Session V1: Detonation and Shock-induced Chemistry VIII: Detonation Science

Detonation shock dynamics with an acceleration relation for nitromethane and TATB

The propagation of curved detonation waves has been treated phenomenologically through models of the speed D of a detonation wave as a function of its curvature K, in the Whitham-Bdzil-Lambourn model, also known as detonation shock dynamics. D(K) relations, and the edge angle with adjacent material, have been deduced from the steady shape of detonation waves in long rods and slabs of explosive. Nonlinear D(K) relations have proven necessary to interpret data from charges of different diameter, and even then the D(K) relation may not transfer between diameters. This is an indication that the D(K) relation oversimplifies the kinematics. It is also possible to interpret wave-shape data in terms of an acceleration relation, as used in Brun's Jouguet relaxe model. One form of acceleration behavior is to couple an asymptotic D(K) relation with a time-dependent relaxation toward it from the instantaneous, local speed. This approach is also capable of modeling overdriving of a detonation by a booster. Using archival data for the TATB-based explosive EDC35 and for nitromethane, we found that a simple linear asymptotic D(K) relation with a constant relaxation rate was able to reproduce the experimental wave-shapes better, with fewer parameters, than a nonlinear instantaneous D(K) relation.   

The Transverse Radial Diverging Initiation Behavior of PBX 9502

A series of experiments examining the transverse radial initiation behavior of PBX 9502 has been fielded in a geometric configuration of PBX 9502 acceptor annulus and PBX 9501 donor core. The experiments were specifically designed to examine diverging initiation from the core. For sufficient diameter, the cylindrical donor core initiates the acceptor annulus with behavior akin to typical corner turning with the expected dead zone features. Even though PBX 9501 is significantly more energetic than PBX 9502, the critical initiation diameter is greater than the critical failure diameter of PBX 9502. The behavior of this initiation threshold is studied along with the dynamics of the shock initiating layer between the two dissimilar explosives. Streak camera imaging is used to examine the wave dynamics at the periphery of the PBX 9502 acceptor annulus, and to take measurements of the initiating layer at the material interface for comparison to the analogous behavior in the layered slab geometry. Additionally, proton radiographic imaging is used to examine the complex internal initiation dynamics, and high fidelity reactive flow modeling is used to accurately predict the transverse radial initiation behavior in the geometry of the test.   

Simulations of the Modified Gap Experiment

Modified Gap (Test) Experiment hydrocode simulations are presented. The modified gap experiment is a variation of the large scale gap test (LSGT) experiment. A 50.8-mm diameter x 12.7-mm long disk of sample explosive replaces the confined sample and witness plate in the LSGT. Either a framing camera or a photonic Doppler velocimeter measures the free surface velocity. The free surface velocity is measured for varying levels of input pressure. The Plexiglas gap thickness controls the input pressure. Features of the free surface velocity versus input pressure curve show the pressure at which detonation and ignition thresholds occur. The amount of reaction in various regions of the sample is predicted by the simulations. Additionally, the simulations will predict how the release waves traveling backward into the sample affect the amount of reaction in the sample. Further, simulations of a non-ideal explosive will predict the response of an explosive whose reaction zone length is on the order of the 12.7-mm sample length.   

An Analytical Approach to Obtaining JWL Parameters from Cylinder Tests

An analytical method for determining parameters for the JWL equation of state (EoS) from cylinder test data is described. This method is applied to four datasets obtained from two 20.3 mm diameter EDC37 cylinder tests. The calculated parameters and pressure-volume (p-V) curves agree with those produced by hydro-code modelling. The calculated Chapman-Jouguet (CJ) pressure is 38.6 GPa, compared to the model value of 38.3 GPa; the CJ relative volume is 0.729 for both. The analytical pressure-volume curves produced agree with the one used in the model out to the commonly reported expansion of 7 relative volumes, as do the predicted energies generated by integrating under the p-V curve. The calculated and model energies are 8.64 GPa and 8.76 GPa respectively.   

Geometric Relations for CYLEX Test Tube-Wall Motion

The CYLinder EXpansion (CYLEX) test is a (precision, instrumented, high-purity annealed copper) pipe bomb. Its essential measured quantities are detonation speed and tube-wall motion. Its main purpose is to calibrate detonation product equations of state (EOS) by measuring how product fluid pushes metal. In its full complexity, CYLEX is an integral test, for which EOS calibration requires the entire system to be computationally modeled and compared to salient data. Stripped to its essence, CYLEX is a non-integral test for which one may perform the inverse problem, to infer the EOS directly from data. CYLEX analysis can be simplified by the fact that the test constituents achieve a steady traveling wave structure; this allows derivation of several useful geometric relationships regarding tube wall motion. The first such treatment was by G.I. Taylor. Although his analysis was limited to small wall deflection angles, he asserted that the results remain valid for arbitrary ones. I confirm this attribute and present additional useful relationships. In the past decade, CYLEX wall-motion instrumentation has migrated almost entirely from streak camera to PDV, yet discrepancies remain between the two methods. I further present geometric relationships that shed light on this issue.   

The Los Alamos Gap Stick Test

In this paper we describe a novel shock sensitivity test, the Gap Stick Test, which is a generalized variant of the ubiquitous Gap Test. Despite the popularity of the Gap Test, it has some disadvantages: multiple tests must be fired to obtain a single metric, and many tests must be fired to obtain its value to high precision and confidence. Our solution is a test wherein multiple gap tests are joined in series to form a rate stick. The complex re-initiation character of the traditional gap test is thereby retained, but the propagation speed is steady when measured at periodic intervals, and initiation delay in individual segments acts to decrement the average speed. We measure the shock arrival time before and after each inert gap, and compute the average detonation speed through the HE alone (discounting the gap thicknesses). We perform tests for a range of gap thicknesses. We then plot the aforementioned propagation speed as a function of gap thickness. The resulting curve has the same basic structure as a Diameter Effect (DE) curve, and (like the DE curve) terminates at a failure point. Comparison between experiment and hydrocode calculations using ALE3D and the Ignition and Growth reactive burn model calibrated for short duration shock inputs in PBX 9501 is discussed.   

Detonation Initiation of Heterogeneous Melt-Cast High Explosives

The melt-cast explosives' shock initiation mechanisms are less investigated than pressed and cast-cured ones. If the existence of hot-spots is widely recognized, their formation mechanism is not yet established. We study here two melt-cast explosives, NTO-TNT 60:40 and RDX-TNT 60:40 in order to establish a relation between the microstructure and the reaction rate using a two-phase model based on a ZND approach. Such a model requires the reaction rate, the equations of state of the unreacted phase and of the detonation products and an interaction model between the two phases to describe the reaction zone thermodynamics. The reaction rate law can be written in a factorized form including the number of initiation sites, the explosive's deflagration velocity around hot spots and a function depending on gas volume fraction produced by the deflagration front propagation. The deflagration velocity mainly depends on pressure and is determined from pop-plot tests using the hypothesis of the single curve build-up. This hypothesis has been verified for our two melt-cast explosives. The function depending on gas volume fraction is deduced from microstructural observations and from an analogy with the solid nucleation and growth theory. It has been established for deflagration fronts growing from grain's surface and a given initial grain size distribution. The model requires only a few parameters, calibrated thanks to an inversion method. A good agreement is obtained between experiments and numerical simulations.