A partially premixed gas turbine model combustor close to an industrial design is investigated using Large Eddy Simulation (LES). Two flames, one stable and another unstable with self-excited oscillations are computed. In particular, this study addresses the previously unexplained transition of flame shape in the experiments, from V-shaped to flat when the flame becomes acoustically unstable, suggesting a notable change of the important convective delay in the thermoacoustic feedback loop. The LES results show good agreement with the measured velocities, temperature and mass fractions. The acoustic power spectral density (PSD) obtained from the LES of the unstable flame also agrees well with the measured amplitudes in the air plenum and combustion chamber, and reasonably captures the frequency with a slight under-prediction. A comparison of the stable and unstable cases shows different mixing and reaction behaviours despite similar mean velocity fields. Further detailed analysis shows that the different mixing behaviour is driven by the significantly varying air mass split between the two air passages during a thermoacoustic oscillation cycle. This variation is due to the different impedances experienced by the pressure oscillations propagating through the two swirling injector passages with different internal geometries. This causes a periodic variation of the radial momentum of the fuel jets injected between the two swirling air flows. The resulting flapping of the fuel jets creates an enhanced radial fuel-air mixing that leads to a flattened flame in the unstable case. This provides a new physical explanation for the transitions of flame shape observed in the experiments.