A Study of Detonation Diffraction in the Ignition-and-Growth Model Page: 5 of 43
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scenarios play a part in the post-diffraction evolution as well. We find, in particular, that for the parameter
set under study the model does show detonation failure, but only locally and temporarily, and that it does
not generate sustained dead zones. Our computations employ adaptive mesh refinement following the work
by Henshaw and Schwendeman , and are finely resolved. To our knowledge diffraction computations
for condensed explosives at such high resolution have not appeared in the literature. In the gaseous phase,
however, high-resolution diffraction computations do exist; see, in particular, Arienti and Shepherd .
Our results are obtained for a rigid confinement of the explosive. Compliant confinement, representing its
own computational challenges, will alter the results to some extent and is currently under study. Also under
development is an extended ignition-and-growth model which takes into account observed desensitization of
heterogeneous explosives by weak shocks.
The framework of the model is presented in section 2. Steady traveling waves are investigated in section 3,
including shock conditions, Hugoniot curves and the Chapman-Jouguet state. The equation set is rendered
dimensionless in section 4. Section 5 displays the LX-17 data set, and the corresponding Hugoniots and
reaction-zone profiles for the CJ detonations. Section 6 outlines the numerical method. The 1-D shock-
initiation problem is investigated in section 7, and the planar and axisymmetric diffraction problems in
sections 8 10. The paper ends with conclusions drawn in section 11.
2 The Model
2.1 Equations of State
The ignition-and-growth model treats the heterogeneous explosive as a homogeneous mixture of two con-
stituents: (i) the unreacted explosive and (ii) the reaction products. The consequences of microstructural
heterogeneity, not reflected in the thermo-mechanical description, are accounted for in an impressionistic
way, as we shall see, in the formulation of the reaction rate. Separate JWL equations of state  are pre-
scribed for each constituent; the equation of state for the reactant is fitted to the available shock Hugoniot
data and the product equation of state to data from cylinder test and other metal acceleration experiments
. These equations have the following mechanical and thermal forms.
ES = psis -F(v8) + F(1), (1)
Eg = - Fg(vg) - Q. (2)
Ws = [Os T + 5,(Vs) + Fy(vy)] (3)
pg = [Ogg+5gvg)5g~v)].(4)
Here, the subscript s refers to the unreacted solid explosive and g to the gaseous products of reaction, p2
is the pressure and T the temperature of constituent i. The quantity v2 , appearing in the arguments of
the functions fl and C , is the specific volume of constituent i scaled by a reference volume vs0 , i.e.,
v2 = v2/vo . We choose v50 to be the specific volume of the solid reactant in the ambient state. In the
equations of state the energies E2 are in units of energy per unit volume of the unreacted solid , and are
related to the specific energies per unit mass, 2 , by
e =vsE1, i = s or g. (5)
The energy of detonation is denoted by Q, and the constant F,(1) has been added to the right-hand side
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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/m1/5/: accessed November 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.