We studied flow dynamics in a model combustion chamber using Large-eddy simulations (LES) and Particle image velocimetry (PIV) at the Reynolds number $Re$ of 15,000. The swirl is produced using a Turbomeca swirler and air flow, while combustion is supported by a central methane/air jet. We compared four flow regimes, assessing the effect of the central jet for isothermal and lean reacting conditions. A detailed comparison for isothermal and reactive cases without the central jet is described, validating the LES results against PIV. We observe that unsteady dynamics are governed by global instability in the form of a well-known precessing vortex core (PVC). The central jet slightly changes the dynamics of PVC in the isothermal case where a strong recirculation zone is still formed. However, for the reacting case, the bubble is completely destroyed with no signs of strong vortical structures in the inner shear layer. These observations are confirmed using spectral analysis and proper orthogonal decomposition, describing the contribution of different flow modes in terms of azimuthal harmonics.