An LES-PBE-PDF approach for predicting the soot particle size distribution in turbulent flames

In this article, we combine the large eddy simulation (LES) concept with the population balance equation (PBE) for predicting, in a Eulerian fashion, the evolution of the soot particle size distribution in a turbulent non-premixed hydrocarbon flame. In order to resolve the interaction between turbulence and chemical reactions/soot formation, the transport equations for the gas phase scalars and the PBE are combined into a joint evolution equation for the filtered pdf associated with a single realization of the gas phase composition and the soot number density distribution. With view towards an efficient numerical solution procedure, we formulate Eulerian stochastic field equations that are statistically equivalent to the joint scalar-number density pdf. By discretizing the stochastic field equation for the particle number density using an explicit adaptive grid technique, we are able to accurately resolve sharp features of evolving particle size distributions, while keeping the number of grid points in particle size space small. Compared to existing models, the main advantage of our approach is that the LES-filtered particle size distribution is predicted at each location in the flow domain and every instant in time and that arbitrary chemical reaction mechanisms and soot formation kinetics can be accommodated without approximation. The combined LES-PBE-PDF model is applied to investigate soot formation in the turbulent non-premixed Delft III flame. Here, the soot kinetics encompass acetylene-based rate expressions for nucleation and growth that were previously employed in the context of laminar diffusion flames. In addition, both species consumption by soot formation and radiation based on the assumption of optical thinness are accounted for. While the agreement of our model predictions with experimental measurements is not perfect, we indicate the benefits of the LES-PBE-PDF model and demonstrate its computational viability.