Lewis number effect on the propagation of premixed flames in closed tubes

The evolution of a premixed flame under conditions of confinement is studied theoretically. The analysis is based on a hydrodynamic model in which the flame is treated as a surface of discontinuity. The flame structure is assumed to be quasi-steady with a high activation energy and a large heat release. Its resolution in the postignition period yields a coupled system of equations for the determination of the pressure and the burning rate. The analysis also resolves the thermal and flow fields on either side of the flame and determines the instantaneous location of the flame front together with the overall time required for the flame to reach the end of the tube. The results indicate that qualitatively distinct behaviors are possible for mixtures depending on whether their Lewis numbers Le are less or greater than one. For Le < 1, the burning rate always increases as the flame travels from one end of the tube to the other. For Le > 1, the evolution is extremely sensitive to the initial conditions. Small changes that occur during the ignition period may yield to a bulk quenching or homogeneous explosion after the flame has reached a certain distance down the tube.