Large-eddy simulation of turbulent flame synthesis of silica nanoparticles with an extended population balance model

In the present study, our recently proposed extended population balance equation (PBE) model for aggregation and sintering is incorporated into a Large-Eddy Simulation - Probability Density Function (LES-PDF) modelling framework to investigate synthesis of silica nanoparticles in a turbulent diffusion flame. The Eulerian stochastic field method is employed to solve the LES-PBE-PDF equations, characterising the influence of the unresolved sub-grid scale motions, and accounting for the complex interaction between turbulence, chemistry and particle dynamics. A different sub-grid mixing time scale is introduced to the model to account for the low diffusivity of nanoparticles. The models for gas-phase chemistry and aerosol dynamics are the same as those recently used by the authors to simulate silica synthesis in a laminar flame (Tsagkaridis et al. 2023). Thus, by retaining the same kinetics without any adjustments in parameters, we focus on the modelling issues arising in silica flame synthesis. The LES results are compared with the detailed experimental in-situ SAXS data of of Camenzind et al (2008). Good agreement is found between numerical predictions and experimental data for temperature along the centreline. However, the LES model underestimates the SAXS data for primary particle diameters by a factor of two. Possible reasons for this discrepancy are discussed by leveraging knowledge acquired from the aforementioned laminar-flame simulations.