On the dynamics of flame edges in diffusion-flame/vortex interactions

We analyze the local flame extinction and reignition of a counterflow diffusion flame perturbed by a laminar vortex ring. Local flame extinction leads to the appearance of flame edges separating the burning and extinguished regions of the distorted mixing layer. The dynamics of these edges is modeled based on previous numerical results, with heat release effects fully taken into account, which provide the propagation velocity of triple and edge flames in terms of the upstream unperturbed value of the scalar dissipation. The temporal evolution of the mixing layer is determined using the classical mixture fraction approach, with both unsteady and curvature effects taken into account. Although variable density effects play an important role in exothermic reacting mixing layers, in this paper the description of the mixing layer is carried out using the constant density approximation, leading to a simplified analytical description of the flow field. The mathematical model reveals the relevant nondimensional parameters governing diffusion-flame/vortex interactions and provides the parameter range for the more relevant regime of local flame extinction followed by reignition via flame edges. Despite the simplicity of the model, the results show very good agreement with previously published experimental results.