Oscillation and extinction in flames

Oscillation phenomena in flames were theoretically investigated for both diffusion and premixed flames. For diffusion flames, oscillations develop intrinsically as a result of thermal-diffusive instability when the Lewis numbers are larger than unity. A nonlinear stability analysis for the intrinsic oscillation in a planar flame was first conducted by deriving an evolution equation for the amplitude of perturbation, through which three possible flame responses were predicted: the flame may be stable, unstable or oscillate persistently. This study was then extended to investigate forced flame oscillations by incorporating imposed flow oscillations. Resonance between the intrinsic and forced oscillations was identified when the flame is close to the marginally stable state and the imposed frequency approaches the intrinsic flame oscillation frequency.;For premixed flames, the study was focused on the linear response of stretch-affected premixed flames to flow oscillations. In particular, the effects of flame stretch on the response of heat release rate in a wedge-shaped flame were studied. It was found that the effects of flame stretch become important through the modulation of the flame surface area when the normalized oscillation frequency is of the order of O( s&d4;-1/2C ), where s&d4;C is the Markstein number characterizing the curvature effect of flame surface. For frequency below this order, the flame responds as an unstretched flame.;The analysis was then extended to radiation-affected diffusion flames. A model accounting for effects of radiative heat loss and nonunity Lewis numbers was first developed to study the structure and extinction characteristics of counterflow diffusion flames. Dual extinction limits in the presence of radiative loss, namely the kinetic and radiative limits at small and large Damkohler numbers, respectively, were identified. Based on this result, the model was then employed to study intrinsic flame oscillations with emphasis on those developed near the radiative extinction limit. It was shown that radiative loss assumes a similar role as increasing the thermal diffusivity of the reactants. Thus, flame oscillation near the radiative limit is still a thermal-diffusive instability phenomenon in nature, although it may develop under unity Lewis number.