The dynamics of flowing non-inertial particles undergoing nucleation, surface growth/loss, agglomeration and sometimes breakage, is usually characterised by the particle size distribution function. This distribution evolves according to a population balance equation. A novel approach combining Monte Carlo and fixed-sectional methods is proposed to minimise the discretisation errors when solving the surface growth/loss term of the population balance equation. The approach relies on a fixed number of stochastic particles and sections, with a numerical algorithm organised to minimise errors even for a moderate number of stochastic particles and sections. Canonical test cases featuring nucleation, agglomeration, and surface growth/loss are simulated. Results against the analytical solutions confirm the improvement in accuracy of the novel approach compared with fixed-sectional methods for the same computational effort. The hybrid method is thus of particular interest for simulating problems where surface growth/loss dominates the particles physics.
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.
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