Recently,metal powders have been conceptualized as carbon-free recyclable energy carriers that may form a cornerstone of a sustainable energy economy.The combustion of metal dusts in oxidizing atmospheres is exotherma...Recently,metal powders have been conceptualized as carbon-free recyclable energy carriers that may form a cornerstone of a sustainable energy economy.The combustion of metal dusts in oxidizing atmospheres is exothermal and yields oxide particles that could,potentially,be retrieved and,subsequently,recharged by conversion to pure metals using green primary energy sources.As a step towards a predictive tool for designing metal dust combustors,we present a fully Eulerian modelling approach for laminar particle-laden reactive flows that is,conceptually,based on a population balance description of the dispersed particles and relies on a stochastic Eulerian solution strategy.While the population balance equation(PBE)is formulated for the number-weighted distribution of characteristic properties among all particles near a spatial location,it is kinetically informed by the rates at which mass,momentum and heat are exchanged between the carrier gas and the particulate phase on the single particle level.Within the scope of the Eulerian Monte Carlo solution scheme,the property distribution is discretely represented in terms of the total number density and a finite number of property samples and the computational work is channelled towards the Eulerian estimation of mean particle properties.For the case of reactive aluminum particles,we combine a kinetic description of the gas-particle heat and mass transfer with a transport-limited continuum formulation to obtain rate expressions that are valid across the entire particle size range from the free molecular through the continuum regime.Besides velocity,the particle properties include only the particle mass,temperature and oxide mass fraction.This set of thermochemical degrees of freedom is retained also as phase transitions due to melting occur,drawing on a smooth blend of the solid and liquid thermodynamic and material properties.The particle-level formulation encompasses aluminum evaporation,surface oxidation,scavenging of oxide smoke,oxide evaporation/dissociation and radiation.After investigating how these effects translate,through the PBE,to the particle population level and affect the combustion in a homogeneous dust reactor,we analyze the combustion of an aluminum dust in a counterflow flame and validate predictions of the particles’centerline velocity profile and the flame speed by comparison with available experimental data.Concomitantly,nitrogen oxide emissions are investigated along with the particle burnout and outlet size distribution.展开更多
Previous work （Hussain et al. （2013）. Chemical Engineering Science, 101, 35） has pointed out that the conventional, one-dimensional population balance equation for aggregation can be expanded to accurately reprodu...Previous work （Hussain et al. （2013）. Chemical Engineering Science, 101, 35） has pointed out that the conventional, one-dimensional population balance equation for aggregation can be expanded to accurately reproduce the results of discrete simulations of spray fluidized bed agglomeration. However, some parameters had to be imported from the discrete simulation （Monte-Carlo）. The present paper shows how the expanded population balance can be run without importing parameters from the Monte-Carlo simulation. The expanded population balance still reproduces the results of Monte-Carlo simulations accurately, taking into account key micro-scale phenomena （sessile droplet drying, efficiency of collisions）, but with much lower computational cost. Required input parameters are just the drying time of sessile droplets （calculated in advance）, and the prefactor of an equation that correlates particle collision frequency with fluidized bed expansion. In this way, the expanded population balance is, apart from autonomous, also （nearly） predictive. Its performance is demonstrated by comparisons with both Monte-Carlo results and experimental data for various operating conditions （binder mass flow rate, gas temperature）. Despite formally being a one-dimensional expression, the expanded population balance captures additional properties, such as the number of wet particles and the number of droplets in the system, which are even difficult to measure in exoeriments.展开更多
Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system.A population balance equation(PBE),a non-linear hyperbolic equation o...Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system.A population balance equation(PBE),a non-linear hyperbolic equation of the number density function,is usually employed to describe the micro-behavior(aggregation,breakage,growth,etc.) of a disperse phase and its effect on particle size distribution.Numerical solution is the only choice in most cases.In this paper,three different numerical methods(direct discretization methods,Monte Carlo methods,and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation,computational load and numerical accuracy.Special attention is paid to the relatively new and superior moment methods including quadrature method of moments(QMOM),direct quadrature method of moments(DQMOM),modified quadrature method of moments(M-QMOM),adaptive direct quadrature method of moments(ADQMOM),fixed pivot quadrature method of moments(FPQMOM),moving particle ensemble method(MPEM) and local fixed pivot quadrature method of moments(LFPQMOM).The prospects of these methods are discussed in the final section,based on their individual merits and current state of development of the field.展开更多
Monte Carlo(MC)方法作为一种求解颗粒群平衡方程(PBE)的有效方法(PBMC),由于它对多维问题的适应性、符合实际颗粒动力学特征的离散和随机本质、程序结构相对简单、易于编程实现等优点受到人们持久、普遍的关注.但在涉及到颗粒凝并问题...Monte Carlo(MC)方法作为一种求解颗粒群平衡方程(PBE)的有效方法(PBMC),由于它对多维问题的适应性、符合实际颗粒动力学特征的离散和随机本质、程序结构相对简单、易于编程实现等优点受到人们持久、普遍的关注.但在涉及到颗粒凝并问题时,常规的PBMC方法计算代价较高,与模拟颗粒数目的平方成正比,限制了其工程应用.并行计算技术的快速发展,特别是近年来NVIDIA公司提出的计算统一设备架构(CUDA)为PBMC的快速高效模拟提供了一个良好的平台.本文在CUDA平台上实现了颗粒凝并动力学PBMC的图形处理器(GPU)并行计算(分别实现了累计概率法和接受-拒绝法选择凝并对)及中央处理器(CPU)的协同处理,与目前广泛运行于CPU的串行计算相比,取得了精确的计算结果和非常明显的加速,计算代价仅与颗粒数目成正比,在当前主流GPU/CPU设备上能够达到上百倍的加速比.展开更多
基金funded by the Deutsche Forschungsgemeinschaft(DFG,German Research Foundation)with in the scope of the Emmy Noether Program(Project number 443546539).
文摘Recently,metal powders have been conceptualized as carbon-free recyclable energy carriers that may form a cornerstone of a sustainable energy economy.The combustion of metal dusts in oxidizing atmospheres is exothermal and yields oxide particles that could,potentially,be retrieved and,subsequently,recharged by conversion to pure metals using green primary energy sources.As a step towards a predictive tool for designing metal dust combustors,we present a fully Eulerian modelling approach for laminar particle-laden reactive flows that is,conceptually,based on a population balance description of the dispersed particles and relies on a stochastic Eulerian solution strategy.While the population balance equation(PBE)is formulated for the number-weighted distribution of characteristic properties among all particles near a spatial location,it is kinetically informed by the rates at which mass,momentum and heat are exchanged between the carrier gas and the particulate phase on the single particle level.Within the scope of the Eulerian Monte Carlo solution scheme,the property distribution is discretely represented in terms of the total number density and a finite number of property samples and the computational work is channelled towards the Eulerian estimation of mean particle properties.For the case of reactive aluminum particles,we combine a kinetic description of the gas-particle heat and mass transfer with a transport-limited continuum formulation to obtain rate expressions that are valid across the entire particle size range from the free molecular through the continuum regime.Besides velocity,the particle properties include only the particle mass,temperature and oxide mass fraction.This set of thermochemical degrees of freedom is retained also as phase transitions due to melting occur,drawing on a smooth blend of the solid and liquid thermodynamic and material properties.The particle-level formulation encompasses aluminum evaporation,surface oxidation,scavenging of oxide smoke,oxide evaporation/dissociation and radiation.After investigating how these effects translate,through the PBE,to the particle population level and affect the combustion in a homogeneous dust reactor,we analyze the combustion of an aluminum dust in a counterflow flame and validate predictions of the particles’centerline velocity profile and the flame speed by comparison with available experimental data.Concomitantly,nitrogen oxide emissions are investigated along with the particle burnout and outlet size distribution.
基金financial support provided by the German Science Foundation(DFG) within the framework of graduate school GRK-1554by the Alexander von Humboldt Foundation(research fellowship for Jitendra Kumar)
文摘Previous work （Hussain et al. （2013）. Chemical Engineering Science, 101, 35） has pointed out that the conventional, one-dimensional population balance equation for aggregation can be expanded to accurately reproduce the results of discrete simulations of spray fluidized bed agglomeration. However, some parameters had to be imported from the discrete simulation （Monte-Carlo）. The present paper shows how the expanded population balance can be run without importing parameters from the Monte-Carlo simulation. The expanded population balance still reproduces the results of Monte-Carlo simulations accurately, taking into account key micro-scale phenomena （sessile droplet drying, efficiency of collisions）, but with much lower computational cost. Required input parameters are just the drying time of sessile droplets （calculated in advance）, and the prefactor of an equation that correlates particle collision frequency with fluidized bed expansion. In this way, the expanded population balance is, apart from autonomous, also （nearly） predictive. Its performance is demonstrated by comparisons with both Monte-Carlo results and experimental data for various operating conditions （binder mass flow rate, gas temperature）. Despite formally being a one-dimensional expression, the expanded population balance captures additional properties, such as the number of wet particles and the number of droplets in the system, which are even difficult to measure in exoeriments.
基金Supported by the National Basic Research Program of China (Grant No. 2004CB720208)the National Natural Science Foundation of China (Grant Nos. 40675011 & 10872159)the Key Laboratory of Mechanics on Disaster and Environment in Western China
文摘Accurate prediction of the evolution of particle size distribution is critical to determining the dynamic flow structure of a disperse phase system.A population balance equation(PBE),a non-linear hyperbolic equation of the number density function,is usually employed to describe the micro-behavior(aggregation,breakage,growth,etc.) of a disperse phase and its effect on particle size distribution.Numerical solution is the only choice in most cases.In this paper,three different numerical methods(direct discretization methods,Monte Carlo methods,and moment methods) for the solution of a PBE are evaluated with regard to their ease of implementation,computational load and numerical accuracy.Special attention is paid to the relatively new and superior moment methods including quadrature method of moments(QMOM),direct quadrature method of moments(DQMOM),modified quadrature method of moments(M-QMOM),adaptive direct quadrature method of moments(ADQMOM),fixed pivot quadrature method of moments(FPQMOM),moving particle ensemble method(MPEM) and local fixed pivot quadrature method of moments(LFPQMOM).The prospects of these methods are discussed in the final section,based on their individual merits and current state of development of the field.
