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Diffusive-thermal instabilities are well known features of premixed and diffusion flames. In one of its form the instability appears as spontaneous oscillations. In premixed systems oscillations are predicted to occur when the effective Lewis number, defined as the ratio of the thermal diffusivity of the mixture to the mass diffusivity of the deficient component, is sufficiently larger than one. Oscillations would therefore occur in mixtures that are deficient in the less mobile reactant, namely in lean hydrocarbon-air or rich hydrogen-air mixtures. The theoretical predictions summarized above are in general agreement with experimental results; see for example [5] where a jet configuration was used and experiments were conducted for various inert-diluted propane and methane flames burning in inert-diluted oxygen. Nitrogen, argon and SF6 were used as inert in order to produce conditions of substantially different Lewis numbers and mixture strength. In accord with the predicted trend, it was found that oscillations arise at near extinction conditions, that for oscillations to occur it suffices that one of the two Lewis numbers be sufficiently large, and that oscillations are more likely to be observed when is relatively large.

In a microgravity environment, molecular diffusion is the primary mechanism by which fuel and oxidizer that are initially separated are brought together to the reaction zone. Combustion systems in microgravity are therefore primed to diffusive-thermal instabilities. One such instability appears in the form of spontaneous oscillations. Oscillations were observed in condensed-phase fuels and gas-jet diffusion flames, and in microgravity jet-flames, candle flames and spherical flames surrounding large fiber-supported fuel droplets. The nature of oscillations is quite different in each of these cases: the droplet flame exhibits radial oscillations, the edge of the candle flame is seen to move back and forth along the hemispherical flame surface and the jet-flame oscillations are primarily up and down along the axis. Despite these differences, associated mainly with the mode of oscillation, one may identify some common factors: in all cases the flame exhibits low-frequency oscillations, oscillations are only observed in special mixtures and their onset occur only at near-extinction conditions.

Some recent results, concerning extinction limits and stability in spherical diffusion flames, cellular diffusion flames and oscillations in diffusion flames are summarized. Results obtained from experiments carried out in microgravity ground facilities are presented.

The spherical geometry is the most suitable one to study fundamental issues concerning the structure and the dynamics of diffusion flames. From a theoretical point of view, it is the only geometry that permits the existence of a truly one dimensional stationary diffusion flame. A stationary planar diffusion flame with the fuel supplied upstream, at x approaches -infinity say, and the oxidant downstream, at x approaches +infinity is not possible. For a steady diffusion flame to exist, one must have nonzero fluxes of fuel and oxidant towards the flame. However, in the unlimited region behind the planar flame the only bounded solutions to the reaction-free convective-diffusive operator are constants. Hence the oxidant concentration behind the flame remains constant and there is no mechanism to generate the necessary flux towards the flame. A one-dimensional problem can be formulated if the reactants are supplied at finite locations; but the boundary conditions in this case introduce unnecessary complications and do not appropriately model the physical reality. Indeed, a planar diffusion flame can be established in the stagnation-point flow of two opposed jets but the flame in this case is stretched and the flow is essentially two-dimensional. The only stationary one-dimensional diffusion flame in an unlimited environment is therefore the spherical flame.

The objectives of this project are to gain insight into diffusion flames by modeling various configurations related to ongoing experimental investigations in the microgravity combustion science program. The emphasis of the work is to understand the structure and dynamics of diffusion flames. Improving our fundamental understanding of diffusion flames is most relevant to issues related to fire safety and fire prevention because most fires consist of diffusion flames.

Previously, the stability of a premixed flame in a stagnation flow was discussed for a restricted class of disturbances that are self-similar to the basic undisturbed flow; thus, flame fronts with corrugations only in the cross stream direction were considered. Here, we consider a more general class of three-dimensional flame front perturbations which also permits corrugations in the streamwise direction. It is shown that, because of the stretch experienced by the flame, the hydrodynamic instability is limited only to disturbances of short wavelength. If in addition diffusion effects have a stabilizing influence, as would be the case of mixtures with Lewis number greater than one, a stretched flame could be absolutely stable. Instabilities occur when the Lewis number is below some critical value less than one. Neutral stability boundaries are presented in terms of the Lewis number, the strain rate, and the appropriate wavenumbers. Beyond the stability threshold, the two-dimensional self-similar modes always grow first. However, if disturbances of long wavelength are excluded, it is possible for the three-dimensional modes to be the least stable one. Accordingly, the pattern that will be observed on the flame front, at the onset of instability, will consist of either ridges in the direction of stretch or the more common three-dimensional cellular structure.