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

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Laminar diffusion flames present an elementary configuration for investigating soot formation and validating kinetic models before these are transferred to turbulent combustors. In the present article, we present a joint experimental and modelling investigation of soot formation in a laminar co-flow burner. The diffusion flames are analysed with the aid of laser diagnostic techniques, including elastic light scattering (ELS), planar laser-induced fluorescence of OH (OH-PLIF) and line-of-sight attenuation (LOSA), to measure the spatial distribution of soot, gas phase species and the line-of-sight integrated soot volume fraction (ISVF), respectively. The experimental dataset is supplemented by location-specific TEM images of thermophoretically sampled soot particles. The simulation of the sooting flames is carried out with a recently developed discretisation method for the population balance equation (Liu and Rigopoulos, 2019, Combust. Flame 205, 506-521) that accomplishes an accurate prediction of the particle size distribution, coupled with an in-house CFD code. By minimising numerical errors, we ensure that the discrepancies on the modelling side are mainly due to kinetics and are able to carry out an investigation of alternative models. We include a complete set of soot kinetics for PAH-based nucleation and condensation, HACA-based surface growth and oxidation as well as size-dependent coagulation and aggregation, and consider three different gas phase reaction mechanisms (ABF, BBP and KM2). Based on predictions of the gas phase composition and particle size distribution of soot, modelled counterparts of the laser diagnostic signals are computed and compared with the experimental measurements. The approach of directly predicting signals circumvents the difficulties of explicitly representing the OH concentration in terms of the measured OH-PLIF data and avoids using 'hybrid' modelled and measured values to approximate the OH concentration. Moreover, the LOSA signal is directly converted to the line-of-sight ISVF instead of a measure of local soot volume fraction to avoid tomographic inversion errors. Lastly, the predicted ELS signal is computed in terms of the particle size distribution resolved by the population balance model, thus circumventing the approximation of an integral soot property using a presumed size distribution. While we cannot obtain quantitative agreement between experiments and simulations, the accuracy of the numerical approach and the direct prediction of experimental signals allow us to conduct sensitivity analyses of key empirical parameters and investigate the importance of the PAH chemistry and its influence on the competition between nucleation, condensation and surface growth.

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