Modelling of soot coalescence and aggregation with a two-population balance equation model and a conservative finite volume method

Abstract

The objective of the present paper is to develop a population balance approach for modelling soot formation that distinguishes between coalescence and aggregation and accounts for finite-rate fusing of primary particles within aggregates, while providing a numerically accurate description of primary particle surface growth and oxidation within aggregates. To this end, the recently developed conservative finite volume sectional method for the solution of the population balance equation (PBE) due to Liu and Rigopoulos (2019, Combust. Flame 205, 506–521) is extended to a two-PBE approach that allows for a more accurate modelling of primary particle surface growth and oxidation and furthermore involves a timescale for the fusing of primary particles. The accuracy of the numerical method is first tested by calculating the self-preserving distributions of aggregates with varying fractal dimension. Subsequently, the one-PBE and two-PBE approaches are coupled with CFD and applied to the simulation of the Santoro laminar non-premixed co-flow sooting flame. The results show that both approaches can provide good prediction of the soot volume fraction, but the two-PBE approach yields a significant improvement in the prediction of soot morphology. At present, the information available for modelling the gradual fusing of soot primary particles is based on experiments on silica and titania nanoparticles, and therefore a comprehensive study of the impact of the sintering model parameters is conducted. Finally, conclusions are drawn regarding the predictive potential of the one-PBE and two-PBE approaches.