Flame-speed sensitivity to temperature changes and the deflagration-to-detonation transition

✍ Scribed by B. Deshaies; G. Joulin

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 845 KB
• Volume: 77
• Category: Article
• ISSN: 0010-2180
• DOI: 10.1016/0010-2180(89)90037-0

✦ Synopsis

To better understand how the dynamics of a folded flame propagating from the closed end of a semiinfinite tube is affected by the blast flow of unburned mixture and the flame-driven acoustics, we study a one-dimensional, unsteady model in which (1) the folded flame is modeled as a planar, markedly subsonic, reactive discontinuity separating the fresh and burned gases, both being chemically inert, and (2) the burning speed of the discontinuity has the same, exponential dependence on the reaction temperature as that of the corresponding laminar flame, but it exceeds the latter by a large factor o(t) (degree of folding) which is prescribed an assumed known dependence on time. Upon use of asymptotic techniques in the limit of large activation energies, a nonlinear, o-dependent, difference equation is obtained for the burning speed history. It shows that (1) two regimes of steady propagation are obtained when o is constant and less than a critical value oc that we compute in terms of the mixture properties (only the slower regime is stable), (2) if o(t) exceeds oc during a long enough period, the reactive discontinuity accelerate limitlessly, and (3) if o(t) never exceeds Oc, and the initial state lies on the lower branch of steady states, the burning speed remains bounded. The results are discussed in terms of the DDT phenomenon.