Numerical investigation of the instability for one-dimensional Chapman–Jouguet detonations with chain-branching kinetics

Abstract

The dynamics of one-dimensional Chapman–Jouguet detonations driven by chain-branching kinetics is studied using numerical simulations. The chemical kinetic model is based on a two-step reaction mechanism, consisting of a thermally neutral induction step followed by a main reaction layer, both governed by Arrhenius kinetics. Results are in agreement with previous studies that detonations become unstable when the induction zone dominates over the main reaction layer. To study the nonlinear dynamics, a bifurcation diagram is constructed from the computational results. Similar to previous results obtained with a single-step Arrhenius rate law, it is shown that the route to higher instability follows the Feigenbaum route of a period-doubling cascade. The corresponding Feigenbaum number, defined as the ratio of intervals between successive bifurcations, appears to be close to the universal value of 4.669. The present parametric analysis determines quantitatively the relevant non-dimensional parameter χ, defined as the activation energy for the induction process ϵ I multiplied by the ratio of the induction length Δ I to the reaction length Δ R . The reaction length Δ R is estimated by the inverse of the maximum thermicity (1/ max) multiplied by the Chapman–Jouguet particle velocity u CJ . An attempt is made to provide a physical explanation of this stability parameter from the coherence concept. A series of computations is carried out to obtain the neutral stability curve for one-dimensional detonation waves over a wide range of chemical parameters for the model. These results are compared with those obtained from numerical simulations using detailed chemistry for some common gaseous combustible mixtures. Keywords: : DetonationsNumerical simulationsInstabilityLimitChain-branching kineticsNonlinear dynamics Acknowledgement H.D. Ng was supported by the NSERC and FQRNT scholarships.