A conservative method for the solution of population balance with coagulation, and application to soot formation

In this work, we propose a conservative finite volume method for the discretisation of the terms arising from the coagulation process in the population balance modelling. The method performs detailed evaluation of the resulting double integrals using a geometric representation. The distribution is accurately predicted and the first moment is conserved. Extensive testing is performed by comparing to analytical solutions and numerical solutions of the discrete PBE. Finally the method is applied to a laminar diffusion sooting flame by solving the spatially dependent population balance equation, in order to assess its feasibility, economy and robustness when coupled with CFD.

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