The Effect of Chain Initiation Reaction on the Stability of Gaseous Detonations

Abstract

The present research is conducted to investigate the instability of
gaseous detonations by emphasizing the role of the initiation step. To proceed
with the study, two characteristic times are defined for the initiation and the
branching steps (sI and sb, respectively). Depending on the values of these characteristic
times, three different modes of detonation failure are observed. It is seen
that the so-called cross over temperature detonability criterion is applicable only
for high values of sb. The present work, in a systematic fashion, revealed the
importance of two length scales that control the instability as well as the failure
of gaseous detonation. These length scales are the induction length and the length
of the main reaction layer. It appears that these two length scales may model a
vast range of chemical kinetics.
For values of sb which are less than 0.033, the front propagates with a constant,
non-oscillatory velocity. For high values of sI, an abrupt failure occurs.
However, for values of sb larger than 0.033, the front propagates in an oscillatory
manner. For values of sb between 0.033 and 0.053, the formation of unburned
pockets of the reactant behind the shock is recognized as the reason of failure
for high values of sI. Further varying of the two parameters cause the appearance
of other modes of the front propagation.