The computational modeling of soot in aircraft engines is a formidable challenge, not only due to the multiscale interactions with the turbulent combustion process but the equally complex physical and chemical processes that drive the conversion of gas-phase fuel molecules into solid-phase particles. In particular, soot formation is highly sensitive to the gas-phase composition and temporal fluctuations in a turbulent background flow. In this work, a large-eddy simulation (LES) framework is used to study the soot formation in a model aircraft combustor with swirl-based fuel and air injection. Two different configurations are simulated: one with and one without secondary oxidation jets. Specific attention is paid to the LES numerical implementation such that the discrete solver minimizes the dissipation of kinetic energy. Simulation of the model combustor shows that the LES approach captures the two recirculation zones necessary for flame stabilization very accurately. Further, the model reasonably predicts the temperature profiles inside the combustor. The model also captures variation in soot volume fraction with global equivalence ratio. The structure of the soot field suggests that when secondary oxidation jets are present, the inner recirculation region becomes fuel lean, and soot generation is completely suppressed. Further, the soot field is highly intermittent suggesting that a very restrictive set of gas-phase conditions promotes soot generation.