Stochastic modeling of soot particle size and age distributions in laminar premixed flames

Abstract

In the present study, the evolution of size distributions of soot particles in premixed laminar flames is investigated. A computationally efficient stochastic approach is used to model the dynamics of the soot particle ensemble. The stochastic method is enhanced to include a formalism for modeling coagulation at high pressures. A detailed kinetic model is used to describe gas phase reactions and the formation, growth, and oxidation of soot particles. Four fuel rich laminar premixed flames at different pressure are investigated. It is found that calculated size distributions vary markedly in shape between the different flames. The distributions calculated in the two flames at elevated pressure and in the sub-atmospheric flame exhibit log-normal shape in the post-flame zone. In contrast, a bimodal distribution is found for the atmospheric flame, which persists throughout the entire flame. The bimodal behavior could be attributed to continuous nucleation. Furthermore, the effect of surface ageing, i.e., the deactivation of sites on the soot particles’ surface available for reaction with gas phase species, is investigated. For this purpose, a definition of a particle’s age is introduced, and age distributions are calculated. Subsequently, it was investigated if the surface reactivity could be correlated with the particle age. Two different correlations were investigated: (a) a step-function attributing a high surface activity to young particles and low activity to old particles and (b) an exponential function giving a smooth transition of surface activity with particle age. Good agreement with measured soot volume fractions could be obtained with both approaches. The decay constant in the exponential correlation was found to be a linear function of maximum flame temperature for three of the four calculated flames. For these three flames, the experimentally established trend that surface deactivation proceeds faster at higher temperatures could thus be reproduced.