Implicit Large Eddy Simulation (ILES) with high-resolution and high-order computational modelling has been applied to flows with turbulent mixing and combustion. Due to the turbulent nature, mixing of fuel and air and the subsequent combustion still remain challenging for computational fluid dynamics. However, recently ILES, an advanced numerical approach in Large Eddy Simulation methods, has shown encouraging results in prediction of turbulent flows. In this thesis the governing equations for single phase compressible flow were solved with an ILES approach using a finite volume Godunov-type method without explicit modelling of the subgrid scales. Up to ninth-order limiters were used to achieve high order spatial accuracy. When simulating non chemical reactive flows, the mean flow of a fuel burner was compared with the experimental results and showed good agreement in regions of strong turbulence and recirculation. The one dimensional kinetic energy spectrum was also examined and an ideal k−5/ 3 decay of energy could be seen in a certain range, which increased with grid resolution and order of the limiter. The cut-off wavenumbers are larger than the estimated maximum wavenumbers on the grid, therefore, the numerical dissipation sufficiently accounted for the energy transportation between large and small eddies. The effect of density differences between fuel and air was investigated for a wide range of Atwood number. The mean flow showed that when fuel momentum fluxes are identical the flow structure and the velocity fields were unchanged by Atwood number except for near fuel jet regions. The results also show that the effects of Atwood number on the flow structure can be described with a mixing parameter. In combustion flows simulation, a non filtered Arrhenius model was applied for the chemical source term, which corresponds to the case of the large chemical time scale compared to the turbulent time scale. A methane and air shear flow simulation was performed and the methane reaction rate showed non zero values against all temperature ranges. Small reaction rates were observed in the low temperature range due to the lack of subgrid scale modelling of the chemical source term. Simulation was also performed with fast chemistry approach representing the case of the large turbulent time scale compared to the chemical time scale. The mean flow of burner flames were compared with experimental data and a fair agreement was observed
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