A Study of Detonation Diffraction in the Ignition-and-Growth Model

Heterogeneous high-energy explosives are morphologically, mechanically and chemically complex. As such, their ab-initio modeling, in which well-characterized phenomena at the scale of the microstructure lead to a rationally homogenized description at the scale of observation, is a subject of active research but not yet a reality. An alternative approach is to construct phenomenological models, in which forms of constitutive behavior are postulated with an eye on the perceived picture of the micro-scale phenomena, and which are strongly linked to experimental calibration. Most prominent among these is the ignition-and-growth model conceived by Lee and Tarver. The model treats the explosive as a homogeneous mixture of two distinct constituents, the unreacted explosive and the products of reaction. To each constituent is assigned an equation of state, and a single reaction-rate law is prescribed for the conversion of the explosive to products. It is assumed that the two constituents are always in pressure and temperature equilibrium. The purpose of this paper is to investigate in detail the behavior of the model in situations where a detonation turns a corner and undergoes diffraction. A set of parameters appropriate for the explosive LX-17 is selected. The model is first examined analytically for steady, planar, 1-D solutions and the reaction-zone structure of Chapman-Jouguet detonations is determined. A computational study of two classes of problems is then undertaken. The first class corresponds to planar, 1-D initiation by an impact, and the second to corner turning and diffraction in planar and axisymmetric geometries. The 1-D initiation, although interesting in its own right, is utilized here as a means for interpretation of the 2-D results. It is found that there are two generic ways in which 1-D detonations are initiated in the model, and that these scenarios play a part in the post-diffraction evolution as well. For the parameter set under study the model shows detonation failure, but only locally and temporarily, and does not generate sustained dead zones. The computations employ adaptive mesh refinement and are finely resolved. Results are obtained for a rigid confinement of the explosive. Compliant confinement represents its own computational challenges 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