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.
The role of unsteadiness in direct initiation of gaseous detonations
