Interactions of inert confiners with explosives

The deformation of an inert confiner by a steady detonation wave in an adjacent explosive is investigated for cases where the confiner is suciently strong (or the explosive suciently weak) such that the overall change in the sound speed of the inert is small. A coupling condition which relates the pressure to the deflection angle along the explosive-inert interface is determined. This includes its dependence on the thickness of the inert, for cases where the initial sound speed of the inert is less than or greater than the detonation speed in the explosive (supersonic and subsonic inert ows, respectively). The deformation of the inert is then solved by prescribing the pressure along the interface. In the supersonic case, the detonation drives a shock into the inert, subsequent to which the ow in the inert consists of alternating regions of compression and tension. In this case reverberations or `ringing' occurs along both the deflected interface and outer edge of the inert. For the subsonic case, the flow in the interior of the inert is smooth and shockless. The detonation in the explosive initially defl ects the smooth interface towards the explosive. For sufficiently thick inerts in such cases, it appears that the deflection of the confiner would either drive the detonation speed in the explosive up to the sound speed of the inert or drive a precursor wave ahead of the detonation in the explosive. Transonic cases, where the inert sound speed is close to the detonation speed, are also considered. It is shown that the confinement affect of the inert on the detonation is enhanced as sonic conditions are approached from either side

Steady non-ideal detonations in cylindrical sticks of expolsives

Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High resolution simulations are then used to investigate the qualitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry

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

Perturbation methods applied to problems in detonation physics

A theoretical study of an explosive which releases a small fraction of its total energy via resolved reactions is presented. Two separate problems are treated. First a time-dependent one-dimensional unsupported detonation is considered. It is shown that the detonation is a reactive simple wave. The particle velocity profiles are calculated for a model explosive. Second, the detonation edge effect for a steady-state semi-infinite unconfined detonation is considered. It is shown that the near-field flow is dominated by the Prandtl--Meyer singularity, whereas the far-field flow is controlled by the reactivity and streamline divergence. The shock locus, sonic locus, and limiting characteristic are calculated and the effects of confinement are discussed

Weakly nonlinear dynamics of near-CJ detonation waves

The renewed interest in safety issues for large scale industrial devices and in high speed combustion has driven recent intense efforts to gain a deeper theoretical understanding of detonation wave dynamics. Linear stability analyses, weakly nonlinear bifurcation calculations as well as full scale multi-dimensional direct numerical simulations have been pursued for a standard model problem based on the reactive Euler equations for an ideal gas with constant specific heat capacities and simplified chemical reaction models. Most of these studies are concerned with overdriven detonations. This is true despite the fact that the majority of all detonations observed in nature are running at speeds close to the Chapman-Jouguet (CJ) limit value. By focusing on overdriven waves one removes an array of difficulties from the analysis that is associated with the sonic flow conditions in the wake of a CJ-detonation. In particular, the proper formulation of downstream boundary conditions in the CJ-case is a yet unsolved analytical problem. A proper treatment of perturbations in the back of a Chapman-Jouguet detonation has to account for two distinct weakly nonlinear effects in the forward acoustic wave component. The first is a nonlinear interactionof highly temperature sensitive chemistry with the forward acoustic wave component in a transonic boundary layer near the end of the reaction zone. The second is a cumulative three-wave-resonance in the sense of Majda et al. which is active in the near-sonic burnt gas flow and which is essentially independent of the details of the chemical model. In this work, we consider detonations in mixtures with moderate state sensitivity of the chemical reactions. Then, the acoustic perturbations do not influence the chemistry at the order considered and we may concentrate on the second effect; the three-wave resonance

Engineering models of deflagration-to-detonation transition

For the past two years, Los Alamos has supported research into the deflagration-to-detonation transition (DDT) in damaged energetic materials as part of the explosives safety program. This program supported both a theory/modeling group and an experimentation group. The goal of the theory/modeling group was to examine the various modeling structures (one-phase models, two-phase models, etc.) and select from these a structure suitable to model accidental initiation of detonation in damaged explosives. The experimental data on low-velocity piston supported DDT in granular explosive was to serve as a test bed to help in the selection process. Three theoretical models have been examined in the course of this study: (1) the Baer-Nunziato (BN) model, (2) the Stewart-Prasad-Asay (SPA) model and (3) the Bdzil-Kapila-Stewart model. Here we describe these models, discuss their properties, and compare their features

Modeling two-dimensional detonations with detonation shock dynamics

In any explosive device, the chemical reaction of the explosive takes place in a thin zone just behind the shock front. The finite size of the reaction zone is responsible for: the pressure generated by the explosive being less near the boundaries, for the detonation velocity being lower near a boundary than away from it, and for the detonation velocity being lower for a divergent wave than for a plane wave. In computer models that are used for engineering design calculations, the simplest treatment of the explosive reaction zone is to ignore it completely. Most explosive modeling is still done this way. The neglected effects are small when the reaction zone is very much smaller than the explosive's physical dimensions. When the ratio of the explosive's detonation reaction-zone length to a representative system dimension is of the order of 1/100, neglecting the reaction zone is not adequate. An obvious solution is to model the reaction zone in full detail. At present, there is not sufficient computer power to do so economically. Recently we have developed an alternative to this standard approach. By transforming the governing equations to the proper intrinsic-coordinate frame, we have simplified the analysis of the two-dimensional reaction-zone problem. When the radius of curvature of the detonation shock is large compared to the reaction-zone length, the calculation of the two-dimensional reaction zone can be reduced to a sequence of one-dimensional problems. 9 refs., 5 figs

Modeling DDT in granular explosives with a multi-dimensional hydrocode

We describe results obtained with the implementation of a new large drag limit, two-phase continuum mixture model of DDT into MESA2D. The kinetics scheme originally described by BN is used to simulate a suite of 1D and 2D experiments. The BN kinetics scheme is found to be inadequate