Abstract

The current work aims to examine how the nature of cellular instabilities controls the re-initiation capability and
dynamics of a gaseous detonation transmitting across a layer of inert (or non-detonable) gases. This canonical
problem is tackled via computational analysis based on the two-dimensional, reactive Euler equations. Two differ-
ent chemical kinetic models were used, a simplified two-step induction-reaction model and a detailed model for
hydrogen-air. For the two-step model, cases with relatively high and low activation energies, representing highly
and weakly unstable cellular detonations, respectively, are considered. For the weakly unstable case, two distinct
types of re-initiation mechanisms were observed. (1) For thin inert layers, at the exit of the layer the detonation
wave front has not fully decayed and thus the transverse waves are still relatively strong. Detonation re-initiation
in the reactive gas downstream of the inert layer occurs at the gas compressed by the collision of the transverse
waves, and thus is referred to as a cellular-instability-controlled re-initiation. (2) If an inert layer is sufficiently
thick, the detonation wave front has fully decayed to a planar shock when it exits the inert layer, and re-initiation
still occurs downstream as a result of planar shock compression only, which is thus referred to as a planar-shock-
induced re-initiation. Between these two regimes there is a transition region where the wave front is not yet fully
planar, and thus perturbations by the transverse waves still play a role in the re-initiation. For the highly unstable
case, re-initiation only occurs via the cellular-instability-controlled mechanisms below a critical thickness of the
inert layer. Additional simulations considering detailed chemical kinetics demonstrate that the critical re-initiation
behaviors of an unstable stoichiometric mixture of hydrogen-air at 1 atm and 295 K are consistent with the finding
from the two-step kinetic model for a highly unstable reactive mixture.