The role of unsteadiness in direct initiation of gaseous detonations

TLDR

The study develops an analytical model for the direct initiation of gaseous detonations by a blast wave, aiming to explain lower critical energy and the observed non‑uniqueness of critical energy. Using numerical simulations of spherical initiation events and local analysis of the unsteady reaction zone, the authors formulate a critical decay rate (CDR) model that yields an analytical expression for the critical energy. The model shows that unsteadiness in the induction zone, rather than a quasi‑steady process, drives failure, and the resulting CDR equation predicts critical energy within an order of magnitude of experimental data without relying on additional parameters.

Abstract

An analytical model is presented for the direct initiation of gaseous detonations by a blast wave. For stable or weakly unstable mixtures, numerical simulations of the spherical direct initiation event and local analysis of the one-dimensional unsteady reaction zone structure identify a competition between heat release, wave front curvature and unsteadiness. The primary failure mechanism is found to be unsteadiness in the induction zone arising from the deceleration of the wave front. The quasi-steady assumption is thus shown to be incorrect for direct initiation. The numerical simulations also suggest a non-uniqueness of critical energy in some cases, and the model developed here is an attempt to explain the lower critical energy only. A critical shock decay rate is determined in terms of the other fundamental dynamic parameters of the detonation wave, and hence this model is referred to as the critical decay rate (CDR) model. The local analysis is validated by integration of reaction-zone structure equations with real gas kinetics and prescribed unsteadiness. The CDR model is then applied to the global initiation problem to produce an analytical equation for the critical energy. Unlike previous phenomenological models of the critical energy, this equation is not dependent on other experimentally determined parameters and for evaluation requires only an appropriate reaction mechanism for the given gas mixture. For different fuel–oxidizer mixtures, it is found to give agreement with experimental data to within an order of magnitude.