Detonation Structure Under Chain Branching Kinetics

Abstract

Hydrogen–oxygen chemistry is characterized by a chain branching mechanism that yields three explosion limits. While a detailed kinetic scheme appropriate for hydrogen–oxygen should produce correct results, in many circumstances, a simpler yet reasonably realistic model will be warranted. In particular, it is easier to develop a clear understanding of the reaction zone structure using a simpler model, that includes only the key mechanisms. To that effect, we consider a four-step chain branching scheme that exhibits an explosion behavior with three limits, which behaves at least qualitatively like hydrogen chemistry. We focus in particular on the structure of the initiation and chain branching zones, using a combination between numerical simulation and analysis. Numerical simulations using this chemical model show distinctive keystone figures in the flow field, close to observations in hydrogen–oxygen detonation experiments. The structure of the chain branching zone is resolved using a perturbation analysis, which clarifies the differences between explosion and no-explosion regions and allows for an evaluation of the induction length in the steady wave. The analysis assumes both high activation energy and a slow initiation. Three cases are identified, respectively, with pressure and temperature located within the explosion region, close to the explosion limit and within the no-explosion region. The induction length is shorter and the reaction rate is faster by several orders of magnitude in the explosion region.