THE FAST-TIME STABILITY OF A SIMPLE DEFLAGRATION

Fast-time instabilities refer to dynamics that may develop within the reaction zone of a flame, where the chemical kinetic time scales are v ery brief. Premixed flames with order one heat losses and diffusion fl ames with order one reactant leakage are known to possess this instabi lity when the Lewis number is one (Peters, 1978). Work by Stewart (198 6) indicates that the instability should also arise for adiabatic flam es with Lewis numbers exceeding one. Recent work in reverse smoulderin g combustion (Lozinski and Buckmaster, 1994) requires an examination o f the combined effect of heat losses and Lewis numbers well below unit y. Because of the general nature pf the results, they are presented he re. The numerical computations reveal that while heat losses tend to d estabilize the flame, small Lewis numbers have a countervailing stabil izing effect, suppressing the instability for an order one range of he at lasses. This plays a key role in selecting the physically significa nt solution to the reverse smouldering combustion model (Lozinski and Buckmaster, 1994). The instability is one-dimensional an examination o f higher dimensions reveals no new instabilities arising for reasonabl e parameter values.