Linear stability analysis of nonadiabatic flames: Diffusional-thermal model

✍ Scribed by G. Joulin; P. Clavin

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 864 KB
• Volume: 35
• Category: Article
• ISSN: 0010-2180
• DOI: 10.1016/0010-2180(79)90018-x

✦ Synopsis

The method of matched asymptotic expansions, in terms of a suitably reduced activation energy, is applied to investigate the effects of heat losses on linear stability of a planar flame, which is governed by a one-step irreversible Arrhenius reaction.

The density change associated with the heat release is neglected in order to eliminate the Landau hydrodynamic instability. Attention is focused on diffusional-thermal instability mechanisms.

The dispersion relation is obtained in terms of the diffusive properties of the limiting reactant and of the heat-loss intensity. For a given loss intensity-less than the critical value leading to extinction-the two steady planar regimes have different stability properties: (1) the "slow" regimes (which do not reduce to the adiabatic one when the heat-loss intensity goes to zero) are shown to be always unstable; and (2) for the "fast" regimes (which include and generalize the adiabatic one) cellular structures are predicted to occur when the limiting component is sufficiently light. If the limiting component is moderately light, the "fast" regimes are stable and unstructured in nearly adiabatic conditions; however, they are destabilized by an increase of heat losses and must exhibit cells before the extinction limit is reached. Similarly, for mixtures involving a realistically heavy limiting component, our analysis predicts the appearance of transverse travelling waves near the extinction limit.