Analytical solutions for steady and unsteady state particle size distributions in FBC and CFBC boilers for non-breaking char particles

Continuous analytical solutions for the particle size distributions of char in steady and unsteady states in fluidized beds, when the inlet fuel feed is presented by monosize, lognormal, Rosin-Rammler or gamma distributions, are derived from a population balance model. The stationary size distribution is directly related to the rate of reduction of the particle size. Combustion and attrition reduce the particle size. Thus, it is possible to extract the dependence of the rate of reduction of radius (affected by a fuel’s reactivity and attrition) on radius from a measured steady-state particle size distribution. Unsteady particle size distributions are derived for impulse, step and square pulse changes in the fuel feed, when the oxygen level in the reactor is maintained constant.     

循环流化床锅炉传热数学模型研究

在国内外研究的基础上,结合环－核结构的流动模型建立了循环流化床锅炉的传热数学模型。利用该模型对循环流化床锅炉的对流、辐射传热特性进行了仿真研究,并对结果进行分析。仿真结果表明,循环流化床锅炉的对流传热系数与截面平均颗粒体积份额有密切关系,而辐射传热系数与环形区内温度密切相关;循环流化床锅炉辐射传热占总传热的份额随炉膛高度的增加而增大．     

微粒群算法反演粒径分布的研究

本文根据多波长下的Mie光散射理论及Lambert-Beer光透射定律,提出一种基于多相微粒群算法(PSO)反演粒子系粒径分布的有效方法.对于独立模式和非独立模式下的粒子粒径分布进行了反演计算,获得了合理的粒径分布.     

Modeling of particulate carbon and species formation in coflowing diffusion flames of ethylene

A model of species and particulate formation in laminar diffusion flames is presented. The kinetic model is based on the chemistry of fuel oxidation and pyrolysis, the formation of aromatics and their growth into particle nuclei, particle growth by surface reactions, coagulation, and finally particle oxidation. A sectional model is used for the particle phase. The sectional method divides the particle mass range into classes of species each with a rate equation for surface growth, coagulation, and oxidation. An inception model links the gas-phase mechanism with the smallest particle section. Predictions are compared with experimental data in two laminar coflowing diffusion flames of ethylene for which experimental profiles of stable species, aromatic compounds, high-molecular-mass precursor species, and soot are available. The predictions show good agreement with data for total particulates, defined as the sum of soot plus nano-organic carbon particles. The model has a continuous size distribution and is able to address nanoparticles which comprise a significant part of the total particle loading. A conclusion from the sensitivity analysis is that the inception process, the molecular growth process by aromatic addition on particle nuclei, and surface addition of C₂H₂ all play important roles which need to be studied in greater detail to predict the right size distribution and volume fraction of particulates formed in flames.     

Coupling a stochastic soot population balance to gas-phase chemistry using operator splitting

The feasibility of coupling a stochastic soot algorithm to a deterministic gas-phase chemistry solver is investigated for homogeneous combusting systems. A second-order splitting technique was used to decouple the particle population and gas phase in order to solve. A numerical convergence study is presented that demonstrates convergence with splitting step size and particle count for a batch reactor and a perfectly stirred reactor. Simulation results are presented alongside experimental data for a plug flow reactor (PFR) and are compared to a method of moments simulation of a perfectly stirred reactor. Coupling of the soot and chemistry solvers is shown to converge for both systems; however, numerical instabilities present significant challenges in the PSR case. Comparison with the experimental data for a PFR showed good agreement of the soot mass and reasonable agreement of the particle size distribution. Two different soot particle models were used to simulate the PFR: a spherical particle model and a surface-volume model that takes some account of particle shape. The results for the two models are compared. Additionally, the stochastic soot solver is used to track the evolution of the C/H ratio of individual soot particles in the PFR for the first time.     

Random-packing model for solid oxide fuel cell electrodes with particle size distributions

A percolation theory based model considering particle size and its distribution is proposed for composite electrodes of solid oxide fuel cells (SOFCs). The model calculation agrees excellently with 3D numerical reconstruction results, suggesting great validity of prediction. Moreover, it is also consistent well with experiment for real LSM (lanthanum strontium manganite)-YSZ (yttria-stabilized zirconia) electrodes with different composition, especially in range from 40:60 to 60:40 wt.% LSM:YSZ. The model can explicitly capture the effects of particle size, distribution, and electrode composition on several basic microstructure features and electrochemical properties of composite electrodes, such as coordination numbers and percolation probability, total and active three-phase boundary length, and interfacial polarization resistance. The model is further used to estimate LSM-YSZ electrode performance with the particle size and distribution of the source materials. The estimation generally coincides with the experiment, showing great potential in predicting power density based on the particle parameters of source materials for SOFCs.     

Thermal simulation of a single particle in a falling-particle solar receiver

A transient simulation of the heat transfer in a particle directly heated by the sun, in a falling-particle receiver, is presented. The local temperature can have a non-uniform distribution, that depends on many factors, such as the size of the particle, its rotation, and the exposition time. This fact should be considered when studying the material resistance and aging, or direct chemical reactions in the falling particle. The single-particle simulation presented here can be useful to test the validity of the global fluid dynamics simulations, to study single-particle related aspects such as aging, thermal stresses and chemical stability, to study the distribution of temperature if the particles are not uniform in size, or to study the efficiency in chemical applications.     

Models for metal hydride particle shape,packing, and heat transfer

A multiphysics modeling approach for heat conduction in metal hydride powders is presented, including particle shape distribution, size distribution, granular packing structure, and effective thermal conductivity. A statistical geometric model is presented that replicates features of particle size and shape distributions observed experimentally that result from cyclic hydride decrepitation. The quasi-static dense packing of a sample set of these particles is simulated via energy-based structural optimization methods. These particles jam (i.e., solidify) at a density (solid volume fraction) of 0.671 ± 0.009 – higher than prior experimental estimates. Effective thermal conductivity of the jammed system is simulated and found to follow the behavior predicted by granular effective medium theory. Finally, a theory is presented that links the properties of bi-porous cohesive powders to the present systems based on recent experimental observations of jammed packings of fine powder. This theory produces quantitative experimental agreement with metal hydride powders of various compositions.     

循环流化床锅炉炉内压降分布及物料粒径分布的计算

根据物料总体平衡建立了循环流化床锅炉炉内压降分布和物料粒径分布的数学模型 ,模型中考虑了颗粒破碎、磨损以及缩核对物料粒径分布变化的影响。作为循环流化床锅炉整体数学模型的基础 ,该模型不仅计算了所有物料的总体粒径分布 ,也计算了焦炭、石灰石和惰性床料单独的粒径分布。最后给出了炉内压降和不同位置处物料粒径分布的仿真结果 ,并对结果进行了分析     

循环流化床流动特性分析

基于循环流化床 ( CFB)的流动特性 ,提出了一个求解其流动结构的模型。模型综合考虑了床内粒子空间分布的轴向和径向不均匀性 ,可以预测各种运行条件下床内颗粒浓度分布情况 ,并能清楚地表示床的几何尺寸、运行工况对循环流化床流动特性的影响。     

Modeling of multiphase combustion and deposit formation in a biomass-fed furnace

A comprehensive computational model for biomass combustion is presented, featuring a solid phase combustion model, a fluid dynamic model for the gas phase, and a solid particle transport and deposit formation model. The submodel developed to track particle trajectories is briefly outlined. The model is implemented on the Finite Element code XENIOS++, and a test case is considered of a furnace burning wooden biomass chips added with water and inert material; a dedicated flamelet library is worked out to model combustion. Results underline the capability of the code to predict combustion conditions and, in particular, the growth rates of deposits of different particle size over the furnace walls, as well as the most critical locations for particle deposition.     

Study of the evolution of particle size distributions and its effects on the oxidation of pulverized coal

This paper discusses the factors influencing the evolution of particle size during the combustion of pulverized coal, as well as their consequences for the interpretation of burnout curves. A detailed experimental characterization of the evolution of the particle size distribution (PSD) of a pulverized coal (anthracite) burned under realistic conditions in an entrained flow reactor is presented and used as the reference data for the subsequent analysis. The data show evidence for particle fragmentation at relatively short times (or, equivalently, high unburnt fractions). The formation of fragments comparable in size to the parent coal/char particles is modeled with a simple fragmentation scheme, which results in an improved reproduction of the PSD's evolution. The effects of fragmentation on the burnout curves are then studied in detail. An enhancement of their curvature is observed, which results in a better fit of the experimental data; in particular, the high conversion range, where the largest discrepancies between predictions and measurements are usually found, is well reproduced with this “extended” model. Simultaneously, the increase of specific surface caused by particle fragmentation causes an increase in the conversion rate, and a smaller total conversion time. To fit the experimental data, new optimal kinetic parameters are calculated. Finally, the potential relevance of fragmentation in the simulation of industrial pf plants is discussed.     

燃用宽筛分煤循环流化床锅炉燃烧模拟计算

建立了循环流化床锅炉炉膛颗粒燃烧和脱硫反应模型。该模型考虑了炉膛下部为高颗粒浓度的密相区和上部为低颗粒浓度稀相区的特征,模拟计算给出了烟气温度,热流密度和各气体成分（Ｏ２,Ｃ２Ｏ,ＣＯ,Ｈ２Ｏ和Ｓ２Ｏ）的轴向分布,模拟计算结果的趋势是合理的。     

干熄炉料钟布料焦炭粒度分布的研究

对于干熄焦工艺,为了改善焦炭在干熄炉径向方向上的粒度偏析,采用料钟进行布料。采用实验和理论模拟相结合的分析方法,对布料焦炭在干熄炉预存段粒度偏析机理进行了研究。实验制作了冷态三维半圆料钟布料模型,考察了不同形状的料钟和不同的料线深度对焦炭粒度在干熄炉半径方向上分布的影响。所采用的理论模拟数学模型针对多尺度焦炭颗粒情况,用极少的参数来模拟半径平均尺度分布和每一种颗粒的半径堆积分布。研究结果表明,实验数据和数值分析结果吻合较好,相互验证了实验和理论模拟的正确性与可靠性。     

The evolution of mineral particle size distributions during early stages of coal combustion

Data are presented which illustrate the evolution of the particle size distribution (psd) of included mineral grains in coal particles during coal particle heatup and the early stages of combustion. The data indicate that pyrite fragments during its thermal decomposition to form pyrrhotite and oxides of iron. Two to three fragments are formed per original pyrite particle. The mineral psd for silica also significantly changes in the early residence time. The data indicate the production of many small particles, with diameters approximately 4–5 times smaller than the original particles. These results indicate that the original mineral grain size distribution in the coal is not a reliable indicator of the grain size distributions in the resultant char.     

凝并作用下火灾烟颗粒粒径分布及变化

预测火灾烟颗粒粒径分布特征参数的动态变化可实现探测系统对环境参数响应的动态模拟.顶棚烟气输运中,烟颗粒的布朗凝并是改变粒径分布的主要过程,应用矩方法求解布朗凝并作用下对数正态颗粒粒径分布的烟颗粒非线性凝并方程,得到随燃烧变化的凝并速率下粒径分布特征参数随时间的计算结果.正庚烷试验火烟颗粒分布的计算预测值与实验测量值相近,结果表明,在烟雾浓度快速上升阶段,烟颗粒凝并造成颗粒浓度损失不明显,几何平均粒径变化很小,而燃烧基本结束后,烟颗粒数密度衰减很快.     

Percolation micro-model to predict the effective properties of the composite electrode with poly-dispersed particle sizes

A percolation micro-model is developed to predict the effective properties of the composite electrode consisting of poly-dispersed electronic and ionic-conducting particles. The analytical expressions for the percolated triple-phase-boundary (TPB) lengths, hydraulic pore radius and intra/inter-particle conductivities have been formed. The model shows that the percolated TPB lengths of a composite electrode consisting of poly-dispersed particle sizes for both materials (i.e., having a normal distribution with a non-dimensional standard deviation of 0.4) are about 32% lower than that of the composite electrode with mono-sized particles. And the higher percolated TPB lengths can be achieved by reducing the mean particle size of each material and narrowing the particle size distribution. A composite cathode may benefit from it, because of its low electrochemical activity. The model also shows that the composite electrode with large mean particle size radii ratio between the electrode- and electrolyte-materials and broad particle size distributions can not only provide higher inter-particle ion conductivity, but also reduce the percolation volume fraction threshold of the electrode-material. And this may be helpful for a composite anode to obtain a higher overall ion conductivity.     

循环流化床锅炉脱硫整体精细模型的研究

针对现有循环流化床锅炉脱硫整体模型存在的问题，建立了一个用于流化床内固体颗粒特性研究的经过商业锅炉数据验证的脱硫整体精细模型。其建模方法能够将单个脱硫剂颗粒的脱硫过程、还原性分解过程和颗粒的磨耗与基础整体模型有机地结合起来，利用物质平衡方程计算得到锅炉不同位置处固体床料的成分、筛分分布和各个粒径脱硫剂的转化程度分布曲线。对变分离器效率、变给石灰石粒径分布、变一次风配比和给入旧脱硫剂的情况进行了份真计算。图20参8     

Distribution of mineral matter in pulverized coal

Mineral transformations, and therefore fly ash evolution, during pulverized coal combustion, depend on the amount, composition and spatial distribution of the inorganic matter within individual pulverized coal particles. Thus, it is necessary to have information on the mineral composition of individual particles, as well as that of the raw pulverized coal. A model is proposed based on the assumption that mineral inclusions of size and composition determined using a CCSEM are distributed randomly in the coal. From this distribution it is possible to generate distributions of mineral content for any particle size and density fraction of coal. The model has been checked by comparing computed results with data on the compositional variations of narrowly and density classified fractions of an Upper Freeport bituminous coal. The results of individual coal particle compositions are used to generate information on the variability of the composition of the fly ash generated during combustion.     

激光衍射粒子测试系统数学模型的研究

从激光衍射粒子测试系统的应用及其工作基本原理出发，系统阐述了激光衍射粒子测试系统在测量粒子尺寸分布中的计算方法。主要完成了抽样粒子尺寸段的划分、光能贡献矩阵元素求解的理论推导和实际的数学表达式的数学拟合，给出了表征粒子尺寸分布的数学模型，确定了系统求解过程中用到的求解病态或元素不确定矩阵的单纯形优化算法，从而为用激光衍射粒子测试系统测量柴油机中油雾粒子的尺寸分布打下了基础。