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Oblique shock wave–interface interactions of gases and liquids have been extensively studied in shock tubes using optical methods to measure equation-of-state (EOS) parameters. However, this is difficult with solids due to their opaqueness to visible light. X ray phase contrast imaging (XPCI) has the penetrative strength to probe solids while still being sensitive to mass density and enhancing the visibility of material boundaries. We investigate the accuracy and repeatability of measuring the mean value of the average mass density (areal density divided by thickness) over region S (B S) and flow deflection angle (θ) from XPCI images of a sample. To that end, a Hough transform-based method for measuring θ is developed. To measure B S , the XPCI image intensity probability density function (PDF) is modeled accounting for the spatial distribution of x ray energy, scintillator response, and pulse-to-pulse variation in the x ray intensity. In addition, a Monte Carlo-based algorithm for computing the B S PDF is developed. Both methods are validated on an impact-generated oblique shock wave interacting at a solid polymer-to-polymer interface. This is accomplished through a comparison to hydrodynamic simulations using well-established EOS. Under the modeling framework for the XPCI image intensity, B S is computed with an accuracy of < 0.1 % and precision of 3%–5%, while θ has an uncertainty of 0.2 ° , respectively. This shows that the XPCI-based model that is developed here could be an invaluable tool for high-fidelity testing of hydrodynamic models in shock polar configurations. [ABSTRACT FROM AUTHOR]

Analytic equations of state (EOS) are intended to reproduce theoretical and experimental data in a single phase portion of the thermodynamic space. We devise a complete and thermodynamically consistent model with four distinct features: (1) a reference isotherm that remains thermodynamically stable, (2) a flexible specific heat model based on a fourth-order rational polynomial, (3) a Grüneisen parameter that depends on specific volume and temperature, and (4) pressure and internal energy functions that can be inverted analytically in temperature. The model aims to improve the accuracy of existing equations of state while remaining computationally efficient. To demonstrate its features, we include calibrations for single-crystal pentaerythritol tetranitrate (PETN), liquid nitromethane (NM), and hexagonal close-packed beryllium (Be) metal. The parameter optimization uses the specific heat capacity, Grüneisen parameter, and static compression curves obtained from density functional theory for the crystalline solids and molecular dynamics simulations for liquid NM. We also present a velocity autocorrelation function that yields accurate phonon densities of states for the EOS calibration from the molecular dynamics trajectories. Each of the three calibrations is constrained to enforce the ambient state from experimental measurements and validated against experimental Hugoniot data from multiple sources. We also include one-dimensional hydrodynamic simulations of the isentropic compression experiments for beryllium conducted at the Z facility. [ABSTRACT FROM AUTHOR]

Recent research has demonstrated that additive manufacturing (AM) can be used to produce directionally sensitive high explosives (HEs), but detonation wave propagation in AM HEs with variable internal structure has not been studied. In this work, samples were printed using a 73 wt. % octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine-based HE ink. Flash x-ray radiography imaging was used to observe density changes in two imaging planes of each sample during detonation, and high-speed imaging was used to calculate the detonation velocity at the HE surface. The detonation front initially appears to fail in internal channel regions of the HE, but late reactions occurred in two samples, which increased the material bulk density by 2.8%, possibly due to shock convergence phenomena. The calculated detonation wave pressure similarly increased, but the accuracy of the results is uncertain because of the deviation of the low bulk density printed samples from the cast charge principal isentrope. This work demonstrates that structure can be effectively utilized to guide detonation wave propagation through HE charges. [ABSTRACT FROM AUTHOR]

Graded density impactors (GDIs) are multi-material composite impactors used in gas gun experiments to tailor the drive conditions imparted to a sample test material. Previous graded density impactors generally rely on thin, but discrete, layers of different materials. The thinner and the greater number of layers will result in smoother compression. Taken to the limit of very thin layers would be pure material 1 at one surface, such as the front surface of an impactor, smoothly transitioning at the atomic scale to pure material 2 on the back surface. Such an impactor can initially shock, then smoothly compresses a material during a dynamic experiment. This type of experiment can serve to explore a larger region of thermodynamic space than a single or even multi-shock experiments. An overview of how graded density impactors are made is reviewed and sample results are given. A strategy for modeling these kinds of impactors is presented. The length scales of constituent mixing are given from the experimental build through electrochemical-deposition. Equation of state models for pure constituents and their subsequent mixtures are presented. It is demonstrated that the time scales for pressure and temperature equilibration, for atomically mixed GDIs, are short enough to be a justifiable closure for the resulting multiphase flow. Furthermore, we present simulation results of dynamic shock followed by a ramp compression, utilizing a silver/gold graded density impactor, onto a tantalum sample. [ABSTRACT FROM AUTHOR]

One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. The relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion. [ABSTRACT FROM AUTHOR]

Many isothermal equations of state lead to numerical problems under tension conditions due to negative bulk modulus. We summarize the properties of four existing models and devise a continuous non-piecewise reference curve to address this issue. The final functional form contains three fitting parameters that are directly related to the bulk modulus and its pressure derivative at the reference state and at infinite pressures. We also include bounds that guarantee the monotonicity of its pressure derivative in all volume space. To demonstrate the qualitative features of each isotherm, we conduct calibrations against experimental data for cyclotetramethylene tetranitramine, magnesium oxide, gold, and platinum. Pressure residuals and root mean square deviations show that the proposed functional form is capable of adequately fitting the data compared to other three-parameter models. [ABSTRACT FROM AUTHOR]

This paper describes the calibration of the Arrhenius Wescott–Stewart–Davis (AWSD) reactive flow model for the recently developed high explosive PBX 9701, which consists of 97% 3, 3 ′ -diamino-4, 4 ′ -azoxyfurazan (DAAF) and 3% FK-800 binder by weight. DAAF-based explosive formulations have several desirable qualities as they are relatively insensitive to non-shock insults but have higher performance than triaminotrinitrobenzene based formulations. Equations of state for the explosive reactants and products are calibrated using a combination of existing and new experimental data and theoretical calculations. The AWSD rate law calibration utilizes both one-dimensional shock-to-detonation and multidimensional rate stick experiments to capture the shock initiation and propagating detonation regimes. Validation of the calibrated model is demonstrated through comparison with recent gas-gun experiments. [ABSTRACT FROM AUTHOR]

This article, titled "An analytic and complete equation of state for condensed phase materials," was originally published online on September 22, 2023, with incorrect captions for Figures 7-10. However, the figures and captions have been corrected and are now accurate. The article discusses thermal and cold calibration for various materials, including single-crystal PETN, liquid nitromethane, and HCP beryllium. It also presents the Grüneisen parameter calibration for HCP beryllium and includes graphs illustrating the Grüneisen parameter surface and non-dimensional thermodynamic space. The online versions of the article were corrected on October 23, 2023. [Extracted from the article]

A novel set of experiments and reactive flow modeling of pentaerythritol tetranitrate (PETN) is presented. Here, the specific phenomenon of shock to detonation transition is examined, where an initial, relatively weak shock is propagated into pressed PETN powder at 1.65 g/cm 3 and the subsequent buildup to detonation is observed experimentally. These experiments, in conjunction with reactant and products' equations of state, are utilized for building reactive flow models. [ABSTRACT FROM AUTHOR]

A new exact solution of an oblique detonation is developed for the supersonic irrotational flow of an inviscid calorically perfect ideal gas, which undergoes a one-step, irreversible, exothermic, zero activation energy reaction as it passes through a straight shock over a curved wedge. The solution gives expressions for the velocity, pressure, density, temperature, and position as parametric functions of a variable characterizing the extent of reaction. For Chapman-Jouguet solutions, an explicit form with dependency on distance is obtained in terms of the Lambert W function. As the simple model employed is a rational limit of models used in the computational simulation of complex supersonic reactive flows, the solution can serve as a benchmark for mathematical verification of general computational algorithms. An example of such a verification is given by comparing the predictions a modern shock-capturing code to those of the full exact solution. The realized spatial convergence rate is 0.779, far less than the fifth-order accuracy that the chosen algorithm would exhibit for smooth flows, but consistent with the predictions of all shock-capturing codes, which never converge with greater than first-order accuracy for flows with embedded discontinuities.

The response of high explosives (HEs), due to mechanical and/or thermal insults, is of great importance for both safety and performance. A major component of how an HE responds to these stimuli stems from its reactant equation of state (EOS). Here, the tri-amino-tri-nitro-benzene based explosive PBX 9502 is investigated by examining recent experiments. Furthermore, a complete thermal EOS is calibrated based on the functional form devised by Wescott, Stewart, and Davis [J. Appl. Phys. 98, 053514 (2005)]. It is found, by comparing to earlier calibrations, that a variety of thermodynamic data are needed to sufficiently constrain the EOS response over a wide range of thermodynamic state space. Included in the calibration presented here is the specific heat as a function of temperature, isobaric thermal expansion, and shock Hugoniot response. As validation of the resulting model, isothermal compression and isentropic compression are compared with recent experiments. [ABSTRACT FROM AUTHOR]

We present methods for computing either the level set function or volume fraction field from the other at second-order accuracy. Both algorithms are optimal in that O( N) computations are needed for N total grid points and both algorithms are easily parallelized. This work includes a novel interface reconstruction algorithm in three dimensions that requires a smaller local block of volume fractions than existing algorithms. A compact local solver leads to better algorithm portability and efficiency: for example, fewer restrictions must be imposed on an adaptive mesh, and fewer grid cells must be communicated between processors in a parallel implementation. We also present a fast sweeping method for computing a unique approximation of the signed distance function to a piecewise linear interface. All of the numerical examples confirm second-order accuracy on both uniform and tree-based adaptive grids. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]