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A lecture on detonation-shock dynamics

Description: 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.
Date: January 1, 1987
Creator: Stewart, D.S. & Bdzil, J.B.
Partner: UNT Libraries Government Documents Department

Modeling two-dimensional detonations with detonation shock dynamics

Description: 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.
Date: January 1, 1988
Creator: Bdzil, J.B. & Stewart, D.S.
Partner: UNT Libraries Government Documents Department

Modeling HE systems using DSD

Description: As a high explosive (HE) ages, those properties of the HE dependent on its global energy-release rate (e.g. shock initiation and detonation propagation speed) are the most likely to be affected. Similarly, any HE replacement will bring with it changes in these same reaction rate dependent characteristics of the HE, in that the new material will not be identical to that being replaced. In this paper the authors describe how detonation shock dynamics (DSD) theory can be used to model how changes in the energy-release rate (as they are embodied in the HE`s detonation speed vs curvature relation) influence the speed of detonation propagation and in turn the performance of a system.
Date: December 1, 1997
Creator: Aslam, T.D. & Bdzil, J.B.
Partner: UNT Libraries Government Documents Department

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

Description: 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.
Date: February 1, 1998
Creator: Aslam, T.D. & Bdzil, J.B.
Partner: UNT Libraries Government Documents Department

Engineering models of deflagration-to-detonation transition

Description: 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.
Date: July 1995
Creator: Bdzil, J. B. & Son, S. F.
Partner: UNT Libraries Government Documents Department

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

Description: 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 ...
Date: April 14, 2006
Creator: Kapila, A K; Schwendeman, D W; Bdzil, J B & Henshaw, W D
Partner: UNT Libraries Government Documents Department

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

Description: 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.
Date: February 2, 1999
Creator: Bdzil, J.B.; Jackson, T.L. & Stewart, D.S.
Partner: UNT Libraries Government Documents Department

Front curvature rate stick measurements and detonation shock dynamics calibration for PBX 9502 over a wide temperature range

Description: Detonation velocity and wave shape are measured for PBX 9502 (95 wt.% TATB, 5 wt.% Kel-F 800) rate sticks at the temperatures {minus}55, 25, and 75 C. At each temperature three different diameters were fired: 50 mm, 18 mm, and 8, 10, and 12 mm respectively for the hot, ambient, and cold sticks. The measured wave shapes are fit with an analytic form and the fitting parameters are tabulated along with thermal expansion and diameter effect data. The simplest detonation shock dynamics (DSD) model assumes a unique calibration function relating the local normal wave speed D{sub n} to the local total curvature {kappa}. The data confirm this notion for sufficiently small curvature, but at large curvature the curves for different charge diameters diverge. Global optimization is used to determine a best single D{sub n}-{kappa} function at each initial temperature T{sub 0}. From these curves a D{sub n}({kappa},T{sub 0}) calibration surface is generated that allows computation of problems with temperature gradients.
Date: December 31, 1998
Creator: Hill, L.G.; Bdzil, J.B. & Aslam, T.D.
Partner: UNT Libraries Government Documents Department

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

Description: 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.
Date: December 31, 1998
Creator: Aslam, T.D.; Bdzil, J.B. & Hill, L.G.
Partner: UNT Libraries Government Documents Department

Inert plug formation in the DDT of granular energetic materials

Description: A mechanism is proposed to explain the {open_quotes}plugs{close_quotes} that have been observed in deflagration-to-detonation transition (DDT) of granular explosives. Numerical simulations are performed that demonstrate the proposed mechanism. Observed trends are reproduced.
Date: September 1, 1995
Creator: Son, S.F.; Asay, B.W. & Bdzil, J.B.
Partner: UNT Libraries Government Documents Department

Modeling DDT in granular explosives with a multi-dimensional hydrocode

Description: 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.
Date: September 1, 1995
Creator: Kober, E.M.; Bdzil, J.B. & Son, S.F.
Partner: UNT Libraries Government Documents Department

Curved detonation fronts in solid explosives: Collisions and boundary interactions

Description: Detonation Shock Dynamics (DSD) can be used to model the effects that shock curvature, {kappa}, has oil detonation speed, D{sub n}({kappa}). At the edges of the explosive, D{sub n}({kappa}) is supplemented with boundary conditions. By direct numerical simulation (DNS). The authors study how the reaction zone interacts with the edge. DSD theory has been integrated with the level-set method of Osher and Sethian and the Los Alamos DNS code Mesa to create a powerful tool for simulating complex explosive containing systems.
Date: September 1995
Creator: Bdzil, J. B.; Aslam, T. D. & Stewart, D. S.
Partner: UNT Libraries Government Documents Department

Synchro-ballistic recording of detonation phenomena

Description: Synchro-ballistic use of rotating-mirror streak cameras allows for detailed recording of high-speed events of known velocity and direction. After an introduction to the synchro-ballistic technique, this paper details two diverse applications of the technique as applied in the field of high-explosives research. In the first series of experiments detonation-front shape is recorded as the arriving detonation shock wave tilts an obliquely mounted mirror, causing reflected light to be deflected from the imaging lens. These tests were conducted for the purpose of calibrating and confirming the asymptotic Detonation Shock Dynamics (DSD) theory of Bdzil and Stewart. The phase velocities of the events range from ten to thirty millimeters per microsecond. Optical magnification is set for optimal use of the film`s spatial dimension and the phase velocity is adjusted to provide synchronization at the camera`s maximum writing speed. Initial calibration of the technique is undertaken using a cylindrical HE geometry over a range of charge diameters and of sufficient length-to-diameter ratio to insure a stable detonation wave. The final experiment utilizes an arc-shaped explosive charge, resulting in an asymmetric detonation-front record. The second series of experiments consists of photographing a shaped-charge jet having a velocity range of two to nine millimeters per microsecond. To accommodate the range of velocities it is necessary to fire several tests, each synchronized to a different section of the jet. The experimental apparatus consists of a vacuum chamber to preclude atmospheric ablation of the jet tip with shocked-argon back lighting to produce a shadow-graph image.
Date: September 1, 1997
Creator: Critchfield, R.R.; Asay, B.W.; Bdzil, J.B.; Davis, W.C.; Ferm, E.N. & Idar, D.J.
Partner: UNT Libraries Government Documents Department

Weakly nonlinear dynamics of near-CJ detonation waves

Description: 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.
Date: January 1, 1993
Creator: Bdzil, J.B. (Los Alamos National Lab., NM (United States)) & Klein, R. (Technische Hochschule Aachen (Germany). Inst. fuer Technische Mechanik)
Partner: UNT Libraries Government Documents Department