Shear flow instabilities in swirl-stabilized combustors and their impact on the amplitude dependent flame response: A linear stability analysis

The hydrodynamic instabilities in the flow field of a swirl-stabilized combustor are investigated theoretically. These instabilities give rise to large-scale flow structures that interact with the flame front causing unsteady heat release rate fluctuations. The streamwise growth of these coherent structures depends on the receptivity of the shear layer, which can be predicted numerically by means of linear stability analysis. This analysis is applied to the reacting flow field of a perfectly premixed swirl-stabilized combustor that is subjected to strong axial forcing mimicking thermoacoustic oscillations. The linear stability analysis reveals a clear correlation between the shear layer receptivity and the measured amplitude dependent flame transfer function. The stability analysis based on the natural flow predicts the distinctive frequency dependent flame response to low amplitude forcing. At these conditions, the flow reveals strong spatial amplification near the nozzle, causing the inlet perturbations to be significantly amplified before they reach the flame. At higher forcing amplitudes, the flow instabilities saturate, which manifests in a saturation of the flame response. The saturation of the shear layers predicted from the linear stability analysis is compared to phase-locked measurements of the forced flow field revealing good qualitative agreement. The analysis of the mean flow stability offers a powerful analytical tool to investigate the impact of shear flow instabilities on the flame describing function.