The onset of oscillations in diffusion flames

We present a theoretical study aimed at understanding the basic mechanisms responsible for the onset of oscillations in diffusion flames. A simple one-dimensional configuration is considered with one reactant supplied in a uniform stream and the other diffusing against the stream. The analysis allows for unequal non-unity Lewis numbers as well as for incomplete combustion. It is found that oscillations are possible when the Damköhler number is sufficiently small, namely at near-extinction conditions. They occur when the reactant diffusing against the stream is more completely consumed and the corresponding Lewis number is sufficiently large (typically larger than one). The conditions also require the Lewis number of the reactant supplied in the stream to be within a certain range (typically also larger than one). In accord with experimental results the onset of oscillations is found to be sensitive to stoichiometric conditions (or mixture strength) and to the temperature differential between the supply conditions. The effect of volumetric heat losses was also studied and it is shown that increased heat losses enhance the onset of instabilities. Predicted oscillations are of low frequency, typically 1-6 Hz for the range of Lewis numbers and mixture strengths used in experiments.