Response of n-Heptane and Dodecane Swirl-Stabilized Spray Flames to Transverse Forcing Characterized by Flame Describing Functions Based on Downstream Acoustic Pressure or Velocity Signals

Predicting thermoacoustic instabilities in annular combustors requires knowledge of the impact of acoustic oscillations on heat release rate (HRR) oscillations. Flame describing functions (FDF) measured at the burner exit using acoustic forcing are key elements of thermoacoustic instability analyses. FDFs based on acoustic pressure measurements, $FP′$⁠, or on axial velocity measurements, $FU′$⁠, are compared here. This study is done on the TACC-Spray bench, an original linear array of spray flames stabilized by a strong swirling flow, representing an unfolded sector of a self-unstable annular combustor. Acoustic forcing of a standing transverse chamber mode is applied downstream of the injectors. Experiments are conducted with liquid n-heptane or dodecane, with the flames placed at a pressure or an intensity antinode (IAN) of the transverse mode. $FP′$ does not depend on the measurement location for acoustically compact flames provided that this location remains in the flame vicinity. $FU′$ can lead to significant discrepancies, as swirling flows present strong velocity gradients, which can be minimized by carefully choosing the measurement location. The injector admittance linking the two FDFs is shown to be quasi-independent of the forcing amplitude here. Consequently, both FDFs show a similar dependence on the forcing amplitude. $FP′$ indicates constructive combustion-acoustics interference whatever the flame location in the acoustic field and the fuel, consistent with self-sustained instabilities observed in the annular combustor. An analysis using the Rayleigh criterion corroborates the results derived from the FDFs. So, $FP′$ appears as a powerful and practical tool for characterizing combustion dynamics.