Ralph Menikoff

Abstract A computational verification and validation study of the Cyclops I experiment [1–7] was conducted using the Los Alamos Eulerian Applications code xRage [8]. The purpose of this study was to validate the Scaled Unified Reactive Front (SURF) plus (SURFplus) model for insensitive high explosives [9–12]. Diagnostics from the experiment included photon doppler velocimetry measurements of the encasing shell for the device and proton radiography photographs of the explosions. This data was compared to the xRage computed data and a convergence study of burn front evolution was conducted. We conclude that the SURFplus high explosive model does an excellent job at predicting the high explosive burn front velocity and shape with results that converge to the experimental data at rates near to or better than first order in most cases. Some companion verification metrics for the solution convergence are also described. These metrics show that the xRage computed solution for the high explosive burn front converges to first order or better, as consistent with the treatment of shock fronts in a higher order Godunov hydrodynamic solver as used in xRage.

We examine shock, release and reshock into the tri-amino-tri-nitro-benzene (TATB) based explosive PBX 9502 (95% TATB, 5% Kel-F 800) from both an experimental and modeling point of view. The experiments are performed on the 2-stage light gas gun at Los Alamos National Laboratory and are composed of a multi-layered impactor impinging on PBX 9502 backed by a polymethylmethacrylate window. The objective is to initially shock the PBX 9502 in the 7 GPa range (too weak to start significant reaction), then allow a rarefaction fan to release the material to a lower pressure/temperature state. Following this release, a strong second shock will recompress the PBX. If the rarefaction fan releases the PBX to a very low pressure, the ensuing second shock can increase the entropy and temperature substantially more than in previous double-shock experiments without an intermediate release. Predictions from a variety of reactive burn models (AWSD, CREST, Augmented Ignition and Growth, SURF) demonstrate significantly different behaviors and thus the experiments are an excellent validation test of the models, and may suggest improvements for subsequent modeling efforts.

SURF is a high explosive burn model based on the ignition & growth concept of hot-spot reaction. For the TATB based explosive PBX 9502, the model has been calibrated to shock-to-detonation transition experiments. To apply the SURF model for propagating detonation waves, the rate has to be extended to a higher pressure regime than is sampled by shock initiation experiments. The experimentally measured curvature effect - detonation speed as a function of front curvature or D n (κ) - provides the appropriate data for calibrating the propagation regime. The calibration to the curvature effect is based on the ODEs for the reaction zone profile of a detonation wave in conjunction with a shooting algorithm to determine the rate model parameters, for a given κ, needed to obtain a specified detonation speed. A complication for calibrating PBX 9502 rate models arises from the kink in the experimentally measured D n (κ) curve. This results from the fast and slow reactions that TATB exhibits. To account for this, we use an extension of the SURF model that utilises a sequence of two reactions. The first, with a fast rate, is due to molecular decomposition and is described by the original SURF formulation. The second, with a slow rate, is due to carbon clustering and is used to contribute additional energy from the formation of carbon bonds. The wave profile equations are generalised to the SURF-plus model. Model parameters are then determined for the propagation regime to fit the curvature effect data. The extended model is applicable to both the shock initiation regime and the propagating detonation wave regime.

Nitromethane is a liquid explosive. It has been extensively studied as an example of a homogeneous condensed phase explosive. Moreover, small particles can be added to obtain a well characterized heterogeneous explosive for experimental studies of shock initiation due to hot spots. Corresponding mesoscale simulations of hot-spot initiation require a model with a good chemical reaction rate and an equation of state with good thermal properties. Here we describe such a model for nitromethane. Detonation wave properties of the model are compared with experimental data. In addition, we discuss issues with the accuracy to which the CJ pressure can be inferred from the available data and the stability of an underdriven or CJ detonation wave in pure nitromethane.

Heterogeneities sensitize an explosive to shock initiation. This is due to hot-spot formation and the sensitivity of chemical reaction rates to temperature. Here, we describe a numerical experiment aimed at elucidating a mechanism for hot-spot formation that occurs when a shock wave passes over a high-density impurity. The simulation performed is motivated by a physical experiment in which glass beads are added to liquid nitromethane. The impedance mismatch between the beads and the nitromethane results in shock reflections. These, in turn, give rise to transverse waves along the lead shock front. Hot spots arise on local portions of the lead front with a higher shock strength, rather than on the reflected shocks behind the beads. Moreover, the interactions generated by reflected waves from neighboring beads can significantly increase the peak hot-spot temperature when the beads are suitably spaced.

Plastic-bonded explosives are heterogeneous materials. Experimentally, shock initiation is sensitive to small amounts of porosity, due to the formation of hot spots (small localized regions of high temperature). This leads to the Ignition & Growth concept, introduced by Lee and Tarver in 1980, as the basis for reactive burn models. A homogenized burn rate needs to account for three meso-scale physical effects: (i) the density of active hot spots or burn centers; (ii) the growth of the burn fronts triggered by the burn centers; (iii) a geometric factor that accounts for the overlap of deflagration wavelets from adjacent burn centers. These effects can be combined and the burn model defined by specifying the reaction progress variable. lambda = g(s) as a function of a dimensionless reaction length s(t) = r(bc)/l(bc), rather than by specifying an explicit burn rate. The length scale l(bc)(P-s) = [ N-bc(P-s)](-1/3) is the average distance between burn centers, where N-bc is the number density of burn centers activated by the lead shock. The reaction length r(bc)(t) = integral(t)(0) D(P(t'))dt' is the distance the burn front propagates from a single burn center, where D(P) is the deflagration speed as a function of the local pressure and t is the time since the shock arrival. A key implementation issue is how to determine the lead shock strength in conjunction with a shock capturing scheme. We have developed a robust algorithm for this purpose based on the Hugoniot jump condition for the energy. The algorithm utilizes the time dependence of density, pressure and energy within each cell. The method is independent of the numerical dissipation used for shock capturing. It is local and can be used in one or more space dimensions. The burn model has a small number of parameters which can be calibrated to fit velocity gauge data from shock initiation experiments.

We are developing a new high explosive pulsed power (HEPP) system based on the 1.4 m long Ranchero generator which was developed in 1999 for driving solid density z-pinch loads. The new application requires approximately 40 MA to implode similar liners, but the liners cannot tolerate the 65 ¿s, 3 MA current pulse associated with delivering the initial magnetic flux to the 200 nH generator. To circumvent this problem, we have designed a system with an internal start switch and four explosively formed fuse (EFF) opening switches. The integral start switch is installed between the output glide plane and the armature. It functions in the same manner as a standard input crowbar switch when armature motion begins, but initially isolates the load. The circuit is completed during the flux loading phase using post hole convolutes. Each convolute attaches the inner (coaxial) output transmission line to the outside of the outer coax through a penetration of the outer coaxial line. The attachment is made with the conductor of an EFF at each location. The EFFs conduct 0.75 MA each, and are actuated just after the internal start switch connects to the load. EFFs operating at these parameters have been tested in the past. The post hole convolutes must withstand as much as 80 kV at peak dI/dt during the Ranchero load current pulse. We describe the design of this new HEPP system in detail, and give the experimental results available at conference time. In addition, we discuss the work we are doing to test the upper current limits of a single standard size Ranchero module. Calculations have suggested that the generator could function at up to ~120 MA, the rule of thumb we follow (1 MA/cm) suggests 90 MA, and simple flux compression calculations, along with the ~4 MA seed current available from our capacitor bank, suggests 118 MA is the currently available upper limit.

Plastic-bonded explosives (PBX) are heterogeneous materials. Nevertheless, current explosive models treat them as homogeneous materials. To compensate, an empirically determined effective burn rate is used in place of a chemical reaction rate. A significant limitation of these models is that different burn parameters are needed for applications in different regimes; for example, shock initiation of a PBX at different initial temperatures or different initial densities. This is due to temperature fluctuations generated when a heterogeneous material is shock compressed. Localized regions of high temperatures are called hot spots. They dominate the reaction for shock initiation. The understanding of hot spot generation and their subsequent evolution has been limited by the inability to measure transients on small spatial (similar to 1 mu m) and small temporal (similar to 1 ns) scales in the harsh environment of a detonation. With the advances in computing power, it is natural to try and gain an understanding of hot-spot initiation with numerical experiments based on mesoscale simulations that resolve material heterogeneities and utilize realistic chemical reaction rates. However, to capture the underlying physics correctly, such high resolution simulations will require more than fast computers with a large amount of memory. Here we discuss some of the issues that need to be addressed. These include dissipative mechanisms that generate hot spots, accurate thermal properties for the equations of state of the reactants and products, and controlling numerical entropy errors from shock impedance mismatches at material interfaces. The later can generate artificial hot spots and lead to premature reaction. Eliminating numerical hot spots is critical for shock initiation simulations due to the positive feedback between the energy release from reaction and the hydrodynamic flow.

We have started a project to verify and validate ASC codes used to simulate detonation waves in high explosives. Since there are no non-trivial analytic solutions, we are going to compare simulated results with experimental data that cover a wide range of explosive phenomena. The intent is to compare both different codes and different high explosives (HE) models. The first step is to test the products equation of state used for the HE models. For this purpose, the cylinder test, flyer plate and plate-push experiments are being used. These experiments sample different regimes in thermodynamic phase space: the CJ isentrope for the cylinder tests, the isentrope behind an overdriven detonation wave for the flyer plate experiment, and expansion following a reflected CJ detonation for the pate-push experiment, which is sensitive to the Gruneisen coefficient. The results of our findings for PBX 9501 are presented here.

A constitutive model for an explosive consists of three parts: equation of state of reactants, equation of state of products, and reaction rate. In the absence of a good physical theory, models are empirical and based on heuristics. For the HMX based plastic-bonded explosive PBX 9501, three models have previously been calibrated and used in numerical simulations. Here, these three models are compared. They illustrate several generic difficulties with developing and validating models. The available data is insufficient to determine a constitutive model uniquely. Different models can be calibrated to fit the available data yet differ significantly in regions of phase space of importance to applications. Comparing models gives an indication of the uncertainty in model predictions outside the domain of the fitting data.