Chemically reacting turbulent flows are investigated using numerical techniques. The main objectives of this work could be classified into two categories: (1) To understand the impact of gravity on transitional and turbulent jet flames. (2) To develop models and algorithms for accurate and efficient simulations of highspeed turbulent flows with hydrocarbon combustion.; In (1), both Direct Numerical Simulations (DNS), and Large Eddy Simulations (LES) of turbulent jet flames have been performed under different gravity conditions. Simplified chemistry without using a model was employed in DNS, while in LES the Filtered Mass Density Function (FMDF) method was used as a closure for the composition and reaction of methane/air combustion.; Both the DNS, and the LES results are consistent with previous findings and indicate that in the absence of gravity, combustion damps the flow instability; hence reduces "turbulence production" and jet growth. However, in the "finite-gravity" conditions, combustion generated density variations may promote turbulence and enhance both the mixing and the combustion through buoyancy effects. Our results also indicate that the gravity effects on a transitional/turbulent jet flame is not limited to large-scale flame flickering, and there is a significant impact on small-scale turbulence and mixing as well.; Furthermore, the analysis of compositional flame structures suggests that the finite-rate chemistry effects are more significant in finite-gravity conditions than in zero-gravity.; In (2) the LES/FMDF method is extended towards multi-step chemistry with realistic thermodynamic properties, such that the predictions could be compared with laboratory flame measurements. In LES/FMDF, the effects of chemical reactions appear in closed forms, allowing for a reliable prediction of complex turbulent reacting flows. The consistency of the Eulerian and the Lagrangian solutions are discussed, and an efficient algorithm for parallelization of the hybrid code is presented.; Comparisons with the Sandia's piloted methane jet flames (flame D and F) are performed and good agreements in the case of the near-equilibrium flame D have been achieved with a flamelet-based chemistry model.; Finite-rate reduced kinetics in the form of the global 1-step, and multi-step kinetics are employed as well. While reasonable predictions have been made in the case of flame D using the 1-step reaction, the extinction predicted by the multi-step methods is more pronounced compared to the experimental measurements. The observations are analyzed and the parameters responsible for this difference are identified.
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