Heat loss and Lewis number effects on the onset of oscillations in diffusion flames

A diffusion flame may be characterized by the response of the burning rate to a properly defined Damköhler number, representing the ratio of diffusion time to chemical reaction time. Depending on the oxidant concentration in the ambient and on the Lewis numbers, the response may be an S-shaped or monotonic curve. While the S curve exhibits ignition and extinction phenomena, the monotonic curve indicates that there is a gradual transition from intense burning to a nearly frozen state and vice versa. Stability considerations indicate that spontaneous oscillations develop when the Lewis number is sufficiently large and/or heat losses are excessive. This suggests that the ignition/extinction conditions, normally associated with the turning points of the S curve, must be modified and related to the points of exchange of stability. For a monotonic response curve, the oscillations lead to extinction that is not predicted otherwise. The near-limit oscillations predicted here are qualitatively similar to those observed in the microgravity candle flame experiment, and the frequencies of oscillations predicted are of the same order of magnitude.