The acoustic response of Burke-Schumann counterflow flames

The acoustic response of strained nonpremixed flames is investigated using as a canonical model problem the planar counterflow configuration subject to small harmonic fluctuations of the stagnation-point pressure and strain rate. To focus on effects of modified transport rates the analysis employs the limit of infinitely fast reaction for a general non-unity Lewis number of the fuel, including values of interest in hydrogen-oxygen and hydrocarbon-oxygen systems. For both acoustic-pressure and acoustic-velocity response, differential-diffusion effects are shown to promote the fluctuations of the flame location and reactant consumption rates (while in the pressure response, distinct behaviors of the flame temperature were observed depending on stoichiometry). The results are used, together with the Rayleigh criterion, to investigate the frequency dependence of the amplification/attenuation rate relevant in computations of acoustic instabilities. The analysis predicts acoustic amplification for all frequencies in the pressure response, whereas a critical crossover frequency is identified in the strain response demarcating the transition from attenuation to amplification of acoustic energy.