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

Detonation front theories: Using high-resolution DNS to define extended asymptotic scalings and models

When the detonation reaction-zone length, {eta}{sub r}, is short in comparison to the dimensions of the explosive piece being burnt, the detonation can be viewed as a propagating surface (or front) separating burnt from unburnt material. If the product of the shock curvature, {kappa} and {eta}{sub r} is small (i.e., the scaled shock curvature satisfies the {vert_bar}{kappa}{eta}{sub r}{vert_bar} {much_lt} 1), then to leading order the speed of this surface, D{sub n}({kappa}) is a function only of {kappa}. It is in this limit that the original version of the asymptotic detonation front theory, called detonation shock dynamics (DSD), derives the propagation law, D{sub n}({kappa}). In this lecture, the authors compare D{sub n}({kappa})-theory with the results obtained with high-resolution direct numerical simulations (DNS), and then use the DNS results to guide the development of extended asymptotic front theories with enhanced predictive capabilities

A lecture on detonation-shock dynamics

We summarize recent investigations into the theory of multi-dimensional, time-dependent detonation. These advances have led to the development of a theory for describing the propagation of high-order detonation in condensed-phase explosives. The central approximation in the theory is that the detonation shock is weakly curved. Specifically, we assume that the radius of curvature of the detonation shock is large compared to a relevant reaction-zone thickness. Our main findings are: (1) the flow is quasi-steady and nearly one dimensional along the normal to the detonation shock; and (2) the small deviation of the normal detonation velocity from the Chapman-Jouguet (CJ) value is generally a function of curvature. The exact functional form of the correction depends on the equation of state (EOS) and the form of the energy-release law. 8 refs

Extensions to DSD theory: Analysis of PBX 9502 rate stick data

Recent extensions to DSD theory and modeling argue that the intrinsic front propagation law can depend on variables in addition to the total shock-front curvature. Here the authors outline this work and present results of high-resolution numerical simulations of 2D detonation that verify the theory on some points, but disagree with it on others. Chief among these is the verification of the extended propagation laws and the observation that the curvature is infinite at the HE boundary. The authors discuss how these results impact the analysis of PBX 9502

Discrete approximations of detonation flows with structured detonation reaction zones by discontinuous front models: A program burn algorithm based on detonation shock dynamics

In the design of explosive systems the generic problem that one must consider is the propagation of a well-developed detonation wave sweeping through an explosive charge with a complex shape. At a given instant of time the lead detonation shock is a surface that occupies a region of the explosive and has a dimension that is characteristic of the explosive device, typically on the scale of meters. The detonation shock is powered by a detonation reaction zone, sitting immediately behind the shock, which is on the scale of 1 millimeter or less. Thus, the ratio of the reaction zone thickness to the device dimension is of the order of 1/1,000 or less. This scale disparity can lead to great difficulties in computing three-dimensional detonation dynamics. An attack on the dilemma for the computation of detonation systems has lead to the invention of sub-scale models for a propagating detonation front that they refer to herein as program burn models. The program burn model seeks not to resolve the fine scale of the reaction zone in the sense of a DNS simulation. The goal of a program burn simulation is to resolve the hydrodynamics in the inert product gases on a grid much coarser than that required to resolve a physical reaction zone. The authors first show that traditional program burn algorithms for detonation hydrocodes used for explosive design are inconsistent and yield incorrect shock dynamic behavior. To overcome these inconsistencies, they are developing a new class of program burn models based on detonation shock dynamic (DSD) theory. It is hoped that this new class will yield a consistent and robust algorithm which reflects the correct shock dynamic behavior

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