Large eddy simulation paradigm is employed to analyse the internal flow field of a lean premixed swirlstabilized combustor with axial air injection at both non-reacting and reacting conditions for a methane and a methane-hydrogen fuel mixture. The Thickened Flame combustion model with the kinetic mechanism GRI 3.0 and the detailed chemical kinetics solver SAGE available in ConvergeCFD is employed to simulate the flow. An adaptive mesh strategy is used to maximise the mesh resolution in the flame and boundary layer regions. The numerical results are first validated against in-house experimental velocity measurements obtained via particle image velocimetry, and then leveraged to provide further insights on the flow behaviour. Significant reductions in CO2, CO and NOx emissions are observed when changing the fuel to the CH4/H2 mixture. From a POD analysis is observed that a Precessing Vortex Core is present in both the reacting and non-reacting conditions. Flashback and severe local extinctions are not observed during the simulated time.