|
Talk Abstract:
Detonation Evolution due to an Initial Disturbance
Ashwani
K. Kapila
Department of Mathematics
Rensselaer Polytechnic Institute
kapila@rpi.edu
A homogeneous explosive system will detonate only when a suitable
spatially-varying disturbance is impressed upon it. Such a disturbance
may be imposed across a boundary (e.g., thermal loading or mechanical
impact) or as an initial state (e.g., a nonuniformity in temperature
or concentration). Spatial nonuniformities may also emerge naturally
as a part of the evolutionary process, as in the transition
of a laminar flame into a turbulent flame brush. For thermally
sensitive reaction rates and relatively simple kinetics, and
for a variety of imposed disturbances, the initiation process
has been the subject of a number of theoretical studies, asymptotic
as well as numerical. Perhaps the simplest model problem considered
is the one suggested and first studied by Zeldovich et al: a
system in which an initial temperature gradient is imposed.
This paper surveys the existing studies of this problem and
supplements them with new results. The intent is to present
a detailed and coherent description of the various initiation
scenarios that are possible, depending upon the size of the
gradient, the extent of the confinement, and the physico-chemical
parameters of the system.
It is shown that depending upon the parameters, a conventional,
ZND detonation may emerge essentially in one of two ways. For
relatively shallow initial gradients, the path to detonation
begins with an induction period that culminates in a localized,
constant-volume thermal explosion at the hot wall. A
supersonic, shockless, weak detonation (the so-called Zeldovich
Spontaneous Wave) emerges from the site of the explosion and
proceeds towards the cold wall, decelerating as it does so.
When the wave speed falls to the CJ value, a weak shock is born
at the rear of the reaction zone. It strengthens, and
moves to the front of the reaction zone with extreme rapidity,
thereby generating the ZND structure.
For relatively moderate initial gradients, the induction process,
now confined to a thin boundary layer near the hot wall, culminates
in a localized constant-pressure explosion. Expansion
within the explosive boundary layer creates a compressive pulse
outside it, which steepens into a weak shock. The system now
consists of the lead shock followed by an induction zone in
which the pressure rises, which in turn is followed by a fast,
diffusionless deflagration where the pressure falls and a bulk
of the chemical activity occurs. If the initial gradient is
too steep, the fast flame and the lead shock remain uncoupled,
the separation between them increases, and the detonation fails
to materialize. Otherwise, the pressure peak behind the lead
shock grows stronger. It either strengthens the lead shock itself,
thereby merging the fast flame and the lead shock and leading
to a conventional detonation, or else, there occurs a constant-volume
explosion some distance behind the lead shock. This explosion
leads to a detonation by the procedure described above for shallow
gradients, which overtakes the lead shock.
The manner in which the above scenarios are affected by flow
divergence is examined as well.
Material used during the talk
Back to Workshop Schedule
|
