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Abstract
Multiphase combustion is a process of economic and environmental importance to our society. As a result, there is a strong motivation to produce accurate, predictive models to simulate them. Transported Probability Density Function (TPDF) methods are attractive for modelling multiphase combustion as many of the non-linear processes are treated without approximation. However, the treatment of unclosed terms in the TPDF method such as the molecular mixing and inter-phase coupling, remain open modelling questions. Direct Numerical Simulation (DNS) can provide both physical understanding of flame phenomena as well as provide guidance for modelling. In this thesis, DNS is used to both provide closure for TPDF simulations to isolate errors in particular models, as well as to probe flame phenomena in multiphase flames. A TPDF mixing model evaluation of sooting non-premixed flames is performed with results compared to a DNS database. The Euclidean Minimum Spanning Tree (EMST) mixing model accurately predicted the soot production in the flame, while other models tested over-predicted extinction and thus under-predicted soot formation. The best results were achieved when the soot moments were given a mixing rate of zero, instead of the gas phase mixing rate. DNS of non-premixed ethanol spray flames were performed in order to understand the effect of Stokes number on flame extinction. Extinction was greater for sprays with larger Stokes numbers as the large droplets penetrate the reaction zone. Extinction was caused by both evaporative cooling and the chemical effect of adding fuel directly to the reaction zone, which depletes radicals like OH. Finally, a parametric study varying Damk\"ohler number was completed to analyse the evaporation distribution models in TPDF methods. The Interaction by Exchange with the Mean (IEM) mixing model failed to predict the correct temperature profile compared to the EMST mixing model. The EQUAL distribution model, which distributed the source term evenly to all particles in a cell, performed best for both cases tested. Models create new particles or moving particles towards saturation could better capture statistics conditioned on mixture fraction, however could not predict the correct temperature profile. This thesis presents new insight into the complex interactions found in multiphase combustion. In addition, this work highlights the manifold complexities involved in modelling multiphase combustion.