Stability of Planar ZND Detonation Waves for Three-Step Chain-Branching Kinetics
Stability analysis of steady ZND detonation waves is of interest mainly because the analysis yields scales, associated with the chemistry, that can be related to cell sizes, which are also associated with chemistry. The simplest kinetic model that describes chain-branching chemistry includes initiation, chain-branching and termination (). Initiation is described by a very stiff Arrhenius rate, chain-branching is also described by an Arrhenius model, and termination can simply be taken as constant. Heat release is associated with termination only. This model is a good prototype for many systems that are dominated by chain-branching. Of particular relevance, hydrogen-air chemistry is characterized by a specific chain-branching behavior leading to an S-shaped explosion diagram; this behavior can be reproduced using a pressure-dependent termination step (). The three step scheme allows much more flexibility, when compared with a single Arrhenius step, which unavoidably associates heat release with initiation and leads to eigenmodes that become more unstable at higher frequencies (), a phenomenon known as the Zaidel paradox ().
KeywordsDetonation Wave Arrhenius Model Simple Kinetic Model Doklady Akademii Nauk SSSR Termination Zone
Unable to display preview. Download preview PDF.
- 4.Zaidel, R.M.: The stability of detonation waves in gaseous mixtures. Doklady Akademii Nauk SSSR 36, 1142 (1961)Google Scholar