The authors were tasked with writing a concise memo (now a short report) that adequately addresses the current ``state-of-the-art'' in the field of reactive flow modeling and burn models for mid-year 2025, along with identifying some of the modeling gaps. It is assumed that the reader has experience with burn models and running hydrocode simulations, and thus every effort is made to ensure brevity, clarity, and utility, so that this document will serve as a quick and useful reference. Note that
Mesoscale modeling of shock waves in Ni+Al multilayers poses significant challenges that are due, in part, to shock-induced chemical reactions. Current modeling approaches utilize reactive molecular dynamics (MD), but they are limited to resolving domains of only a few hundred nanometers. In contrast, actual multilayer superlattices can be tens of micrometers thick, and they exhibit non-ideal (i.e., wavy) interfaces. The second part of our research builds upon previous work developing physically based, thermodynamically complete equations of state for various Ni and Al intermetallic compositions. Here, we introduce a novel workflow for high-fidelity mesoscale simulations of Ni+Al multilayers using a continuum hydrocode. By increasing the simulation domain size beyond MD limitations (e.g., 2 × 6 μm2) and incorporating explicit interfacial roughness, we investigate the shock response of Ni+Al multilayers at previously unexplored scales. Our experimental design encompasses nine multilayer geometries with varying roughness amplitudes and tilt angles (θ = 15°, 30°, and 45°), alongside 19 flyer impact velocities ranging from 0.3 to 3.0 km/s, resulting in a total of 171 high-fidelity simulations. The bulk shock state from inert 2D mesoscale simulations aligns with the law of mixtures, while temperature and pressure fluctuations strongly correlate with multilayer geometry types. A new metric dubbed the “hot spot probability integral” shows a greater dependence on a tilt angle than interfacial roughness.
Continuum shock mixture models are reviewed and applied to determine the equations of state for five different compositions of Ni xAl y, as well as bulk Ni+Al reactive multilayers, by combining the fundamental property data for elemental nickel and aluminum. From the literature, we down-select and evaluate two analytical models for the mixture Hugoniot, i.e., the well-known method of kinetic energy averaging (KEA) and a recent model proposed by Jordan and Baer [J. Appl. Phys. 111, 083516 (2012)]. Fundamentally, the former method assumes pressure equilibrium, whereas the latter assumes a common particle velocity and mixture sound speed from compressible two-phase cavitating flows. Additionally, we construct thermodynamically complete equations of state by fitting Einstein oscillator series models for the specific heat at constant volume. Finally, the solid solution approximation is invoked for intermetallic compositions, which are not strictly physical mixtures. Overall, the KEA model provides a better fit to the available Ni xAl y and Ni+Al multilayer shock compression data; however, there are combinations of material properties where the performance of these two models is thought to be reversed. Moreover, the results of this work include the first analytical solution of Jordan–Baer that does not require numerical root finding, as well as proposed modifications to the Einstein oscillator series to incorporate some effects of local pressure–temperature equilibrium and reaction–diffusion. Future work is planned that will use these equations of state in mesoscale simulations to study shock-induced reaction in Ni+Al multilayers, and the intended application is illustrated with a brief 2D hydrocode example.
Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. In this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy ZS, and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. In this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy ZS, and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
There has always been a desire to port high-fidelity reactive flow models from one code to another. For example, the AWE reactive burn model known as CREST has been or is being implemented in several of the U.S. Department of Energy hydrocodes. Those involved with reactive burn model implementation recognize the challenges immediately, e.g., Eulerian versus Lagrangian frameworks, the form of the equation of state, the closure relations, etc. In this work, we report the development of the CREST reactive burn model in CTH, a multidimensional, multi-material hydrocode developed by Sandia National Laboratories, following an earlier implementation shown at the last International Detonation Symposium. Results include code-to-code comparisons between CTH and the AWE hydrocode PERUSE, focusing on the simulated particle velocity histories during a shock-to-detonation transition, and corresponding to previous gas gun impact experiments as well as new model verification studies. Lessons learned are provided, including discussions of the numerical accuracy, in addition to the role of artificial viscosity and artificial viscous work. Finally, simulation results are shown to compare the Snowplough versus P-Alpha porosity model options.
Explosives exposed to conditions above the Chapman-Jouget (CJ) state exhibit an overdriven response that is transient. Reactive flow models are often fit to the CJ conditions, and they transition to detonation based on inputs lower than or near CJ, but these models may also be used to predict explosive behavior in the overdriven regime. One scenario that can create a strongly overdriven state is a Mach stem shock interaction. These interactions can drive an already detonating or transitioning explosive to an overdriven state, and they can also cause detonation at the interaction location where the separate shocks may be insufficient to detonate the material. In this study, the reactive flow model XHVRB utilizing a Mie-Grüneisen equation of state (EOS) for the unreacted explosive, and a Sesame table for the reacted products, will be used to examine Mach stem interactions from multi-point detonation schemes in CTH. The effect of the overdriven response driven by PETN-based explosive pellets will be tracked to determine the transient detonation behavior, and the predicted states from the burn model will be compared to previously published data.
Vapor-deposited PETN films undergo significant microstructure evolution when exposed to elevated temperatures, even for short periods of time. This accelerated aging impacts initiation behavior and can lead to chemical changes as well. In this study, as-deposited and aged PETN films are characterized using scanning electron microscopy and ultra-high performance liquid chromatography and compared with changes in initiation behavior measured via a high-throughput experimental platform that uses laser-driven flyers to sequentially impact an array of small explosive samples. Accelerated aging leads to rapid coarsening of the grain structure. At longer times, little additional coarsening is evident, but the distribution of porosity continues to evolve. These changes in microstructure correspond to shifts in the initiation threshold and onset of reactions to higher flyer impact velocities.
There has always been a desire to port high-fidelity reactive flow models from one code to another. For example, the AWE reactive burn model known as CREST has been or is being implemented in several of the U.S. Department of Energy hydrocodes. Those involved with reactive burn model implementation recognize the challenges immediately, e.g., Eulerian versus Lagrangian frameworks, the form of the equation of state, the closure relations, etc. In this work, we report the development of the CREST reactive burn model in CTH, a multidimensional, multi-material hydrocode developed by Sandia National Laboratories, following an earlier implementation shown at the last International Detonation Symposium. Results include code-to-code comparisons between CTH and the AWE hydrocode PERUSE, focusing on the simulated particle velocity histories during a shock-to-detonation transition, and corresponding to previous gas gun impact experiments as well as new model verification studies. Lessons learned are provided, including discussions of the numerical accuracy, in addition to the role of artificial viscosity and artificial viscous work. Finally, simulation results are shown to compare the Snowplough versus P-Alpha porosity model options.
Explosives exposed to conditions above the Chapman-Jouget (CJ) state exhibit an overdriven response that is transient. Reactive flow models are often fit to the CJ conditions, and they transition to detonation based on inputs lower than or near CJ, but these models may also be used to predict explosive behavior in the overdriven regime. One scenario that can create a strongly overdriven state is a Mach stem shock interaction. These interactions can drive an already detonating or transitioning explosive to an overdriven state, and they can also cause detonation at the interaction location where the separate shocks may be insufficient to detonate the material. In this study, the reactive flow model XHVRB utilizing a Mie-Grüneisen equation of state (EOS) for the unreacted explosive, and a Sesame table for the reacted products, will be used to examine Mach stem interactions from multi-point detonation schemes in CTH. The effect of the overdriven response driven by PETN-based explosive pellets will be tracked to determine the transient detonation behavior, and the predicted states from the burn model will be compared to previously published data.
Vapor-deposited PETN films undergo significant microstructure evolution when exposed to elevated temperatures, even for short periods of time. This accelerated aging impacts initiation behavior and can lead to chemical changes as well. In this study, as-deposited and aged PETN films are characterized using scanning electron microscopy and ultra-high performance liquid chromatography and compared with changes in initiation behavior measured via a high-throughput experimental platform that uses laser-driven flyers to sequentially impact an array of small explosive samples. Accelerated aging leads to rapid coarsening of the grain structure. At longer times, little additional coarsening is evident, but the distribution of porosity continues to evolve. These changes in microstructure correspond to shifts in the initiation threshold and onset of reactions to higher flyer impact velocities.
The eXtended History Variable Reactive Burn (XHVRB) model is parameterized for hexanitrostilbene (HNS) and pentaerythritol tetranitrate (PETN) based on data collected from a series of high-throughput initiation (HTI) experiments. The HTI experiment has generated a wealth of thin-pulse, sub-millimeter shock initiation data for a variety of vapor deposited explosive films. This is because it provides access to growth-to-detonation information for explosives that exhibit a shock-to-detonation transition (SDT) with length and time scales that are too short to be resolved by conventional experiments. The XHVRB model was selected because previous work has shown that simpler, homogeneous reactive burn models (RBMs) were incapable of reproducing the particle velocity buildup observed in experiments with heterogeneous explosives. Therefore, calibrated XHVRB models are developed in an attempt to capture the heterogeneous behavior not captured previously and to assess the models’ ability to capture the SDT across multiple explosive film thicknesses.
For reactive burn models in hydrocodes, an equilibrium closure assumption is typically made between the unreacted and product equations of state. In the CTH [1] (not an acronym) hydrocode the assumption of density and temperature equilibrium is made by default, while other codes make a pressure and temperature equilibrium assumption. The main reason for this difference is the computational efficiency in making the density and temperature assumption over the pressure and temperature one. With fitting to data, both assumptions can accurately predict reactive flow response using the various models, but the model parameters from one code cannot necessarily be used directly in a different code with a different closure assumption. A new framework is intro-duced in CTH to allow this assumption to be changed independently for each reactive material. Comparisons of the response and computational cost of the History Variable Reactive Burn (HVRB) reactive flow model with the different equilibrium assumptions are presented.
The notion of plane shock waves is a macroscopic, very fruitful idealization of near discontinuous disturbance propagating at supersonic speed. Such a picture is comparable to the picture of shorelines seen from a very high altitude. When viewed at the grain scale where the structure of solids is inherently heterogeneous and stochastic, features of shock waves are non-laminar and field variables, such as particle velocity and pressure, fluctuate. This paper reviews select aspects of such fluctuating nonequilibrium features of plane shock waves in solids with focus on grain scale phenomena and raises the need for a paradigm change to achieve a deeper understanding of plane shock waves in solids.
The propagation of self-sustained formation reactions in sputter-deposited Co/Al multilayers is known to exhibit a design-dependent instability. Multilayers having thin bilayers (<55 nm period) exhibit stable propagating waves, whereas those with a larger period react unstably. The specific two-dimensional (2D) instability observed involves the transverse propagation of a band in front of a stalled front commonly referred to as a “spin band.” Previous finite-element studies have shown that these instabilities are thermodynamically driven by the forward conduction of heat away from the flame front. However, the magnitude of that loss is inherently tied to the bilayer design in traditional bimetallic multilayers, which couples any proposed stability criteria to a varying critical diffusion distance. This work utilizes a recently developed class of materials known as “inert-mediated reactive multilayers” to decouple the thermodynamic and kinetic contributions to propagating wave stability by reducing the stored chemical energy density in normally stable bilayer designs. By depositing an inert product phase (B2-CoAl) within the mid-plane of Co and Al reactant layers, spin instabilities arise as a function of both diluted volume and critical diffusion distance. From there, a stability criterion is determined for Co/Al multilayers based on enthalpy loss from the reaction zone, and its physical significance is explored.
Reactive Co/Al multilayers are uniformly structured materials that may be ignited to produce rapid and localized heating. Prior studies varying the bilayer thickness (i.e., sum of two individual layers of Co and Al) have revealed different types of flame morphologies, including: (a) steady/planar, (b) wavy/periodic, and (c) transverse bands, originating in the flame front. These instabilities resemble the “spin waves” first observed in the early studies of solid combustion (i.e., Ti cylinder in a N2 atmosphere), and are likewise thought to be due to the balance of heat released by reaction and heat conduction forward into the unreacted multilayer. However, the multilayer geometry and three-dimensional (3D) edge effects are relatively unexplored. In this work, a new diffusion-limited reaction model for Co/Al multilayers was implemented in large, novel 3D finite element analysis (FEA) simulations, in order to study the origins of these spinlike flames. This reaction model builds upon previous work by introducing three new phase-dependent property models for: (1) the diffusion coefficient, (2) anisotropic thermal conductivity tensor, and (3) bulk heat capacity, as well as one additional model for the bilayer-dependent heat of reaction. These novel 3D simulations are the first to predict both steady and unsteady flames in Co/Al multilayers. Moreover, two unsteady modes of flame propagation are identified, which depend on the enhanced conduction losses with slower flames, as well as flame propagation around notched edges. Future work will consider the generality of the current modeling approach and also seek to define a more generalized set of stability criteria for additional multilayer systems.
