What role do instabilities have on detonation limits?

The key question in detonation research is being able to predict limits. How easy is it to initiate a detonation? What are the limits of propagation in the presence of attenuating boundary conditions?

Most models developed over the past decades rely on one-dimensional formulations - resulting in simple models. Nevertheless, detonations in reality are plagued by instability, which takes the form of cellular structures in gases and localized heterogeneities involving hot spots in condensed media.

The question that arises, is what role do these non-homogeneities have on the limits of detonations?

A very recent study from Li, Mi and Higgins tackles this central issue in detonation science. By introducing non-heterogeneities in their explosive medium, they find that the detonation limits become wider. Localized unsteady effects sensitize the propagation of detonations.

The problem they address is the detonation propagation in a unconfined charge, the so-called critical tube problem. Owing to the lack of confinement, the gases undergoing reaction expand laterally. If the charge is too small, the lateral expansion is too strong and the detonation may quench.

The figure below shows their set-up. They consider a homogeneous charge bounded by an inert medium. They monitor the propagation of the detonation. The detonation front takes on its characteristic curved structure, which is due to the lateral expansion of the reactive gases into the inert layer.

The curved detonation wave propagating to the right in a channel confined by an inert medium.
They then consider the same problem in a charge in which periodic ripples of density have been introduced (as seen below), while not altering the energy content of the mixture. As expected, the ripples trigger a cellular type instability.
The curved detonation wave propagating to the right in a channel confined by an inert medium; the reactive medium has density non-homogeneities, which trigger frontal instabilities.

The authors find that the instability makes the front more resilient to the failure process. The detonation wave can propagate in charges of dimension smaller than the homogeneous case. In same charge sizes, the detonation with triggered instability displays wave speeds higher than the homogeneous one, closer to the ideal value of loss-less detonation.
The detonation wave speed V dependence on channel thickness t for homogeneous and heterogeneous detonations; L1/2 denotes the reaction zone thickness and VCJ the ideal detonation speed; the limit of propagation corresponds to the channel thickness at which the speed suddenly drops.

Experiments seem to confirm these findings, as for example determined by Radulescu and Lee (2002) in leaky tubes and by Lee et al. (2013) in narrow channels with boundary losses.

Nevertheless, the issue is not yet closed, however.  There is also evidence pointing in the opposite direction.  Sow et al. (2014) look at the limit of 1D detonations with friction in the presence of pulsating instabilities. They find that pulsating detonations are more prone to failure as predicted without account of pulsations.  Radulescu et al. (2007) find that cellular detonations without dissipation are more difficult to ignite with a perturbed shock then by a homogeneous shock.  The role of dissipative effects remains to be further explored.  More to come on this subject from our group. 

Stay tuned...

An abridged version of my unpublished work can be found here:
Radulescu, M. I., Sharpe, G. J., Law, C. K. Effect of cellular instabilities on the blast initiation of weakly unstable detonations.  20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Poitiers, France, August 2007.  
- email me for the paper matei@uottawa.ca.

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