Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is dominated by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the Multi-Microphone-Method, high-speed OH*-chemiluminescence measurements, and high-speed Particle Image Velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is a dominant driver for heat release fluctuations and their saturation.

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