Ignition and extinction fronts in counterflowing premixed reactive gases

Abstract

We describe two-dimensional steady propagating flame fronts in the stagnation mixing layer between two opposed streams of the same reactive mixture, the propagation taking place in the direction perpendicular to the plane of strain. The front, which is curved by the nonuniform flow field, separates a chemically frozen region from a region with a twin-flame configuration. The front velocity is calculated in terms of the Lewis number, Le(F), and the Damkohler number, Da. Da, equal to the inverse of the Karlovitz number, is defined as the ratio of the strain time to the transit time through the planar unstrained flame. For the cases corresponding to large Da, difficult to tackle numerically, analytical expressions are given, characterizing the flame shape, and the variation of the burning rate along the flame front from the nose up to the planar trailing branches. For moderately large and low values of Da, the study is carried out numerically, yielding, in particular, the propagation velocity in terms of Da, for different values of Le(F). Different combustion regimes are thus described including flames propagating toward the unburnt mixture, or ignition fronts, standing flames and retreating flames, or extinction fronts. We also describe stationary cylindrical flames of finite-extent, or 2D burning spots. In particular, a critical Lewis number is found, below which negative propagation speeds do not exist while the 2D burning spots mentioned may be encountered. Typically, these exist only for sufficiently small Le(F) if the Da is within a range [Da(min), Da(max)], depending on Le(F). For Da < Da(min), the 2D spots are quenched, whereas as Da is increased, they grow in size, tending to give birth to propagating (ignition) fronts; Da(max) is indeed found to be the smallest Da allowing for ignition fronts. We notice that the range of existence of the 2D spots, for a given Le(F), can overlap with that of retreating (extinction) fronts, and possibly with that of 3D spots, or flame balls, in this flow. However, the 3D case is not addressed in this work.