Ralph Menikoff

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.

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.

Forest fire is a burn model for reactive hydro simulations that is widely used to describe both initiation and propagation of detonation waves in solid high explosives. Here we thoroughly review the assumptions of the model. In analogy with Whitham-Chisnell shock dynamics, we derive the Forest fire rate based on a characteristic analysis of a shock-to-detonation transition. Code issues with implementing the Forest fire model are also discussed. The analysis leading to the Forest fire rate is more general than the simplifying assumptions used by the model. The Forest fire analysis provides important constraints needed for any burn model to fit shock initiation data. This data is fundamental to ignition sensitivity of high explosives.

For a planar detonation wave propagating in the plastic-bonded explosive PBX 9501, measurements of the reaction zone display a classical ZND profile. Moreover, the reaction-zone width is substantially less than the average size of an explosive grain. We show that the reaction zone is compatible with realistic constitutive properties and an Arrhenius reaction rate based on the bulk temperature. Thus, contrary to conventional wisdom, hot spots are not needed to propagate a detonation wave. Conventional wisdom is based, in part, on shock desensitization experiments; the observation that precompressing a PBX with a weak shock - which eliminates voids as nucleation sites for hot spots - can quench a propagating detonation wave. By analysing the temperature behind two shocks compared to a single shock and the corresponding change of the induction time, we show that a detonation wave sustained by the bulk reaction rate from shock heating is compatible with shock desensitization. Shock desensitization depends on having a temperature sensitive rate, which usually is associated with detonation wave instability. However, for PBX 9501 the temperature variation in the reaction zone is small, and one-dimensional simulations show that this results in a stable detonation wave. Furthermore, we show that two additional phenomena are compatible with the perspective that bulk burn can sustain a planar detonation wave: failure diameter, which does depend on the heterogeneous structure of a PBX; and PBXs with a lower HE content which display an irregular detonation front.