Diffusive -thermal instabilities in non-premixed combustion

The objective of this work has been to develop a general theory of diffusive-thermal instabilities in non-premixed combustion (diffusion flames). Although fragments of a theory have appeared in the literature, no comprehensive study has existed that identifies the dependence of these instabilities on the fuel and oxidizer properties, the supply conditions and the underlying flow. A stability analysis was performed for a simple one-dimensional flame configuration using an asymptotic model that treats the thin reaction zone as a free surface. Depending on the flow time relative to the chemical time (the Damkohler number D), there may be significant reactants leakage which causes flame extinction. Instabilities were typically found at high flow rate, or sufficiently low values of D, i.e. at near extinction conditions. The instabilities were found to evolve on one of two scales, one of the order of the diffusion length and time, the other of the order of the reaction zone thickness and reaction time. The results map the entire parameter space and identify regions where instabilities occur in the form of cells from regions where oscillatory flames occur. Contrary to earlier suppositions, and in accord with experiments, it is not necessary for both Lewis numbers to be less than one for cells to develop on the flame front or for both Lewis numbers to be larger than one for oscillations to occur. Furthermore, the importance of the initial mixture strength has been illustrated. Fuel rich flames are more likely to develop cellular structures and fuel lean flames more likely to become oscillatory. Finally, the roles of radiative heat losses and thermal mass diffusion (the Soret effect) on flame stability have been clarified. Heat losses will enhance the onset of diffusivethermal instabilities with flames which are fuel lean found more susceptible. Thermal mass diffusion of the fuel may either enhance or delay the onset of instabilities, but only for an inverted flame when the fuel diffuses against an oxidizer stream. Lighter fuels will have the transition to a secondary state delayed by the Soret effect, while heavier fuels will have the transition enhanced.