A mathematical model of ash formation during pulverized coal combustion

A mathematical model of ash formation during high-rank pulverized coal combustion is reported in this paper. The model is based on the computer-controlled scanning electron microscope (CCSEM) characterization of minerals in pulverized coals. From the viewpoint of the association with coal carbon matrix, individual mineral grains present in coal particles can be classified as included or excluded minerals. Included minerals refer to those discrete mineral grains that are intimately surrounded by the carbon matrix. Excluded minerals are those liberated minerals not or at least associated with coal carbon matter. Included minerals and excluded minerals are treated separately in the model. Included minerals are assumed to randomly disperse between individual coal particles based on coal and mineral particle size distributions. A mechanism of partial-coalescence of included minerals within single coal particles is related to char particulate structures formed during devolatilization. Fragmentation of excluded minerals, which is important particularly for a coal with a significant fraction of excluded minerals, is simulated using a stochastic approach of Poisson distribution. A narrow-sized sample of an Australian bituminous coal was combusted in a drop-tube furnace under operating conditions similar to that in boilers. The particle size distribution and chemical composition of experimental ash were compared to those predicted with the model. The comparisons indicated that the model generally reflected the combined effect of coalescence of included minerals and fragmentation of excluded minerals, the two important mechanisms governing ash formation for high-rank coals.     

Zur Bewegung feiner Partikeln,die in turbulent strömenden Medien suspendiert sind

Motion of fine grained particles, suspended in turbulent flow . This article considers the motion of particles, suspended in turbulent flow. If the particles are sufficiently small to respond to turbulence, their motion includes stochastic components. Concerning processes like air classification or separation of fine powders the stochastic contribution – characterized by the conception of a particle diffusivity – the particle motion exhibits a detrimental influence. Sharpness of cut and separation efficiency are reduced. The paper aims to present the state of the art in particle diffusion. First, theoretical investigations are reported, attention being focused on the equation of motion of the particle which is the link between the motion of the fluid and the motion of the particle. Then, experimental results are reviewed. The following tendencies can be seen: Particles which response to turbulence of fluid flow show increasing diffusivity with increasing inertia. Field forces like gravity or electrical field forces exhibit a damping effect on diffusivity.     

A numerical study of fluidization behavior of Geldart A particles using a discrete particle model

This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid-particle interaction, the particle-particle collisions (and particle-wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid-particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.     

水力旋流器内非牛顿流体多相流场的数值模拟

利用一种非牛顿流体黏度修正模型描述水力旋流器内高浓度矿浆的非牛顿流动特性,并结合雷诺应力模型(RSM)、混合多相流模型(Mixture)以及拉格朗日颗粒追踪模型(LPT)建立了一种适用于模拟水力旋流器内非牛顿流体多相流场的数学模型。模拟结果与报道的实验值的相对误差均在10%以内,表明了该模型的可靠性。结果表明,非牛顿流体黏度的空间分布与矿浆密度的空间分布类似。沿零轴速包络面(LZVV)的轮廓存在一个高密度环,其原因为某粒径范围内的颗粒受到的径向合力为零,颗粒群沿LZVV做高速旋转运动。分散相的空间分布取决于不同粒径的颗粒受力。对于不同粒径的单位质量颗粒,向外离心力的数值大约为向内压力梯度力的两倍左右,使得大颗粒进入下行流并在底流口收集。随着颗粒粒径的减小,总体向内且具有波动性的流体曳力呈指数增长。向内的流体曳力将部分颗粒推向轴心,经上行流逃逸,同时也增强了颗粒运动的随机性。当颗粒粒径小于一定值后,流体曳力远远大于离心力和压力梯度力,颗粒运动的随机性非常强,宏观表现为均匀分布。     

Effect of Sub-Grid Scales on Large Eddy Simulation of Particle Deposition in a Turbulent Channel Flow

Large-eddy simulations (LES) of particle transport and deposition in turbulent channel flow were presented. Particular attention was given to the effect of subgrid scales on particle dispersion and deposition processes. A computational scheme for simulating the effect of subgrid scales (SGS) turbulence fluctuation on particle motion was developed and tested. Large-eddy simulation of Navier-Stokes equations using a finite volume method was used for finding instantaneous filtered fluid velocity fields of the continuous phase in the channel. Selective structure function model was used to account for the subgrid-scale Reynolds stresses. It was shown that the LES was capable of capturing the turbulence near wall coherent eddy structures.

The Lagrangian particle tracking approach was used and the transport and deposition of particles in the channel were analyzed. The drag, lift, Brownian, and gravity forces were included in the particle equation of motion. The Brownian force was simulated using a white noise stochastic process model. Effects of SGS of turbulence fluctuations on deposition rate of different size particles were studied. It was shown that the inclusion of the SGS turbulence fluctuations improves the model predictions for particle deposition rate especially for small particles. Effect of gravity on particle deposition was also investigated and it was shown that the gravity force in the stream wise direction increases the deposition rate of large particles.     

Probabilistic micromechanical model for two-dimensional slow particulate flow: Dry friction

This paper presents a probabilistic micromechanical model for the slow shearing motion of particulate systems dominated by inter-particle frictional forces. A particle can either slide, roll or jump relative to neighboring particles, or can be involved in a solid body rotation. The flow phenomenon is viewed as a Markov process in discrete time and continuous space. The relative position vector between a pair of neighboring particles is taken as the primary variable in the probabilistic approach. The physical constrains are implemented by considering the dynamic equilibrium of a particle interacting with its surrounding particles. The two-dimensional idealized motion of circular cylinders with negligible effects of the interstitial fluid is analyzed in detail in this paper. The macroscopic properties and rheological behavior are predicted starting from the material microstructure, which include the inter-particle friction laws, the number of contact points between particles and the local orientations of the relative position vector.     

Application of a modified Eulerian model to study the particle deposition on a vertical surface in turbulent flow

In this study the v2-f model was used with the two-phase Eulerian approach to predict the particle deposition rate on a vertical surface in a turbulent flow. The standard Eulerian particle model was adopted from the literature and modified, considering the majority of particle transport mechanisms in the particle deposition rate. The performance of the modified model was examined by comparing the rate of particle deposition on a vertical surface with the experimental and numerical data in a turbulent channel flow available in the literature. The model took into account the effects of drag force, lift force, turbophoretic force, electrostatic force, inertia force and Brownian/turbulent diffusion on the particle deposition rate. Electrostatic forces due to mirror charging and charged particles under the influence of an electric field were considered. The predictions of the modified particle model were in good agreement with the experimental data. It was observed that when both electrostatic forces are present they are the dominant factor in the deposition rate in a wider range of particle sizes.     

Effect of Interparticle Potentials and Sedimentation on Particle Packing Density of Bimodal Particle Distributions During Pressure Filtration

Effect of interparticle forces, bimodal particle size distribution, and slurry viscosity on particle packing in alumina bodies consolidated by pressure filtration is presented. The requirements for packing colloidal particles to their highest density are strong repulsive interparticle forces and optimum particle size distribution. Even though these conditions are met, the high packing density in consolidated bodies may be adversely affected by particle segregation resulting from sedimentation. Therefore, the slurry during consolidation must have a sufficiently high viscosity to prevent sedimentation.     

Transport analysis and model for the performance of an ultrasonically enhanced filtration process

This paper presents an analysis of a filtration technique that uses ultrasound to aid the collection of small particles (tens of microns in diameter) from suspension. In this method, particles are retained within a porous mesh that is subjected to a resonant ultrasonic field, even though the pore size of the mesh is two orders of magnitude greater than the particle diameter. The role of acoustic forces in driving the retention phenomena has previously been studied on a micro-scale, which included modeling and experimental verification of particle motion and trapping near a single element of the mesh. Here, we build on this work to develop an overall transport model to predict macroscopic performance criteria such as breakthrough times and the dynamics of the filtration performance. Results from this model compare favorably to experimental studies of the filtration phenomena; simulation results scale appropriately with experimental results in which inlet feed concentration and flow rate are varied.     

Particle Deposition in Parallel-Plate Reactors: Simultaneous Diffusion and External Forces

Particle deposition resulting from uniform external forces and Brownian motion is modeled in a parallel-plate reactor geometry characteristic of a wide range of semiconductor process tools: uniform, isothermal, downward flow exiting a perforated-plate showerhead separated by a small gap from a parallel, circular wafer. Particle transport is modeled using a Eulerian approach neglecting particle inertia and interception. Particles are assumed to originate in a planar trap located between the plates, such as would result for particles released from a plasma-induced particle trap after plasma extinction. Flow between infinite parallel plates is described by an analytic quasi-one-dimensional creeping flow approximation, where the showerhead is treated as a porous plate. An analytic, integral expression for particle collection efficiency (fraction of particles that end up on the wafer) is derived as a function of four dimensionless parameters: the flow Reynolds number, a dimensionless trap height, a dimensionless particle drift velocity, and the particle Peclet number. Numerical quadrature is used to calculate particle collection efficiency in terms of the controlling dimensionless parameters for external forces, which either enhance or inhibit particle deposition. Example calculations of collection efficiency are also presented in dimensional terms for a representative set of process conditions. Strategies to reduce particle deposition include the use of a protective external force and manipulation of the trap to keep it as far from the wafer as possible.     

Some Remarks on the Removal of Adhered Particles by Oscillating Air Flows

On the background of technical concepts for the removal of particles from moving textiles by linear as well as oscillating air flows, some theoretical remarks on particle adhesion forces and the hydrodynamical and acoustic forces acting on particles are given. As the main removal forces in linear air flows, drag and lift are taken into consideration and analytical expression derived from the Bernoulli equation. For a hypothetical example of particles in the size range from below 0.5 to 7 μm on a cotton fiber, hydrodynamic forces are compared to van der Waals interaction, electrostatic forces and capillary forces. In this work, a special focus is placed on the application of high-frequency oscillating air flows which results in a direct coupling of ultrasound to the particles. The theoretical calculation of resulting forces showed that the detachment threshold is determined not only by sound intensity level, but also by the frequency of the ultrasonic wave. If capillary forces act, the coupling of ultrasound alone does not suffice to detach particles within the considered size range.     

Adhesion-induced deformations of polyurethane substrates in contact with spherical glass particles: the effect of particle size on the radius of contact

Spherical glass particles having radii between approximately 0.5 and 100 *m were deposited onto a polyurethane substrate and the radii of contact, resulting from the adhesion forces between the particles and the substrate, were determined using SEM. For particles having radii less than approximately 5 μm, it was found that the contact radius varied as the particle radius to the 0.75 power. In addition, large menisci, presumably resulting from tensile interations, were observed. For particles having radii between 5 and 60 μm, the contact radius varied as the particle raidus to the 2/3 power. Stretching of the substrate was also observed for particles having radii of approximately 100 μm. This is probably a harbinger of the impending separation of the particle from the substrate, due to gravitational forces. The thermodynamic work of adhesion was calculated from the data and the results were compared with the predictions of several theories of particle adhesion.     

Radial particle mixing in gas-solids fluidized beds

Difficulties involved in experimentally determining the mixing coefficients of particles in a gas-solids fluidized bed are well known. From the theoretical point of view, the mechanism of particle mixing in such a fluidized bed is influenced profoundly by complicated and stochastic phenomena, such as jetting and bubbling. It appears that a sufficiently effective deterministic approach is not available to analyse the mechanism.In the present work, the particle mixing in the radial or lateral direction of a gas-solids fluidized bed was studied by using heated particles as the tracer particles. The transient concentration distribution of these particles in the lateral direction was obtained by means of an impulse response technique; sensitive thermocouples were used for measurement. The mixing coefficients of particles have been estimated from the distribution by a stochastic approach, and the resultant coefficients are compared with those obtained by other investigators.     

Particle Resuspension in Turbulent Flow: A Stochastic Model for Individual Soil Grains

A stochastic model for the motion of a particle initially at rest on a surface is explored. Fluid and adhesive forces are quantified based on first principles, and turbulent fluctuations are addressed probabilistically from probability distribution functions. A Monte Carlo process yields the distributions of particle position and velocity under a wide range of wind conditions and soil sizes. Results indicate that particle size and friction velocity are the most important factors in determining if a particle will resuspend and in predicting its subsequent motion. Larger wind speeds produce more violent fluctuations, which have a greater effect on small particles than on large particles. A theoretical analysis of the threshold friction velocity supports earlier experimental findings. The aerodynamic lift force cannot be neglected, and the torque exerted on a particle can be important in some cases. Applying the results of this work may contribute to reducing uncertainty in large-scale aerosol models.     

Detachment of rough particles with electrostatic attraction from surfaces in turbulent flows

The detachment of particles with coarse and fine roughnesses from surfaces in a turbulent boundary layer flow including electrostatic effects is studied. It is assumed that the real area of contact is determined by elastic deformation of asperities, and the effect of topographic properties of surfaces is included. The Johnson-Kendall-Roberts (JKR) adhesion model is used for analyzing the behavior of individual asperities. For an average Boltzmann charge distribution, the saturation charge condition as well as a fixed charge per unit mass, the Coulomb, the image, the dielectrophoretic, and the polarization forces acting on the particle in the presence of an imposed electric field are evaluated. The theories of rolling and sliding detachment are used to study the onset of removal of bumpy particles and those with fine roughness from plane surfaces. The hydrodynamic forces and torques acting on the particle attached to a wall, along with the adhesion force for the particle, are used in the model development. The minimum critical shear velocities needed to detach particles of different sizes from plane surfaces in the presence of an applied electric field are evaluated and discussed. The electric detachment of the particles is also studied and the field strength needed for particle removal is determined. It is shown that the surface charge distribution significantly affects the removal of particles from surfaces.     

The Factors Affecting the Particle Distributions Inside the Silane PCVD Reactor for Semiconductor Processing

The distributions of particles inside the silane plasma chemical vapor deposition (PCVD) reactor were theoretically investigated by analyzing the transport phenomena of particles for various plasma conditions. We included the effects of fluid convection, particle diffusion, and external forces (ion drag, electro static, and gravitational forces) onto the particles to analyze the movements of particles inside the plasma reactor. Initially, we assumed that the particles are uniformly distributed inside the plasma reactor and showed how these particles move and how they are distributed for various plasma conditions. The dominant force for the particle movement is the electrostatic force in the sheath region and the ion drag force in the bulk plasma region. Both the electrostatic and ion drag forces are towards the sheath boundaries and most of the particles are concentrated in the regions near the sheath boundaries by the balance of both forces, but the particle concentrations in the sheath region and in the bulk plasma region are almost 0. The particle concentrations at the down stream sheath boundary become higher than at the upstream sheath boundary by the effect of fluid convection. As the electric field strength increases, the particles are pushed more strongly towards the bulk plasma region and the peaks of particle concentrations are shifted more away from the electrodes. As the particle diameter increases from 0.1 mu m to 10 mu m, the relative importance of fluid convection on the particle movement becomes more significant than those of particle diffusion, ion drag force, and electrostatic force and the particle concentrations at the down stream sheath boundary increase, while those at the upstream sheath boundary decrease. It is found that the movements of negative ions as well as the positive ions are also important for determining the ion drag force onto the particles in silane PCVD.     

Micromechanic modeling and analysis of the flow regimes in horizontal pneumatic conveying

Pneumatic conveying is an important technology for industries to transport bulk materials from one location to another. Different flow regimes have been observed in such transportation processes, but the underlying fundamentals are not clear. This article presents a three‐dimensional (3‐D) numerical study of horizontal pneumatic conveying by a combined approach of discrete element model for particles and computational fluid dynamics for gas. This particle scale, micromechanic approach is verified by comparing the calculated and measured results in terms of particle flow pattern and gas pressure drop. It is shown that flow regimes usually encountered in horizontal pneumatic conveying, including slug flow, stratified flow, dispersed flow and transition flow between slug flow and stratified flow, and the corresponding phase diagram can be reproduced. The forces governing the behavior of particles, such as the particle–particle, particle‐fluid and particle‐wall forces, are then analyzed in detail. It is shown that the roles of these forces vary with flow regimes. A general phase diagram in terms of these forces is proposed to describe the flow regimes in horizontal pneumatic conveying. © 2011 American Institute of Chemical Engineers AIChE J, 2011