A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames

We introduce an efficient stochastic approach to solve the population balance equation that describes the formation and oxidation of soot particles in a laminar premixed flame. The approach is based on a stochastic particle system representing the ensemble of soot particles. The processes contributing to the formation and oxidation of soot particles are treated in a probabilistic manner. The stochastic algorithm, which makes use of an efficient majorant kernel and the method of fictitious jumps, resolves the entire soot particle distribution (PSDF) without introducing additional closure assumptions. A fuel-rich laminar premixed acetylene flame is computed using a detailed kinetic soot model. Solutions are obtained for both, the stochastic approach and the method of moments combined with a modified version of the Premix, CHEMKIN code. In this manner, the accuracy of the method of moments in a laminar premixed flame simulation is investigated. It is found that the accuracy for the first moment is excellent (5% error), and mean error for rest of the moments is within 25%. Also the effect of the oxidation of the smallest particles (burnout) has been quantified but was found not to be important in the flame investigated. The time evolution of computed size distributions and their integral properties are compared to experimental measurements and the agreement was found to be satisfactory. Finally, the efficiency of the stochastic method is studied.