Asymptotic theory of ignition and failure of self-sustained detonations

Abstract

Based on a general theory of detonation waves with an embedded sonic locus that we have developed in Kasimov (2004) and Stewart & Kasimov (2004), we carry out asymptotic analysis of weakly-curved slowly-varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman??Jouguet detonation speeds and is capable of predicting quasi-steady, normal detonation shock speed, curvature (D??k) curves with multiple turning points. An evolution equation that retains the shock acceleration, D(dot), namely a D(dot)??D??k relation is rationally derived and its solution for spherical (or cylindrical) detonation is shown to reproduce the ignition/failure phenomenon observed in both numerical simulations of blast wave initiation and in experiments. A simple physically transparent explanation of the ignition phenomenon is given in terms of the form of the evolution equation. A single-step chemical reaction described by one progress variable is employed, but the kinetics is sufficiently general and is not restricted to Arrhenius form, although most specific calculations in this work are performed for Arrhenius kinetics. As an example, we calculate critical energies of direct initiation for hydrogen??oxygen mixtures and find close agreement with available experimental data.published or submitted for publicationis peer reviewe