Non-adiabatic modulation of premixed-flame thermoacoustic frequencies in slender tubes

This paper presents an experimental study of the influence of heat losses on the onset of thermoacoustic instabilities in methane–air premixed flames propagating in a horizontal tube of diameter, $D = 10$ mm. Flames are ignited at the open end of the tube and propagate towards the closed end undergoing strong oscillations of different features owing to the interaction with acoustic waves. The frequency of oscillation and its axial location are controlled through the tube length $L$ and the intensity of heat losses. These parameters are respectively modified in the experiments by a moveable piston and a circulating thermal bath of water prescribing temperature conditions. Main experimental observations show that classical one-dimensional predictions of the oscillation frequency do not accurately describe the phenomena under non-adiabatic real scenarios. In addition to the experimental measurements, a quasi-one-dimensional analysis of the burnt gases is provided, which introduces the effect of heat losses at the wall of the tube on the interplay between the acoustic field and the reaction sheet. As a result, this analysis provides an improved description of the interaction and accurately predicts the excited flame-oscillation harmonics through the eigenvalues of the non-adiabatic acoustics model. Unlike the original one-dimensional analysis, the comparison between the flame oscillation frequency provided by the non-adiabatic extended theory and the frequencies measured in our experiments is in excellent agreement in the whole range of temperatures considered. This confirms the importance of heat losses in the modulation of the instabilities and the transition between different flame oscillation regimes.