Spheroidal Dielectric Microparticles

Our recent research has been pioneering the generation of single solid particles with adjustable eccentricity. This new technique permits the production of particles in the range of 200 w m to 2 mm and an approximate eccentricity of 1:1.2 to 1:1.8 along an axis. Single droplets consisting of multiacrylate monomers were levitated by an ultrasonic levitator and were cured by UV illumination after adjusted eccentricity. For special applications we can produce particles that are attached to a stem (optical fiber), which allows a controlled orientation of the particle. One possible application for such particles is the investigation of light scattering on nonspherical particles.     

The Effects of Differential Diffusion on Nanoparticle Coagulation in Temporal Mixing Layers

The effects of size-independent diffusive transport on nanoparticle growth is studied by performing direct numerical simulation of nanoparticle coagulation in temporal mixing layers. The flow field is obtained by solving the incompressible Navier-Stokes equations, while the evolution of the particle field is obtained by using a nodal approach to approximate the aerosol general dynamic equation. Simulations are performed where particles diffuse according to their size and also where all particles have the same diffusivity. For the latter, the model assumes that all particles of different sizes have the same diffusivity as the smallest particles. The advantage of the second approach is the length scales that need to be resolved are larger, facilitating more affordable computations. Simulations are performed at two volume fractions to assess the effects of the models under different growth rates. The results indicate the use of size-independent diffusion coefficients predicts particle sizes and geometric standard deviations that are larger than those obtained with size-dependent diffusion coefficients.     

A new method for evaluating the size of moving particles with a fiber optic probe

The size of solid particles moving in an equipment can be measured simultaneously with the velocity of the particles by using a small optic fiber probe. The principle of the measurement is presented on the basis of the “characteristic length”, which is the product of the particle velocity and the width of the reflected light pulse detected when each particle is illuminated by the optic fiber.The relationship between the characteristic length and the diameter of a spherical particle can be determined from model calculation and is represented by an approximate equation. The experimental data for spherical glass beads were found to conform to the model calculation. All experimental data were correlated in terms of equations similar to those by model calculation.     

Study on the Dynamics of Tribocharged Coal and Mineral Particles in Free-Fall Triboelectric Separator

The dynamics of 2.0?0.8 mm or 0.8?0.5 mm size fraction of tribocharged organic coal, pyrite, and calcite particles were studied under the electric field using the high-speed dynamic camera combined with high-speed motion analysis system. Motion images of these particles were obtained and used to analyze their dynamic parameters. Organic coal particles tribocharged positively move to the negative plate, while pyrite and calcite particles reach the positive plate under the influence of electric force. These results indicate that the trajectories of all 2.0?0.8 mm particles are similar to parabolic curves. For 0.8?0.5 mm particles, the trajectories are approximate straight line, except for the calcite. The vertical velocities of all particles increase with a fluctuant acceleration as a result of gravity and drag force. The horizontal velocities of all particles vary slightly. The dynamics of 0.8?0.5 mm particles prove that size is very important for the triboelectric separation. The actions of electric force and drag force are increased with the decrease of particle size.     

Experiments with concentrated slurries of particles with densities near that of the carrier fluid

Experimental investigations of headlosses and particle velocity distributions have been undertaken for water slurries of polystyrene particles of diameter d₅₀ = 0.3 and 1.4 mm. At concentrations greater than 40–45% by volume, nearly linear headloss vs. velocity relationships were obtained. These suggested laminar flow but the particle velocity measurements showed the flow to be turbulent. The results have been interpreted with an approximate theory based upon lubrication mechanics. The investigation illustrates the limitations of slurry viscometry in predicting pipeline behaviour for slurries of particles of this size.     

基于MATLAB随机试验的砂细度模数公式优化研究

细度模数是衡量砂粗细程度的重要指标。当前国标细度模数公式未涉及粒级为0.15 mm以下的颗粒,本文将粒级0.15 mm以下颗粒进一步细分为0.075~0.15 mm粒级与0.075 mm以下粒级,将这两粒级纳入细度模数公式后形成了三个新的细度模数公式。通过MATLAB软件中rand函数随机大量生成四种不同细度模数试验,结合花岗岩机制砂、凝灰岩机制砂、天然砂的筛分试验进一步验证不同细度模数公式的优劣性,在筛分的同时即可测得机制砂近似石粉含量,将近似石粉含量与标准方法测得的石粉含量进行线性回归,可拟合出两者之间的经验公式。研究表明:原细度模数公式分子上增加0.075~0.15 mm粒级颗粒筛分含量后,更有利于表征砂的粗细程度。近似石粉含量与标准石粉含量差值为1.346 6%,经SEM对不同砂样表面放大100倍后,发现砂样表面越粗糙对石粉的吸附性越大,近似石粉含量与标准石粉含量差值的波动性也越大。     

Mathematical simulation of mass transfer processes under heterogeneous reactions in polydisperse porous media

Submitted is a theoretical study of mass transfer processes in polydisperse porous media in the presence of chemical reactions. Kinetic regime of methane pyrolysis in a porous carbon skeleton considering external and internal diffusion resistances for different initial distributions of particles forming the porous medium is investigated. Derived is a general analytical expression describing the influence of the inner reaction surface variation on the degree of the pore filling for an arbitrary initial particle size distribution. Expressions defining the time of pores filling by pyrocarbon based on approximate and exact solutions of the equation for the probability density function (PDF) of particle size distribution are received. Dependence of pore filling time on effective diffusion coefficient and initial particle size distribution using both solutions for PDF-equation is compared. It is shown, that the dominant factor influencing the pore filling time is the dispersion of particle size distribution.     

甲酸盐在纳米AgBr／I粒子乳剂中的增感作用

分别以鱼明胶和骨明胶(惰胶)作为分散介质制备了两种不同形貌与粒径的纳米AgBr／I粒子乳剂．利用掺入作为正空穴捕获剂的甲酸盐，可以使本征感光度很低的纳米粒子乳剂的感光度有相当大的提高，显示甲酸盐具有很好的增感效果．对鱼明胶介质中制备的纳米AgBr／I粒子乳剂，甲酸盐掺杂方式不同其增感效果不一样．在乳剂颗粒中均匀掺杂增感效果最好，而趋向于近表面掺杂则增感效果降低，显示出甲酸盐掺杂的位置效应．籽晶掺杂后包壳的复合结构乳剂颗粒与均匀掺杂乳剂颗粒的增感效果近似．对鱼明胶介质中制备的掺杂甲酸盐的纳米AgBr／I粒子乳剂再进行硫增感或硫加金增感，乳剂感光度可进一步提高，表明甲酸盐掺杂与常规的硫增感或硫加金增感有很好的协同作用．     

The Virtual Cyclone: A Device for Nonimpact Particle Separation

ABSTRACT

The virtual cyclone, a geometrically uncomplicated device that separates particles from a flow stream by nonimpact particle separation, is discussed. In contradistinction to a cyclone, the particle-laden flow is deflected from its original direction by a wall that curves away from the original flow direction, rather than into it. The computational fluid dynamics code FIDAP (Fluid Dynamics International) is used to perform two-dimensional fluid-flow and particle-motion calculations for a representative device geometry. Flow patterns are found to be insensitive to Reynolds number for values above 100 regardless of whether the flow is laminar or turbulent. Particle-motion calculations for laminar-flow cases indicate that the virtual cyclone geometry examined accomplishes nonimpact particle separation. An approximate analytical relation describing virtual cyclone nonimpact particle separation is developed and found to be in agreement with the numerical simulations.