Soot is carbonaceous particulate matter formed due to the incomplete combustion of hydrocarbon fuels. The prediction of soot emissions is crucial if next-generation combustion devices are to mitigate the deleterious effects of particulate matter on human health and the environment. Theories for the distribution of size and shape of soot particles in turbulent reacting flows are required, not only for accurate predictions related to flame characteristics but also to meet increasingly stringent regulations. Over the last decades, advances in the understanding of key processes controlling soot formation and oxidation have led to the development of models that can replicate soot emissions and size in laminar flames, sometimes even at a quantitative level. However, predictions in turbulent flames still lack behind due to uncertainties in the intricate coupling between kinetics, aerosol dynamics and turbulence, and the wide range of scales that have to be simulated. There is a clear need to explore the fundamentals of soot evolution in turbulent conditions and develop effective methodologies to predict the soot particle size distribution (PSD) accurately and rapidly. This thesis presents a step in this direction for flames in geometrical configurations of high relevance to aviation combustors. In the first part of the thesis, a comprehensive modelling strategy is proposed using a detailed physicochemical sectional soot model coupled with the Conditional Moment Closure (CMC) turbulent combustion model and Large Eddy Simulation (LES). This modelling approach allows for an elaborate description of the unsteady reacting field and explicitly accounts for transport, history and finite-rate chemistry effects on soot precursors and the PSD. The soot PSD evolution is investigated first in simplified configurations followed by detailed simulations of a canonical turbulent jet flame. The results are analysed to reveal the hierarchy of reaction pathways during soot formation and oxidation and demonstrate the effects of residence time, micromixing and differential diffusion of soot particles. These analyses are necessary to understand the sooting flame structure and act as preparatory investigations for the rest of the thesis. In the second part, a lab-scale swirl flame with addition of dilution air is simulated to explore soot PSD evolution in a Rich-Quench-Lean (RQL) burner configuration widely used in practice for emissions control. Results show a reasonably good agreement with experiments for the mean reaction zone and soot locations and their variations with different airflow provided in the burner primary and dilution regions. The predicted PSDs at the burner exit are fairly well captured for a high-dilution condition but show too few and too small particles for a dilution-free condition, which may be due to an over-prediction of the oxidation rates or the underlying assumptions for particle transport. The results are then used to indicate how dilution air modifies the soot PSD within the primary zone. The method is shown to reproduce the known sensitivity of soot and its precursors on history and scalar dissipation rate effects, a prerequisite for reliable predictions. As a result, it offers a framework for accurately capturing soot PSD in realistic combustion devices. In the third part of the thesis, a new approach based on Incompletely Stirred Reactor Network (ISRN) modelling is presented. The aim is to develop an emissions screening tool that can be utilised during the design phase of combustors. ISRN modelling simplifies calculations so that parametric studies with very complex chemistry and soot models can be performed, or a large number of geometries can be explored, all at a modest computational cost. The approach shares similarities with reactor network and compartmental modelling methods from chemical engineering but offers elaborate molecular mixing and transport treatment. It relies on a network of incompletely stirred reactors, which are inhomogeneous in terms of the flow and mixing fields but characterised by homogeneous conditional averages, with the conditioning performed on the mixture fraction. The ISRN approach is demonstrated on an ethylene model RQL combustor and a single sector lean-burn model combustor operating on Jet-A1 fuel in pilot-only mode, showing very good accuracy in reproducing the mean reaction zone as revealed by LES-CMC or experiments. It is then found that reasonable accuracy can be produced for soot emissions at a significantly reduced computational cost, further enabling the use of multiple chemical mechanisms and soot models and provide estimates of the soot PSD. Finally, a new framework for analysing turbulent non-premixed flames and history effects on soot evolution is presented. The framework is formulated based on the concept of conditional particle age, denoting the total time the mixture or particles have spent at a particular mixture fraction, and conditional thermal age, which allows for a quantification of time-temperature history. Without the need for strong modelling assumptions, governing equations for the two age types are derived that can be used both in the CMC or ISRN context. The approach is then demonstrated on a simple 1D configuration and an ISRN computation of a model RQL combustor. The findings suggest that the concept of conditional age has excellent potential for estimating particle surface reactivity and develop age-dependent closure for soot surface growth and oxidation
