Ignition and extinction in combustion of initially unmixed reactants

Abstract

The adequacy of direct one-step chemical kinetics for describing ignition and extinction in initially unmixed gases is studied through the particular case of inviscid axisymmetric stagnation-point flow. Oxidant is assumed to blow from upstream infinity at a non-gaseous reservoir of pure fuel at its boiling (or sublimating) temperature. Before reaching the reservoir the oxidant reacts with gaseous fuel flowing in the opposite direction to form product and release heat. This heat is in part conducted and diffused to the reservoir interface to transform more fuel into the gaseous state and continue the steady-state burning. Second-order Arrhenius kinetics for Lewis-number unity is examined. A critical parameter characterizing the phenomenon is shown to be the first Damkohler similarity group D1, the ratio of a time characterizing the flow to a time characterizing the chemical activity.For small D1 the reactants convect away heat without releasing the energy stored in their chemical bonds. Regular perturbation about chemically frozen flow establishes this condition as the weak burning limit. For large D1 singular perturbation describes a narrow region of intense chemical activity. For infinite D1 (indefinitely fast rate of reaction) the region is reduced to a surface of discontinuity (the thin-flame kinetics of Burke & Schumann).For intermediate D1 numerical techniques establish that a solution describing burning of moderate intensity joins the two previously mentioned asymptotic limits. It is suggested that sudden transition of the system between the various branches in this domain of intermediate D1 accounts for the phenomena of ignition and extinction of burning.