Session C1: Detonation and Shock-induced Chemistry II: Reactive Burn Models

Modeling of the Jack Rabbit Series of Experiments with a temperature-based reactive burn mode

A reactive burn model based on shocked explosive temperature has been presented at the previous joint AIRAPT/APS-SCCM in Seattle. It has been shown that the temperature of the unburnt shocked explosive is a good candidate to drive rate laws of decomposition. Such models are able to reproduce the evolution of the sensitivity of explosives with porosity. They also predict a drastic reduction of the reactivity in the case of multi-shock compression without any bolt-on desensitization model. In this work, we apply our temperature-based reactive burn model to the data of the Jack Rabbit Series of Experiments. Indeed, these experiments dedicated to the study of detonation wave corner turning and shock desensitization in LX-17 are harsh tests for reactive burn models. Details of our model together with preliminary results will be shown.   

Calibration of reaction rates for the CREST reactive-burn model

In recent years, the hydrocode-based CREST reactive-burn model has had success in modelling a range of shock initiation and detonation propagation phenomena in polymer bonded explosives. CREST uses empirical reaction rates that depend on a function of the entropy of the non-reacted explosive, allowing the effects of initial temperature, porosity and double-shock desensitisation to be simulated without any modifications to the model. Until now, the sixteen reaction-rate coefficients have been manually calibrated by trial and error, using hydrocode simulations of a subset of sustained-shock initiation gas-gun experiments and the detonation size-effect curve for the explosive. This paper will describe the initial development of an automatic method for calibrating CREST reaction-rate coefficients, using the well-established Particle Swarm Optimisation (PSO) technique. The automatic method submits multiple hydrocode simulations for each ``particle'' and analyses the results to determine the ``misfit'' to gas-gun and size-effect data. Over $\sim$40 ``generations,'' the PSO code finds a best set of reaction-rate coefficients that minimises the misfit. The method will be demonstrated by developing a new CREST model for EDC32, a conventional high explosive.   

An explanation for the anomalous wave profiles obtained in Composition B-3 impacted by flat nosed steel rods

When firing flat nosed steel rods into the 60/40 RDX/TNT explosive Composition B-3, Gustavsen et al.(``Initiation of Composition B-3 by impact of flat nosed rods,'' in 15$^{th}$ Int. Det. Symp.) found an apparently anomalous ``hump'' in particle velocity wave profiles. The hump occurred on the center-line established by the rod, and at relatively late times, $>$ 1 $\mu$s, after detonation onset. Several explanations, including that of a late time reaction, were postulated. This report will present evidence that the anomalous late time ``hump'' is due to the arrival of rarefaction waves from the rod periphery. Simple analytic calculations and reactive-burn hydro-code calculations will be presented supporting this hypothesis.   

Pseudo-Reaction Zone model calibration for Programmed Burn calculations

The Programmed Burn (PB) engineering methodology for efficiently calculating detonation timing and energy delivery within high explosive (HE) engineering geometries separates the calculation of these two core components. Modern PB approaches utilize Detonation Shock Dynamics (DSD) to provide accurate time-of-arrival information throughout a given geometry, via an experimentally calibrated propagation law relating the surface normal velocity to its local curvature. The Pseudo-Reaction Zone (PRZ) methodology is then used to release the explosive energy in a finite span following the prescribed arrival of the DSD propagated front through a reactive, hydrodynamic calculation. The PRZ energy release rate must be coupled to the local burn velocity set by the DSD surface evolution. In order to synchronize the energy release to the attendant timing calculation, detonation velocity and front shapes resulting from reactive burn simulations utilizing the PRZ rate law and parameters will be fitted to analogues generated via the applied DSD propagation law, thus yielding the PRZ model calibration for the HE.   

Numerical simulation study on thermal response of PBX explosive by low velocity impact

It is a great threat for both bare dynamite and shell charge when subjected to low velocity impact involved in traffic accidents or charge piece drops. The impact sensitivity is an important index in evaluating the safety and performance of explosives. The Steven Test is an effective tool to evaluate the relative sensitivity of various explosives. In 1993, Chidester et al. preliminarily designed the Steven Test, and then applied it to delay detonation (XDT) phenomenon study. Subsequently, a series of low velocity impact Steven Tests on HMX based explosives were carried out by S K Chidester, D J Idar, R J Scammon, S Wortley et al. In this paper, we built the numerical simulation method involving mechanical, thermo and chemical properties of Steven Test based on the thermo-mechanical coupled material model. In the model, the stress-strain relationship is described by dynamic plasticity model, the thermal effect of the explosive induced by impact is depicted by isotropic thermal material model, the chemical reaction of explosives is described by Arrhenius reaction rate law, and the effects of heating and melting on mechanical properties and thermal properties of materials are also taken into account. Specific to the standard Steven Test, the thermal and mechanical response rules of PBX9501 at different impact velocities were numerical analyzed, and the threshold velocity of explosive initiation was obtained. In addition, the effect of confine condition of test device to the threshold velocity was explored.   

Cell Length Independent PBRB Model for Simulations of HE Reaction Initiation, Growth, and Detonation

It has been our focus to use the Physics Based Reaction Burn (PBRB) model to simulate reaction initiation, growth, and detonation of HE composites at the mesoscale. The idealization of hot spots as planar surfaces reduces the 3D model to a 1D hot spot cell (1DHSC) model. The idealization also renders the model dependent on the 1DHSC length and mesh size. New developments are presented making the PBRB model 1DHSC length independent. First, the accurate prediction of the gas-solid interface temperature and thermal gradient are essential, achieved through a finite difference scheme with 500-2000 thermal grid points. Second, keeping the burn mass constant while varying the 1DHSC length is essential, achieved by varying the hot spot specific surface area. 1D and 2D simulation results are presented for shock response of RDX at 1 km/s and 2 km/s impact velocities. The 5, 10, and 50 micro meters 1DHSC lengths yield near identical run-to-detonation, time-to-detonation, and detonation velocity in agreement with experimental data. It is concluded that the new developments make the PBRB model well suited as a generic EOS model for HE composites. -- Dr. John Brennan, ARL is acknowledged for his interactions and support.