A Two-Dimensional Discrete-Sectional Model for Metal Aerosol Dynamics in a Flame

Abstract

Aerosol nucleation and growth in a laminar flame or a gas-phase reaction jet were considered in the free-molecular regime. A two-dimensional, axisymmetric, discrete-sectional model was developed based on a species equation. Parabolic conservation equations resulted from the formulation of the governing equations in boundary layer form, neglecting axial diffusion and axial thermophoretic velocities. The source terms of the equations included monomer formation by gas-phase chemical reaction, and growth or reduction by coagulation and condensation among all aerosol particles. A binomial expansion was used to approximate the collision rate. The equations were linearized by Newton's method and solved with a block tridiagonal solver. The results of the model exhibited reasonable agreement with an aerosol size distribution measured by dynamic light scattering. Spatial transport processes that could influence the aerosol dynamics included convection, diffusion, and thermophoresis. Their impact on the development of the aerosol and its distribution in the flame was investigated; thermophoresis was found to have the greatest impact on the spatial distribution of aerosol mass, although the amount of aerosol was not affected significantly. AEROSOL SCIENCE AND TECH

Bivariate Extension of the Quadrature Method of Moments for Modeling Simultaneous Coagulation and Sintering of Particle Populations

“…However, the intervening 35 years have seen unprecedented development in computational resources, along with the above-mentioned advances in the method of moments itself. In view of these developments, and the complexity of alternative simulation methods based on sectional discretization (see, e.g., [11][12][13][14][15], the feasibility of multivariate extensions of the MOM is ripe for reexamination.…”

“…The six diagonal elements of M are [12] where A i ≡ v i a i . The superdiagonal and subdiagonal elements are…”

“…Equations [12] and [14] represent nine moments and these equations can be solved simultaneously to obtain three quadrature points {v i , a i , w i }, i = 1-3. This is accomplished by first performing a one-dimensional quadrature with the diagonal moments using the routine ORTHOG of Press et al (26), which will yield the {A i , w i }.…”

Nanoparticle Coagulation in a Planar Jet

“…Direct numerical simulation (DNS) may be able to provide insights into the relationship between fluid field, particle properties, and collision kernels. Yu et al (1998) developed a DNS technique to simulate particle formation and growth in laminar flames which correlated well with experiment. Large-scale industrial flow reactors typically operate under turbulent flow conditions.…”

Simulation of aerosol dynamics and transport in chemically reacting particulate matter laden flows. Part I: Algorithm development and validation

“…In addition to the method of moments, several other methods have been used for solving the GDE, such as continuous methods (Tsang and Brock, 1983;Tsang and Rao, 1990), Monte Carlo methods (Kourti and Schatc, 1998;Rosner and Yu, 2001), sectional methods Park et al, 1999), moving-sectional methods (Gelbard, 1990;Kim and Seinfeld, 1990) and discrete-sectional methods (Wu and Flagan, 1988;Landgrebe and Pratsinis, 1990;Wu and Biswas, 1998;Okuyama et al, 1991;Lu et al, 1999;Park et al, 1999;Yu et al, 1998;Pyy onen and Jokiniemi, 2000;Rao and McMurry, 1989). Among all these methods, the discrete-sectional approach remains one of the primary and most accurate ways of simulating aerosol dynamics in a variety of processes.…”