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Large-scale unsteady flow structures play an influential role in the dynamics of many practical flows, such as those found in gas turbine combustion chambers. This thesis is concerned primarily with large-scale unsteady structures that arise due to self-sustained hydrodynamic oscillations, also known as global hydrodynamic instability. Direct numerical simulation (DNS) of the Navier--Stokes equations in the low Mach number limit is used to obtain a steady base flow, and the most unstable direct and adjoint global modes. These are combined, using a structural sensitivity framework, to identify the region of the flow and the feedback mechanisms that are responsible for causing the global instability. Using a Lagrangian framework, the direct and adjoint global modes are also used to identify the regions of the flow where steady and unsteady control, such as a drag force or heat input, can suppress or promote the global instability. These tools are used to study a variety of reacting and non-reacting flows to build an understanding of the physical mechanisms that are responsible for global hydrodynamic instability in swirling diffusion flames. In a non-swirling lifted jet diffusion flame, two modes of global instability are found. The first mode is a high-frequency mode caused by the instability of the low-density jet shear layer in the premixing zone. The second mode is a low-frequency mode caused by an instability of the outer shear layer of the flame. Two types of swirling diffusion flames with vortex breakdown bubbles are considered. They show qualitatively similar behaviour to the lifted jet diffusion flames. The first type of flame is unstable to a low-frequency mode, with wavemaker located at the flame base. The second type of flame is unstable to a high-frequency mode, with wavemaker located at the upstream edge of the vortex breakdown bubble. Feedback from density perturbations is found to have a strong influence on the unstable modes in the reacting flows. The wavemaker of the high-frequency mode in the reacting flows is very similar to its non-reacting counterpart. The low-frequency mode, however, is only observed in the reacting flows. The presence of reaction increases the influence of changes in the base flow mixture fraction profiles on the eigenmode. This increased influence acts through the heat release term. These results emphasize the possibility that non-reacting simulations and experiments may not always capture the important instability mechanisms of reacting flows, and highlight the importance of including heat release terms in stability analyses of reacting flows.

A swirl injector for a rocket engine being developed by \emph{AESIR} (Association of EngineeringStudents in Rocketry) was simulated with different geometric parameters. The swirl injector is usedto atomize the ethanol used as fuel and to create a spray that mixes well with the oxidizer withinthe combustion chamber. Inlet slot angle (90, 75, 60 and 45 degrees), swirl chamber length (15, 20and 25 mm) and outlet orifice diameter (3, 6 and 9 mm) were examined.Previous studies in swirl injectors show that CFD can be used to analyze the flow in such aninjector, furthermore theoretical models exist that can predict some of the general characteristicsof the flow. Previous studies have also simulated transient behavior and flow features effectingbreakup of fuel flowing through a swirl injector.A steady state simulation using Volume of Fluid (VOF) multiphase modeling and $k$-$\omega$ \emph{SST}turbulence modeling was used to simulate the swirl injector intended for the rocket engine. It wasfound that a wider outlet orifice would give a wider cone angle of spray. This is desirable in thecurrent rocket engine design as it will promote greater mixing of fuel and oxidizer higher up in thecombustion chamber. No large variances was observed when different inlet slot angles was simulated. Ashorter swirl chamber length reduced the amount of losses in energy due to viscous forces. The flowafter the outlet orifice was not simulated so the effect of turbulence kinetic energy and energylosses outside of the swirl injector have not been analyzed, previous studies have indicated thatturbulent kinetic energy does have an effect on the breakup and atomization of the fuel.It was concluded that using a wider outlet orifice of 9 mm gave the best results out of the differentgeometric parameters analyzed and the swirl chamber length should be a short as possible.

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Les écoulements vrillés, qui sont largement utilisés dans les turbines à gaz, sont connus pour être sujet à des bifurcations entre différentes topologies (grandes reconfigurations de l'écoulement) qui peuvent affecter les performances et la sécurité du moteur. Ce travail se concentre sur l'étude de ces bifurcations en utilisant la Simulation aux Grandes Echelles (SGE). Cette étude montre qu'un petit changement dans les conditions dynamique du fluide, induite par les différents modèles de sous-maille utilisés, peut provoquer une transition entre deux régimes d'écoulement distincts lorsque l'écoulement tourbillonnaire est proche des conditions critiques de transition. La sensibilité de la SGE aux modèles de sous-maille est également identifiée comme le résultat d'un manque de résolution à certains endroits critiques, un problème qui est analysé en utilisant une méthode d'adaptation de maillage. L’adaptation de maillage est testée sur des cas académiques et industriels. Ici, par ajustement de la résolution du maillage sur la base des caractéristiques de l'écoulement étudié (raffinement et grossissement de la grille en maintenant constant le coût numérique), des améliorations substantielles peuvent être obtenues, en terme de prédictions de la SGE. Ce travail peut être considéré comme une des premières étapes vers la mise en place d'une procédure standard (reproductible et indépendante de l’utilisateur) de maillage pour la SGE. / Swirling flows, which are widely employed in gas turbines, are known to undergo bifurcation between different topologies (large reconfigurations of the flow field) affecting the engine performance and safety. This work focuses on the study of such bifurcations using Large-Eddy Simulation (LES). It shows that a small change in the fluid dynamics conditions, induced by the different Sub-Grid Scale (SGS) models used in the simulations, can cause a transition between two, distinct, flow states when the swirling flow is close to transition conditions. The sensitivity of LES to SGS modeling is also identified as the result of a lack of mesh resolution at some critical locations, a problem which is analyzed using mesh adaptation. Mesh adaptation is tested on canonical and industrial flows. Here, by adjusting the mesh resolution based on the characteristics of the flow examined (refining and coarsening the grid keeping constant the numerical cost), substantial improvements of the LES predictions can be obtained. This work can be considered as the first step toward the establishment of a standard (repeatable and user independent) meshing procedure for LES.

[pt] Chamas pré-misturadas em escoamentos turbulentos com rotação são encontradas em diversos sistemas de engenharia, como turbinas a gás e motores a jato. Neste trabalho, regimes de chamas característicos de tais sistemas são estudados numericamente num queimador de escala laboratorial. O estado da arte dos estudos numéricos de tais chamas é revisado, com respeito a simulações de grandes escalas, bem como o de modelos computacionais baseados em médias de Reynolds. Um estudo isotérmico é feito no escoamento turbulento, num domínio computacional que consiste de um swirler radial e uma câmara de combustão. O impacto de diferentes modelos de turbulência, níveis de refinamentos de malha e condições de contorno no número de swirl e na estrutura do escoamento é investigado. Os resultados revelam que os três modelos de turbulência propostos resultam em campos de escoamento e número de swirl similares, enquanto o nível de refinamento de malha e a condição de contorno de parede deslizante alteram o número de swirl significativamente. Utilizando as equações de média de Reynolds, com o fechamento do modelo k − E realizável, acoplado a um modelo de duas equações para chamas pré-misturadas de metano e ar, dois regimes de chamas são analisados. Estes regimes correspondem à chama de recirculação externa (chama tipo M) e um regime de instabilidade, que ocorre na transição entre a chama tipo V e chama tornado. A estrutura do escoamento é caracterizada em termos de velocidade e propriedades de turbulência e combustão. Uma comparação entre variáveis de progresso também é feita, utilizando resultados experimentais prévios, levando a boa concordância qualitativa para os dois regimes estudados. / [en] Lean premixed turbulent swirling flames are found in many engineering systems, such as gas turbines and jet engines. This work aims to numerically study flame regimes, representative of such systems, stabilized in a laboratory scale burner. The state of the art of the numerical studies concerning these types of flames is reviewed, with respect to Reynolds-Averaged NavierStokes and Large Eddy Simulations. A turbulent, isothermal flow study is performed within the radial swirler and the combustion chamber. The impact of different turbulence models (realizable k − E, RNG k − E and SST k−W), mesh refinement levels and boundary conditions on the swirl number and overall flow structure is investigated. The results show that the three tested turbulence models yield similar results, with respect to the obtained flow field, whereas the mesh refinement level and slip wall boundary condition alter the swirl number significantly. Using Reynolds-Averaged NavierStokes transport equations, closed by the realizable k − E model, coupled with a two-equation premixed combustion model for methane/air mixtures, two combustion regimes are analyzed. These regimes correspond to the outer recirculation zone flame (M-shaped flame) and an unstable regime, which occurs at the transition between the V-shaped flame and tornado-flame. The flow structure is characterized in terms of velocity fields, turbulence and combustion properties. A reaction progress variable comparison is also performed, using existing experimental results, yielding qualitatively similar results for both studied regimes.