Analysis of the Soot Particle Size Distribution in a Laminar Premixed Flame: A Hybrid Stochastic/Fixed-Sectional Approach

Abstract

The numerical simulation of the soot particle size distribution in flames is addressed by solving the balance equations for total number density and the probability density function (PDF) of particle sizes, leading to a hybrid stochastic/fixed-sectional method for solving soot population balance equation. Well established models are introduced in these equations for the chemistry of PAH in ethylene combustion, for particle nucleation, growth, agglomeration and oxidation. These closures are combined with a stochastic approach, which drives the evolution of a fixed number of computational particles used to solve for the particle size distribution with a control of agglomeration and numerical roundoff error through a fixed sectional discretisation. A laminar sooting flame is simulated to compare the results against measurements and previous numerical simulations, confirming the validity of the novel approach in terms of accuracy and CPU efficiency. The relation between the mobility diameter, measured in the experiments, and the equivalent sphere diameter, introduced in the modeling, is discussed under this novel numerical framework. The influence of the fractal particle shape on the simulated particle size distribution is explored. Finally, Particle Size Distributions obtained from the hybrid method are compared to the ones obtained with a representative fixed-sectional method.

Solving the population balance equation for non-inertial particles dynamics using probability density function and neural networks: Application to a sooting flame

“…The influence of the fractal particle shape on the simulated particle size distribution was also explored. 25 The introduction of artificial neural networks in reactive flow simulation is a rapidly growing field, to reduce both computing cost and memory requirements. The optimisation of networks 3 This is the author's peer reviewed, accepted manuscript.…”

“…s k is the particle surface and χ is the number of sites per unit surface of soot. Mature particles are expected to provide a lower proportion of active sites per unit of surface and this is accounted for using 25,62 α…”

“…7 shows the comparison between the PSD predicted with the hybrid stochastic/fixed-sectional method to solve for the population balance equation and the results obtained with Eq. (25). The reference simulation of this flame by direct Monte Carlo solutions of non-inertial particles dynamics, which aims at performing a direct numerical 16 This is the author's peer reviewed, accepted manuscript.…”

High-order polynomial approximations for solving non-inertial particle size density in flames

“…Numerous approaches and numerical methods have been discussed and applied [2][3][4][5][6][7][8][9][10][11] and many references therein. The thermophysical models are usually developed by comparing their predictions against experimental results after solving the PBE.…”