Advances in numerical methods for the solution of population balance equations for disperse phase systems  

作　　者：SU JunWei1,GU ZhaoLin2,3 & XU X.Yun41 Department of Mechanical Engineering and Automation,School of Mechanical Engineering,Xi’an Jiaotong University,Xi’an 710049,China 2 Key Laboratory of Mechanics on Disaster and Environment in Western China,Ministry of Education,Lanzhou 730000,China 3 Department of Environmental Science and Technology,School of Human Settlements and Civil Engineering,Xi’an Jiaotong University,Xi’an 710049,China 4 Department of Chemical Engineering,Imperial College London,London SW7 2AZ,UK 

出　　处：《Science China Chemistry》2009年第8期1063-1079,共17页中国科学（化学英文版）

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

摘　　要：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.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.

关 键 词：population balance equation direct DISCRETIZATION METHOD MONTE Carlo METHOD MOMENT methods disperse PHASE system 

分 类 号：O241[理学—计算数学]