A Study of Detonation Diffraction in the Ignition-and-Growth Model Page: 4 of 43
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projectile, a detonation is initiated. Our knowledge of the thermo-mechanical behavior of the material over
the broad ranges of pressure and temperature encountered in a detonation is incomplete, and the same is
true of the complex set of reactions that are responsible for the liberation of energy. The morphological
complexity, the dearth of information, and the multi-scale nature of material response are insurmountable
blocks in the way of any attempt at ab-initio modeling of the detonation phenomena, at least at the present
On certain aspects of the problem, however, there is broad agreement. It is known that while the
crystalline explosive possesses a strong ignition threshold, relatively weaker stimuli are sufficient to initiate
the heterogeneous explosive. This propensity is attributed to the creation of a nonuniform temperature
distribution when the heterogeneous aggregate is exposed to the initiating shock. Discrete sites, where the
local temperature far exceeds the bulk average, are generated as a result of mechanical processes such as
friction, pore collapse, shear banding and local plastic deformations. These sites, or hot spots, act as preferred
locations of ignition, where burning commences and then spreads to consume the entire bulk. With this
picture in mind, efforts have been directed at constructing phenomenological, macro-scale, continuum-type
models. These include the Forest-fire model [1, 2], the JTF model  and the HVRB model , but the
most celebrated of the lot is the ignition-and-growth model, originally derived by Lee and Tarver  and
later refined and utilized by Tarver and colleagues [6, 7, 8, 9, 10]. Additional references can be found in the
recent paper by Tarver .
The model treats the explosive as a homogeneous mixture of two distinct constituents: (i) the unreacted
explosive and (ii) the products of reaction. To each constituent is assigned an equation of state, and a
single reaction-rate law is postulated for the conversion of the explosive to products. It is assumed that
the two constituents are always in pressure and temperature equilibrium, and that the energy and volume
of the mixture is the sum of the corresponding quantities for the individual constituents, weighted by the
variable that measures the progress of reaction. The model contains a large number of parameters which are
experimentally calibrated to the explosive of interest.
The model has had considerable success, though less as a tool which, once calibrated to a certain suite of
experiments, has the ability to predict behavior broadly, such as in an entirely different set of experiments.
Rather, its success lies in it providing a framework within which different classes of experiments can be
simulated and studied. While the framework holds firm, each new class of experiments may, and indeed
does, require tuning of the parameters within the general framework. For example, experiments in which the
initiation process is the focus of interest require a significantly different parameter set than experiments that
concern propagation of established detonations [7, 11]. The phenomenology exhibited by the model depends
upon the resolution of the computations as well, and it appears that some of the simulations reported in the
literature are not adequately resolved [12, 13].
Recently the model has been applied to study diffraction of detonations as they turn sharp corners [11, 13].
Experiments suggest that dead zones, or sustained pockets of unreacted material, may appear in the vicinity
of the corners . There appears to be some disagreement in the literature as to exactly what the model
predicts in these situations; studies on similar configurations reach opposite conclusions. For example, in the
so-called hockey-puck geometry, Souers et al  report no sustained dead zones while Tarver  suggests
that the model does capture failure.
The purpose of this paper is to examine in detail the solution set of the model, in the context of diffraction,
to find out exactly what phenomena are contained within the model. We believe that once a model has been
constructed for any physical situation, it is essential that it be thoroughly analyzed, and its properties
exhaustively investigated, so that its strengths and weaknesses are fully understood. Here we proceed by
selecting a single set of parameters for the explosive LX-17, this set having been reported as being more
appropriate for detonation propagation rather than detonation initiation . We examine it analytically for
steady, planar, 1-D solutions and determine the reaction-zone structure of Chapman-Jouguet detonations.
We then carry out a computational study of two classes of problems. The first class corresponds to planar,
1-D initiation by an impact, and the second to corner turning and diffraction in planar and axisymmetric
configurations. The 1-D initiation is interesting in its own right, and one can argue that it should properly
be studied by using the parameter set prescribed for it . However, our purpose here is to employ the
1-D initiation results as a means by which the 2-D results can be profitably interpreted. We find that
there are two generic ways in which 1-D detonations are initiated according to the model, and that these
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Kapila, A K; Schwendeman, D W; Bdzil, J B & Henshaw, W D. A Study of Detonation Diffraction in the Ignition-and-Growth Model, article, April 14, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc901185/m1/4/: accessed October 17, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.