The initial development of a tulip flame

The initial development of a "tulip flame," often observed during flame propagation in closed tubes, isattributed to a combustion instability. The roles of hydrodynamic and of the diffusional-thermal processes on the onset of instability are investigated through a linear stability analysis in which the growth or decay of small disturbances, superimposed on an otherwise smooth and planar flame front, are followed. A range of the Markstein parameter, related to the mixture composition through an appropriately defined Lewis number, has been identified where a tulip flame could be observed. For a given value of the Markstein parameter within this range, a critical wavelength is identified as the most unstable mode. This wavelength is directly related to the minimal aspect ratio of the tube where a tulip flame could be observed. The time of onset of instability is identified as the time when the most unstable disturbance, associated with the critical wavelength, grows at a faster rate than the flame front itself and exceeds a certain threshold. This occurs after the flame has propagated a certain distance down the tube: a value which has been explicitly determined in terms of the relevant parameters. Experimental records on the tulip flame phenomenon support the findings of the analysis. That is, the tulip flame forms after the flame has traveled half the tube's length, it does not form in short tubes, and its formation depends on the mixture composition and on the initial pressure in the tube.