Moment-Distribution Coupling Method For Population Balance Modeling And Its Applications

Particle size distributions are very important for characterizing the physicochemical properties of aerosols.Generally,the time evolution of the particle size distribution can be described by population balance equation(PBE)or general dynamic equation.The highly nonlinear,partial integral-differential characteristics of the PBE bring great challenges to the solution of this equation.Thus,it is of great theoretical and practical significance to study the numerical solution of the PBE.Among the several major numerical methods,the method of moments(MOM)has high computational efficiency and has been widely used in engineering applications.Although the existing moment methods can give good predictions for the moments,they have difficulties in predicting the particle size distribution,which limits further applications of the moment methods.Due to the problem of existing moment methods in predicting the particle size distribution,the purpose of this dissertation is to develop a moment-distribution coupling methodology to achieve fast and reliable predictions of the particle size distribution from the viewpoint of moment methods.The basic idea is to couple the solution of moment equations with a certain particle size distribution function.First,this dissertation started from the classical log-normal method of moments(LNMOM),extended it to the general case,and then established the general model of the moment-distribution coupling method.Meanwhile,the LNMOM was used to analytically solve the simultaneous Brownian and shear coagulation in the continuum regime and thermophoretic coagulation in the low Knudsen number limit.In addition,the evolution characteristics of the two coagulation problems were deeply analyzed.Then this dissertation revealed that the classical LNMOM is unable to describe asymmetric distributions during particle coagulation.To solve this problem,the log skew normal method of moments(LSNMOM)was proposed based on the log skew normal distribution function.Among the several moment methods,the LSNMOM has the highest accuracy in predicting the distribution parameters and gives good predictions for the self-preserving distribution.Moreover,the computational efficiency of the LSNMOM is close to that of the quadrature based method of moments.Based on the proposed LSNMOM,the coagulation behaviors of graphite dust particles in high temperature gas-cooled reactors(HTGRs)were analyzed under large temperature gradients.An enhancement factor was defined to quantify the thermophoretic enhancement effects on coagulation rates.The time evolution of the graphite dust size distribution was calculated under various HTGR conditions and the results revealed the importance of thermophoretic coagulation in HTGRs.Finally,a multi-modal moment method was proposed to resolve the multi-modal size distribution during simultaneous nucleation,coagulation and surface growth.This method can give reliable predictions for the initial unimodal distribution and the transition from unimodal to multi-modal distributions.Based on the multi-modal moment method,the dynamic problem of flame synthesis of Ti O₂ nanoparticles was simulated.The simulation results are in good consistency with the results of the discretized population balance method.The analysis showed that increasing the flame synthesis temperature and the molar fraction of Ti Cl₄ can greatly accelerate the growth of Ti O₂ nanoparticles.