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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Empirical correlations between the function of entropy ( Z S ) and net artificial viscous work in a shock physics hydrocode

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. Here, 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 Z S , 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.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Investigating growth to detonation in vapor-deposited hexanitrostilbene and pentaerythritol tetranitrate films using high-throughput methods

In this work, a high-throughput experimental setup was used to characterize initiation threshold and growth to detonation in the explosives hexanitrostilbene (HNS) and pentaerythritol tetranitrate (PETN). The experiment sequentially launched an array of laser-driven flyers to shock samples arranged in a 96-well microplate geometry, with photonic Doppler velocimetry diagnostics to characterize flyer velocity and particle velocity at the explosive–substrate interface. Vapor-deposited films of HNS and PETN were used to provide numerous samples with various thicknesses, enabling characterization of the evolution of growth to detonation. One-dimensional hydrocode simulations were performed with reactions disabled to illustrate where the experimental data deviate from the predicted inert response. Prompt initiation was observed in 144 μm thick HNS films at flyer velocities near 3000 m/s and in 125 μm thick PETN films at flyer velocities near 2400 m/s. This experimental setup enables rapid quantification of the growth of reactions in explosive materials that can reach detonation at sub-millimeter length scales. These data can subsequently be used for parameterizing reactive burn models in hydrocode simulations, as discussed in Paper II [D. E. Kittell, R. Knepper, and A. S. Tappan, J. Appl. Phys. 131, 154902 (2022)].

36 MATERIALS SCIENCE↗
DOE OSTI2022

Explosive dispersal of particles in high speed environments

In this paper, we present the results of the explosive dispersal of particles in high-speed environments. We carry out Euler–Lagrange numerical simulations of a source at quiescent ambient conditions as well as moving at Mach numbers of 3 and 6. Particle volume fractions of 0%, 1%, and 4.5% are presented. The detonation profile is computed with the Jones–Wilkins–Lee equation of state using a reactive burn model. Non-static cases provide a framework to consider the effect of a bow shock and pre-existing high-speed flow conditions on the dispersal process. We also compute averages of both static and dynamic pressures, as well as impulse density histories on virtual probe planes to characterize the momentum of the flow and particles that would deposit on a target. Results suggest that the presence of the particles can have a substantial effect on the pressure average of the virtual target planes.

Durant, B. A.↗
DOE OSTI2020

Effect of Heterogeneities on the Reaction-zone of a Propagating Detonation Wave

Reactive burn models for propagating detonation waves in an explosive are based on the ZND (Zel'dovich-Von Neumann-Doring) theory. A key property of the ZND theory, which leads to self-sustaining detonation waves, is a sonic point relative to the front in the reaction zone. Moreover, burn models assume the explosive is a homogeneous material. This assumption is used for plastic-bonded explosives, even though they are heterogeneous materials. The heterogeneities are accounted for only with an empirical burn rate. Furthermore, the reaction-zone width can be less than the length scale of heterogeneities. This raises the question of the effect of heterogeneities on the reaction zone. In particular, whether the reaction zone can be steady and have a well defined sonic point. To examine this question we focus on PBX 9501 since there is data on the grain-binder heterogeneities and on the reaction-zone velocity time history of a steady planar detonation wave. Using pseudo-mesoscale 1-D simulations, we examine the effect of a detonation wave transversing explosive and binder segments of random length. The simulations show that the reaction zone is quasi-steady with only short wavelength small amplitude variations in the detonation wave pressure and speed. The main effect of the heterogeneities is to introduce noise in the pressure and velocity fields that propagates into the Taylor wave behind the detonation. This is consistent with the scatter in the reaction-zone measurements for PBX 9501.

42 ENGINEERING↗
DOE OSTI2020

PBX9502 PAGOSA/SURF Calibration for 100 µm Grid Size

There are two methods to calibrate the SURF reactive burn explosives model.The first is to calibrate using Pop plot data. Because there are only two main parameters in SURF, called A and B, there is just enough flexibility in SURF to determine the Pop plot line, i.e., equivalent information to a slope and a single point on the line. However, due to the linearity of the Pop plot being based on logarithmic scales, a slight deviation off the Pop plot (though the fit to the Pop plot might be very good overall) can make considerable difference when comparing with the velocity profile data. The second calibration method thusly focuses strongly on matching entire velocity profile data. This is to say that individual velocity profiles extracted from embedded gages (in the case of PBX 9502, we refer to R. Gustavsen’s experimental data) may fit poorly, while the overall fit to the Pop plot may seem reasonable. In addition, there are other factors that could produce slightly different calibrations for SURF, while leading to an overall acceptable fit to data. One of those may be the physics code used and here we use Pagosa. Another is mesh size dependence. A third one stems from fitting a reactive burn model being done in conjunction with an equation of state (EOS) of the reactants and one for the products – different EOS can result in slightly different parameterizations. Finally, there are several secondary material parameters in SURF, and the overall fit will depend on the entire parameterization. The goal of this report is to clarify some of our previously made statements about SURF calibration, as well as to redo a systematic calibration using 100 µm grid resolution.

42 ENGINEERING↗
DOE OSTI2023

Pinwheel Experiment Confirmatory Shot 1 Pre-Shot Report

The purpose of this experimental series is to validate the reactive burn model in the PAGOSA hydrodynamic code. It will also help validate the EOS and Strength models for the aluminum and tantalum cylinders. C4 high explosive (HE) is used to drive an aluminum cylinder into an aluminum sandwiched PBX-9501. The follow-on experiment will drive the aluminum cylinder into a tantalum sandwiched PBX-9501. The experiment will provide time of arrival (TOA) data for the burn front in the HE through the metal cylinders using Fiber Bragg Gratings (FBG). Photon Doppler Velocimetry (PDV) will provide shock wave TOA and the velocity of the inward moving cylinder. The PAGOSA code will be used to predict TOA and cylinder wall velocity using PDV and tracers.

42 ENGINEERING↗
DOE OSTI2023

Notes on Davis EOS: Historical Perspective, Derivations & Physical Considerations

Davis reactant and product semi-empirical EOS have been introduced in a series of publications by W. C. Davis. These EOS are convenient to use in conjunction with reactive burn models to parameterize the thermodynamic response of quiescent high explosives (HE) and the mixture of HE decomposition products. There is a history of development of these EOS with different formulae and functional forms found in different papers. The goal of the present notes is to track that history, clarify the physical motivation behind various modifications to Davis EOS over time, and collect all the relevant formulae in one place.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Pinwheel Experiment Tantalum Shot 1 Pre-Shot Report

The purpose of this experimental series is to validate the reactive burn model in the PAGOSA hydrodynamic code. It will also help validate the EOS and Strength models for the aluminum and tantalum cylinders. C4 high explosive (HE) is used to drive an aluminum cylinder into a tantalum sandwiched PBX‐9501. The experiment will provide time of arrival (TOA) data for the burn front in the HE through the metal cylinders using Fiber Bragg Gratings (FBG). Photon Doppler Velocimetry (PDV) will provide shock wave TOA and the velocity of the inward moving cylinder. The PAGOSA code will be used to predict TOA and cylinder wall velocity using PDV and tracers.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Predicting the effects of thermally-induced density gradients on the hydrodynamic behavior of PBX 9502

High explosives are often exposed to thermal and mechanical stimuli within normal and abnormal environments. These stimuli can introduce density gradients in the explosive charge but the effect of such gradients is not well-understood. The goal of this work is to develop a comprehensive methodology to model the evolution of density gradients under various thermal conditions and then to predict shock initiation and detonation behavior of the gradated sample. PBX 9502 was chosen for these scoping studies because it has a large coefficient of thermal expansion and because the available shock initiation data indicates that initial temperature strongly affects the shock-to-detonation transition (SDT). The multiphysics code COMSOL was first used to model induced density gradients in a slab of PBX 9502 with asymmetric heating. Then, the gradated sample was constructed in the Pagosa hydrocode to simulate steel flyer impact scenarios, with SDT and detonation propagation following a calibrated Scaled Uniform Reactive Front (SURF) burn model. Furthermore, the gradated material exhibited very different initiation and corner turning behavior compared to homogeneous materials, and the orientation of the gradation was also found to have some effect. The methodology used here can estimate thermomechanical response of the material for non-uniform thermal environments and compute the resulting detonation properties of the PBX.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Detonation performance experiments and modeling for the DAAF-based high explosive PBX 9701

Detonation performance experiments and modeling are reported for the explosive PBX 9701, which is composed of 97% 3,3$\acute{-}$diamino-4,4$\acute{-}$azoxyfurazan (DAAF) and 3% vinylidene uoride-chlorotriuoroethylene copolymer (Kel-F 800) binder by weight. PBX 9701 is a newly-developed reducedsensitivity explosive with increased performance relative to the triaminotrinitrobenzene or TATB-based PBX 9502 while still retaining low sensitivity to mechanical insult. The first detonation performance measurements for this formulation are presented, including front-curvature ratesticks and cylinder expansion test data. Prior shock initiation data is also reviewed. These data are used to develop programmed burn and reactive flow calibrations for existing commonly-used performance models which allow engineering calculations with PBX 9701. The calibration process involves several enhancements relative to conventional approaches including the use of an analytical scaling correlation to speed the calibration process and development of a new methodology to improve the consistency between the programmed burn and reactive model calibration process and the resulting calculations. Overall, PBX 9701 is seen to exhibit improved performance relative to insensitive explosives, with a trinitrotoluene (TNT) equivalence of 1.24. The detonation performance properties are found to be well captured by existing models.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1980

A numerical study of the NOL large-scale test

The large-scale gap test was modeled numerically using the reactive hydrodynamics code 2DE with forest fire burn rates. The model gives good agreement between calculated and experimental critical gap values. The calibration of peak pressure in the gap versus gap length is obtained from these calculations, and is in good agreement with the published experiment curve. The two dimensional nature of the gap test is evident from the curvature of the shock wave in the gap and test sample, and from the observed distance of run to detonation in the test samples.

Bowan, A. L.↗
NASA NTRS1980

Sympathetic reaction tests and analyses

The critical separation distances for explosive reactions of a solid rocket propellant were measured. Explosive reactions included low order explosion, low order detonation, and high order detonation. The effects of sample size, shape, damage and temperature on sympathetic reaction were determined experimentally. The sympathetic detonation of small cubes of solid rocket propellant was modelled numerically, using the Eulerian reactive hydrodynamic code 2DE with Forest Fire burn rates. The model was applied to cubes of 2.54 - 7.62 cm (1 - 3 in.), with agreement between calculated and experimental results.

Ricardson, D. E.↗
DOE OSTI2022

Effect of void positioning on the detonation sensitivity of a heterogeneous energetic material

We show although it is well-established that voids profoundly influence the initiation and reaction behaviors of heterogeneous energetic materials such as polymer-bonded explosives (PBX) and propellants, there has been little study of how void location in different constituents in the microstructures of such materials affect the macroscale behavior. Here, we use three-dimensional (3D) mesoscale simulations to study how void placement within the reactive grains versus the polymer binder influences the shock-to-detonation transition (SDT) in a polymer-bonded explosive. The material studied here has a microstructure comprised of 75% PETN (pentaerythritol tetranitrate) grains and 25% HTPB (hydroxyl-terminated polybutadiene) polymer binder by volume. Porosities up to 10% in the form of spherical voids distributed in both the grains and polymer are considered. An Arrhenius reactive burn relation is used to model the chemical kinetics of the PETN grains under shock loading, thereby resolving the heterogeneous detonation behavior of the PBX. The influence of void location on the shock initiation sensitivity of the material is quantitatively ranked by comparing the predicted run distance to detonation (RDD) for each sample. The analysis includes inherent quantification of uncertainties arising from the stochastic variations in the microstructure morphologies and void distributions by using statistically equivalent microstructure sample sets (SEMSS), leading to probabilistic formulations for the RDD as a function of shock pressure. The calculations reveal that the location of voids in the composite microstructure significantly affects the RDD. Specifically, voids exclusively within the grains cause the PBX to be more sensitive (having shorter RDD) than voids in the polymer binder. Unique probabilistic relationships are derived to map the probability of observing RDD for each void location material case, allowing for prediction of initiation behavior anywhere in the shock pressure – RDD space. These findings agree with trends reported in the literature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

AWSD reactive flow model for PBX 9404

An Arrhenius–Wescott–Stewart–Davis (AWSD) reactive flow model for high explosive PBX 9404 is developed. We specifically calibrate an AWSD model for PBX 9404 by fitting equations of state for reactants and detonation products to the results of thermochemical calculations and to experimental data from multiple sources. The calibrated equations of state are then coupled with an Arrhenius rate law based on shock temperature that describes the reaction progress during PBX 9404 detonation. The parameter values in the rate law are calibrated to experimental gas-gun data and diameter effect results. The results of the calibrated AWSD model are in strong agreement with available experimental data for PBX 9404. A similar level of agreement between predicted and experimental results is observed when the calibrated model is validated on data that were not used in the model parameterization procedure. Our results illustrate that the AWSD model is capable of accurately describing the many important properties and observables in the reactive burn of PBX 9404. Because of the historical significance of PBX 9404 in high explosives research and its current use in aging studies, this work provides an important model of a legacy material, which can be used to make comparisons to new high explosive formulations.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2026

Model Data Archive Associated with Manuscript "Fire-altered Carbon Pools Create Disturbance Memory in Stream Dissolved Organic Carbon"

This data package supports the publication “Fire-altered Carbon Pools Create Disturbance Memory in Stream Dissolved Organic Carbon” by Li et al. (2026). The package contains processed model inputs, configuration files, restart files, simulation outputs, scripts, and visualization products used to evaluate post-fire dissolved organic carbon (DOC) dynamics in the Naches River Watershed, Washington, USA, following the 2021 Schneider Springs Fire. The modeling workflow couples ELM-BGC, the biogeochemistry-enabled Energy Exascale Earth System Model Land Model; ATS, the Advanced Terrestrial Simulator for integrated surface-subsurface hydrology; and PFLOTRAN, a reactive transport model for multicomponent aqueous geochemistry. Together, these models simulate how wildfire-induced changes in vegetation, litter, coarse woody debris, and soil organic matter influence DOC production, transport, and reaction from burned hillslopes to stream networks. The archive includes preprocessed meteorological, geospatial, hydrologic, and biogeochemical forcing data; ELM-BGC-derived DOC source terms; ATS mesh files; PFLOTRAN reactive-transport inputs; model configuration files; spin-up and transient restart files; watershed-scale diagnostic outputs; stream concentration time series; and figures or visualization files used to inspect and reproduce key results. File types include Hierarchical Data Format 5 (HDF5) files for gridded forcing and model-coupling data, model input and configuration files for ELM-BGC, ATS, and PFLOTRAN, restart and simulation-output files generated by the modeling workflow, tabular or time-series diagnostic outputs, scripts for post-processing and figure generation, and image or visualization products associated with the manuscript. Use of the package depends on the intended task. Re-running the simulations requires the relevant modeling software, including ELM-BGC, ATS, and PFLOTRAN as ATS's geochemical engine. Inspecting outputs and reproducing figures requires Python with scientific plotting libraries such as Matplotlib, and three-dimensional model outputs may be viewed with ParaView. Geographic information system files or maps may be inspected with ArcGIS Pro or comparable GIS software. The data package is intended to enable traceability, reuse, and partial reproduction of the coupled land-to-watershed hydro-biogeochemical modeling workflow used to test how wildfire disturbance affects terrestrial carbon pools and downstream DOC dynamics.

ATS↗
DOE OSTI2020

Theory of ignition and burn propagation in inertial fusion implosions

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, $f_α$ ~ 1.4, where $f_α$ = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles $θ_α$ is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when $θ_α$ is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter $\chi^{53}_α$ to the yield amplification and the burning-plasma parameter $Q^{\text{hs}}_α$ = alpha energy deposited/total input work delivered to the hot spot

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗