The role of unsteadiness in direct initiation of gaseous detonations
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.
© 2000 Cambridge University Press. Reprinted with the permission of Cambridge University Press. Received January 5 1998; revised May 19 2000. The authors would like to thank Dr Tom Jackson for the provision of the one-dimensional detonation stability code used to produce figure 1. This research has been supported by Los Alamos National Laboratory- subcontract 319AP0016-3L under DOE Contract W-7405-ENG-36.
Published - ECKjfm00.pdf