Réaction diffusion en écoulement stationnaire rapide

This Note is concerned with the speed of propagation of a chemical reaction in a fast, steady and non uniform flow, which may apply to flame propagation in some instances. The structure of the flow is 1) a parallel shear flow with velocity perpendicular to the average front, where the flame speed is close to the maximum flow speed toward the fresh gases 2) a periodic cellular structure where the speed of propagation of the reaction grows like the fourth root of the fluid speed. Short English version : We examine the propagation of a reaction front in a fast steady flow with a given structure in space. We assume that this is actually a premixed flame without claims of an accurate representation of any real combustion process. The basic equations are given in (1) and would correspond in combustion theory to a Lewis number equal to unity. The flow field is Aq(r), r position in space and we study the limit A ! 1. We assume furthermore that the typical length scale of the flow q(r), denoted as is much bigger than the flame thickness . Two types of flow structures are studied, a parallel shear flow,("case a") and a spaceperiodic flow pattern ("case b"). In case "a", the eikonal approximation applies, because of the separation of scales between the flow structure and the reaction zone. When the flame front propagates in the flow