This thesis investigates the predictability of non-reacting and reacting anistropic turbulent, swirling flows using popular turbulence models with a robust numrical procedure.\ud \ud The performance of these turbulence models is assessed and compared against experimental data for anisotropic, turbulent swirling flow in a cylindrical pipe and\ud non-reacting and reacting combustion chambers. The transport equations for title k -e and k - w two-equation turbulence models are presented along with the LRR and SSG second-moment closure models for isothermal and variable density flows. The effect of anisotropy in the Reynolds stress dissipation rate tensor is accounted for by the inclusion of an algebraic model for the dissipation anistropy tensor dependent 0n the mean strain and vorticity of the flow.\ud \ud The implementation of the SMART and CUBISTA boundedness preserving, high order accurate convective discretisation schemes is shown to yield superior predictive accuracy compared to previous methods such as Upwinding. The PISO and SIMPLE solution algorithms are employed to provide a robust calculation procedure.\ud \ud The second moment closure models are found to provide increased predictive accuracy compared to those of the two-equation models. Mean flow properties are predicted well, capturing the effects of the swirl in the experimental flow field. The LRR model shows a premature decay of swirl downstream compared to the more accurate predictions of the other models. The effect of dissipation anistropy on the\ud SSG model shows an over-prediction of the turbulent properties in the upstream region followed by premature decay downstream. In the near field of the non-reacting\ud combustion chamber flow, the anisotropic dissipation model corrects the SSG model over-prediction of the veloocities at the central axis.\ud \ud A combined CMC flamelet combustion model is employed alongside the anisotropic dissipation Reynolds stress model to predict the flow field and combustion related\ud properties of the TECFLAM swirl burner. The species mass \ud fractions are conditioned on the mixture fraction to provide an accurate model for the determination of the probability density functions governing the reactions within the turbulent flamelet.\ud \ud The turbulent model shows an ability to provide accurate predictinS for the aerodynamic properties of the flow whilst providing accurate determination of combustion\ud related phenomena alongside the combnstion model. A limitation of the flamelet assumption was identified with the over-prediction of CO due to the larger\ud lengthscales of the oxidation reactions present in such flows
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