Cellular Flame Instabilities

The onset of Darrieus Landau and thermo-diffusive instabilities in an exploding spherical laminar flame is marked by the value of the Peclet number, Pecl, which is dependent upon the Markstein number. Values of Pecl for a number of different mixtures have been measured at 0.5 and 1.0 MPa in a spherical explosion bomb. These values are presented as a function of the flame speed Markstein number, Mab, and it is found that neither different pressures nor the different mixtures have a great effect on this correlation. Values derived from much larger scale atmospheric explosions of methane/air and propane/air also closely follow the same correlation. This suggests data from high pressure laboratory explosions might be used to predict the effects of large scale atmospheric explosions. Findings from other workers follow the same trend, although different detailed results can arise from both different definitions of Markstein number, and different measurement techniques. Because of the importance of a necessary minimal stretch rate to stabilise a flame, a more logical and fundamental criterion for the onset of this type of instability is one based on the flame stretch rate, such as a critical Karlovitz stretch factor, Kcl. As a result, the correlations are also expressed in terms of Kcl, instead of Pecl. As Masr becomes highly negative, the regime of stability is severely reduced.