Premixed hydrogen-oxygen flames. Part II: Quasi-isobaric ignition near the flammability limits

Abstract

A numerical study of one-dimensional and time-dependent problems in quasi-isobaric combustion of H 2O 2 mixtures is carried out with a complex chemical network and detailed molecular transport mechanisms. The numerical results are then compared with analytical developments on a simplified model exhibiting the basic mechanisms. Particular attention is devoted to compositions close to the flammability limits of planar flames. A first numerical result shows that a diffusive-thermal instability corresponding to a Hopf bifurcation appears in the propagation of planar flames in the neighborhood of the hydrogen-rich flammability limit. The corresponding critical mole fraction of hydrogen is 0.947 at ordinary conditions with a flame velocity of about 45 cm/s, compared with 0.96 for the flammability limit. The quasi-isobaric ignition by a hot pocket of combustion products, which is used as an ignition source, is also investigated numerically. The critical size of the hot pockets for initiating a deflagration wave is determined as a function of the equivalence ratio. It is found that when the hydrogen-rich flammability limit is approached, the critical radius becomes much larger than the flame thickness and, moreover, it diverges before reaching the planar flammability limit, at a critical hydrogen mole fraction about 0.945 at ordinary conditions (compared with 0.96). Thus, planar flames cannot be ignited in this way in the range of hydrogen mole fractions between 0.945 and 0.96 where the burning velocity varies from about 50 cm/s to few millimeters per second. Near the hydrogen lean flammability limit the situation is quite different. The critical size is smaller than the planar flame thickness, and spherical flames with a very small initial radius may grow in lean mixtures even beyond the flammability limit of planar flames. These phenomena are explained by an elementary analytical study of a minimal model coupling preferential diffusion mechanisms with the kinetic effects controlling the planar flammability limits.