Dynamics and quenching of non-premixed edge-flames in oscillatory counterflows

The dynamics of non-premixed edge-flames, including the generation of cellular structures, in an unsteady, symmetric counterflow are examined for positive rates of strain. A one-step reaction is assumed, νYF+νXO→νpPνYF+νXO→νpP, in which the oxidizer Lewis number is 1. For a variety of Damköhler numbers, we examine the edge-flame evolution for two values of the fuel Lewis number LeYLeY, 0.3 and 1, and two values of the initial mixture fraction γ  , 0.36 and 1, representing fuel lean and stoichiometric supply conditions. For LeY=0.3LeY=0.3 and γ=0.36γ=0.36, unsteady forcing can convert non-cellular edge-flames into ones containing various characteristics of near- or sub-limit cellular structures, including drifting, splitting and stationary flame strings. The transition regimes between the different edge-flame structures are examined as a function of the amplitude and frequency of the strain rate variations in the unsteady counterflow and also as a function of the instantaneous and equivalent strain rate functions. For LeY=0.3LeY=0.3 and γ=1γ=1, while no cellular edge-flames can be generated for steady counterflows, we show that cellular structures can be observed in the presence of unsteady forcing. For LeY=1LeY=1 and γ=1γ=1, it is shown that unsteady forcing can significantly modify the mean propagation speeds of both ignition and failure waves. Finally, the quenching boundaries of two-dimensional edge-flames induced by the unsteady counterflow are examined for LeY=0.3LeY=0.3, γ=0.36γ=0.36 and LeY=1LeY=1, γ=1γ=1.