Bluff-body stabilized turbulent premixed flames can experience hydrodynamic instability caused by the interaction of the flame with small-scale vortices in the separated shear layer around the recirculation region, as well as with the large-scale coherent structures in the far-wake. A globally hydrodynamically unstable system, for example one which involves vortex shedding, can exhibit limit-cycle behaviour due to the coupling between pressure oscillation and velocity fluctuations. In this work, the hydrodynamic behaviour of a bluff-body stabilized turbulent premixed propane/air flame in a model jet-engine afterburner is investigated using Computational Fluid Dynamics (CFD). A URANS approach was found to be appropriate for the range of frequencies considered in this study. Combustion is modelled using a modified flame surface density (FSD) approach. The observed self-excited hydrodynamic oscillations are analyzed using a nonlinear dynamical framework which is capable of capturing elaborate nonlinear behaviour including quasiperiodicity and chaos. The results from the CFD are first validated using available experimental data. The velocity at the inlet is gradually increased from 14 m/s to 33 m/s and the global flame structure is observed. With increasing inlet velocity, the flame first transitions from steady state to an oscillating state with a symmetrical flame structure, and eventually to an asymmetrical flame structure at higher velocities. The flame is essentially steady in the lower range of velocities considered before transitioning to a limit cycle oscillation after a critical velocity is exceeded. A doubling in the frequency of the hydrodynamic oscillation is also observed at intermediate values of inlet velocity. This investigation demonstrates that turbulent premixed reacting flows can exhibit strong hydrodynamic oscillation. An understanding of such behaviour can assist in developing methods to control flow instabilities and therefore help in suppressing thermoacoustic oscillation.