A hybrid stochastic/fixed-sectional method for solving the population balance equation. (14th December 2019) - Bouaniche, Alexandre; Vervisch, Luc; Domingo, Pascale
Highlights: Solving population balance equation for non-inertial particles: Novel hybrid stochastic/fixed-sectional method. Balance equation for the probability density function of particle sizes. Monte Carlo simulation of agglomeration and nucleation from fixed-sectional source terms. Validation against canonical cases with analytical particle size distributions. Convergence diagram versus number of particles and fixed-sections. Abstract: 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.