| Summary: | In this thesis, a discretised Population Balance Equation (PBE) model is coupled with a detailed in-house Computational Fluid Dynamics code to study soot formation in axisymmetric diffusion flames with comprehensive gas-phase chemistries for C2H4 and CH4 fuels. The main aim of this study is to predict the complete Particle Size Distribution (PSD) of soot particles in turbulent non-premixed flames via a transported Probability Density Function approach. The PSD is obtained from the solution of the PBE without any prior assumption on its shape, using volume or diameter to describe the size of soot particles. However, due to a great number of uncertainties that appear from the turbulence interactions with chemistry, radiation and particle formation, the main objective is divided into smaller tasks where these complexities are avoided. Initially, the performance of the PBE is assessed under several numerical methods on an initial distribution-convection test, 0D reactors and 1D flamelet framework. The PBE has been originally discretised via a collocation type finite element method, and in the present work Finite Volume (FV) methods are used. The PBE with Total Variation Diminishing (TVD) scheme demonstrates better performance. The FV-TVD PBE with suitable soot kinetics is employed in 2D laminar flames where overall good agreement is achieved for the velocity, temperature, mole fraction of C2H2 and OH species and the mean properties of PSD (i.e. total number density and soot volume fraction). However, the temperature and soot volume fraction profiles on the turbulent flames do not exhibit similar accuracy as the laminar flames and there is still room for improvement. The evolution of the PSD is computed for both flames in the entire flame region exhibiting weak bimodal distribution in some points. The performance of complex coupled phenomena in PBE modelling via soot kinetics, detailed chemistry, radiation and turbulence interactions is explored.
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