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Lean Direct Injection (LDI) emerged as an interesting concept to limit NOx emissions in aero engines at the cost of operating close to the flame lean blow-off limit. In this technology, fuel is injected into a swirled airstream that generates recirculating flow structures that stabilize the flame. It is then of paramount importance at the design stage to understand the effect of various features on these structures. The present investigation makes use of Eulerian-Lagrangian Large-Eddy Simulations (LES) previously validated against existing experimental data for a reference condition to study the liquid non-reacting flow inside the CORIA Spray LDI burner with the help of Adaptive Mesh Refinement (AMR). A Design of Experiments (DoE) is proposed to analyze the significance of several geometrical features on the flow field, namely the combustor width, the air swirler vane angle, the number of swirler vanes and the axial location of the fuel injector tip. The study covers the qualitative appearance of the flow and the quantitative characterization of the spray dispersion and fuel-air mixing process. In this way, the chosen response variables include the size of the relevant coherent flow structures (Central Toroidal Recirculation Zone induced by the Vortex Breakdown Bubble, Corner Recirculation Zone and Swirled Jet) and their associated velocities, spray features (global drop sizes and spray penetration), pressure drop across the swirler and induced swirl number. Besides, the Precessing Vortex Core (PVC) relevance and frequency content is studied through Proper Orthogonal Decomposition (POD). Results from the statistical analysis show that the number of swirler vanes and their angle are the geometrical parameters that most importantly influence the flow features: stronger recirculation zones leading to an improved atomization and mixing have been found both when decreasing the number of swirler blades and increasing the blade angle. However, both solutions also increase the pressure losses across the swirler. As far as the spectral analysis is concerned, the number of swirler vanes is the most influencing factor on both the frequency and intensity of the PVC modes, being crucial for the possible activation and the energetic content of a double-helix PVC mode. [ABSTRACT FROM AUTHOR]