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We have studied flame propagation in a strained mixing layer formed between a fuel stream and an oxidizer stream, which can have different initial temperatures. Allowing the Lewis numbers to deviate from unity, the problem is first formulated within the framework of a thermo-diffusive model and a single irreversible reaction. A compact formulation is then derived in the limit of large activation energy, and solved analytically for high values of the Damkohler number. Simple expressions describing the flame shape and its propagation velocity are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse enthalpy gradients in the frozen mixing layer leads to flame-front velocities which grow with decreasing values of the Lewis numbers.The analytical results are complemented by a numerical study which focuses on preferentialdiffusion effects on triple flames. The results cover, for different values of the fuel Lewis number, a wide range of values of the Damkohler number leading to propagation speeds which vary from positive values down to large negative values. IntroductionFlame propagation in inhomogeneous mixtures occurs in most practical situations. For example, spatial non-uniformities in the enthalpy of the reactants are frequently encountered in unpremixed-combustion devices. Even when such non-uniformities are weak, their impact on the initiation process and the dynamics of burning is generally important. This is due to the typical large activation energies of the chemical reactions encountered in combustion, which make their rates very sensitive to the surrounding conditions. In many instances, composition and temperature inhomogeneities are essentially transverse to mixing layers, along which flames can propagate, as in lifted jet diffusion flames. Because the combustible mixture varies from lean to rich across a mixing layer, triple flames, consisting of two premixed branches and a trailing diffusion flame, are expected. Therefore, they have been the subject of a number of experimental, analytical and numerical studies [1][2][3][4][5][6].The main purpose of the present investigation is to determine how the propagation of the triple flame is influenced by transverse enthalpy gradients in the fresh mixture and by differential diffusion. We shall select for definiteness the strained mixing layer configuration as a frame for the investigation, and adopt additionally the constant-density approximation [7] to make the analytical description tractable. The configuration of the study is sketched Oxidizer side Figure 1. The strained mixing layer configuration. The fuel stream has temperature 7p, a fuel mass fraction >>F,F and contains no oxidizer. The oxidizer stream has temperature 7b, an oxidizer mass fraction >>o.o and contains no fuel. The density being assumed constant, the velocity field considered is a two-dimensional stagna...

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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 p , 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.