On intrinsic oscillation in radiation-affected diffusion flames

Abstract

A linear stability analysis is conducted to study the onset of near-limit flame oscillation with radiative heat loss in 1-D chambered planar flames using multi-scale activation-energy asymptotics. The oscillatory instability near the radiation-induced extinction limit at large Damköhler numbers is identified, in additional to the one near the kinetic limit at small Damköhler numbers. It is shown that radiative loss assumes a similar role as varying the thermal diffusivity of the reactants. Thus, flame oscillation near the radiative limit is still thermal-diffusive in nature although it may develop under unity Lewis numbers. The unstable range of Damköhler numbers near the radiative limit shows quite similar parametric dependence on the Lewis numbers of reactants, Le F and Le O, the stoichiometry, ϕ, and the radiative loss as that near the kinetic limit. They both increase monotonically with Le O and ϕ and increase then decrease with Le F. Increasing radiative loss extends the parameter range under which flame oscillations may develop. However, they show different dependence on the temperature difference between the supplying reactants. Unless radiative loss approaches its maximum value the system can sustain, flame oscillation near the radiative limit is only possible within a limited range of Δ T, whereas it is promoted monotonically with decreasing Δ T near the kinetic limit. Furthermore, while radiative loss shows small effect on the nondimensional oscillation frequency, the dimensional frequency of flame oscillations near the radiative limit can be substantially smaller than that near the kinetic limit.