The Analysis And Applications Of Taylor-series Expansion Method Of Moments In Aerosol Dynamics

The general dynamic equation (GDE) forms a general mathematical framework for describing the particle dynamical evolution under all kinds of processes (i.e., coagulation, growth, diffusion, transport and so on) in a wide range of energy, atmospheric environment, Chemical, and pharmacy. Therefore, there are important scientific values and practical significance to study this equation. Among all of the numerical methods, the moment method has become a powerful tool for investigating aerosol microphysical processes in most cases for its low computational cost, and the most difficult is the closure of the moment equations. Recently, a new moment method called as the Taylor-series expansion method of moments (TEMOM) has been proposed and been recognized as a promising method for its relative simplicity of implementation, which could achieve the closure of moment equations by using Taylor-series expansion approximation without any other prior assumption of particle size distribution. Using this method, we mainly study the evolution process of Brownian coagulation, laminar shear coagulation, diffusion and transport.A simple introduction of TEMOM is firstly given in the second chapter, and then some fundamental problems of this model for particle Brownian coagulation in the free molecule and continuum regime have been clarified, such as the uniqueness of the expansion, the effectiveness of the closuring fractional moments, the choice of the expansion point, the error of the high-order moment equations and the inverse problems. Moreover, a bimodal Taylor-series expansion method of moments is proposed to deal with Brownian coagulation in the continuum-slip regime, where the nonlinear terms in the Cunningham correction factor is approximated by Taylor-series expansion technology. The results show that the asymptotic behavior of the larger mode is as same as that in the continuum regime.In the third chapter, the analytical solutions of particle coagulation due to Brownian motion in the free molecule and continuum regime and the asymptotic solution in the transition regime is derived based on the TEMOM. The results show that the coagulation rate in the transition regime is the highest, and its asymptotic behavior is consistient with that in the continuum regime. Using the same derivations, the solutions for particle agglomeration can be also gotten, and the results show that the aggregate growth rate increases with decreasing fractal dimension of the colliding particles.The fourth chapter is to study the particle evolution in the Poiseuille flow and 2D compressible viscous flow, in which particle Brownian coagulation, laminar shear coagulation, diffusion and convection exits simultaneously. If only the Brownian coagulation and diffusion are considerd, the value of Mq in the neighborhood of the interface between the particle laden and particle free domain will be greater than that in other places for a larger Peclet or Damkohler number. The results also show that the flow structure palys a significant role in the process of particle evolution when the particle phase is dilute and the effect of particles on the fluid can be ignored.Lastly, an exact solution is developed to predict the single-fiber interception efficiency of spherical micron particles carried by a potential flow over a circular-arc fibrous filter, in which case interception and inertial impaction play a major role at normal temperatures and pressures and diffusion is ignored. It is shown that the interception efficiency is a function of three parameters:the arc shape parameter, the flow-approaching angle, and the particle size. The results show that slim and long arc fibers have higher interception efficiency. The interception efficiency increases as the particle diameter increases. The orientation angle also affects the interception efficiency, but when the arc is close to a circle, the interception efficiency approaches a limited value independent of the flow orientation angle. The results demonstrate the importance of flow asymmetry and singular points on the interception efficiency.Overall, this work is a summary and development about the TEMOM model. In this dissertation, we have derived some analytical and asymptotic solutions of this model, and simulated the particle evolution in the Poiseuille flow and 2D compressible viscous flow, including Brownian coagulation, laminar shear coagulation, diffusion and convection simultaneously. Furthermore, a study on the particle capture is also been presented.