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Sierra/SD provides a massively parallel implementation of structural dynamics finite element analysis, required for high-fidelity, validated models used in modal, vibration, static and shock analysis. This document provides a user's guide to the input for Sierra/SD. Details of input specifications for the different solution types, output options, element types and parameters are included.
A laser-driven shock propagating through an isolated particle embedded in a plastic (CH) target was studied using the radiation-hydrodynamic code FLASH. Preliminary simulations using IONMIX equations of state (EOS) showed significant differences in the shock Hugoniot of aluminum compared to experimental data in the low-pressure regime [O(10) GPa], resulting in higher streamwise compression and deformation of an aluminum particle. Hence, a simple modification to the ideal gas EOS was developed and employed to describe the target materials and examine the particle dynamics. The evolution of the pressure field demonstrated a complex wave interaction, resulting in a highly unsteady particle drag which featured two drag minima due to shock focusing at the rear end of the particle and rarefaction stretching due to laser shut-off. Although ~30% lateral expansion and ~25% streamwise compression were observed, the aluminum particle maintained considerable integrity without significant distortion. Additional simulations examined the particle response for a range of particle densities, sizes, and acoustic impedances. The data revealed that lighter particles such as aluminum gained significant momentum, reaching up to ~96% of the shocked CH's speed, compared to ~29% for the heavier tungsten particles. Despite the differences seen in the early stage of shock interaction, particles with varying acoustic impedances ultimately reached the same peak velocity. This identified particle-to-host density ratio is an important factor in determining the inviscid terminal velocity of the particle. In addition, the modified EOS model presented in this study could be used to approximate solid materials in hydrocodes that lack material strength models.
We report that solid particles can be fragmented by a fast-moving fluid if their velocity difference is great enough, such as during the atmospheric entry of meteoroids or the shock compression of engineered particulate composites. The extent of particle deformation and breakup in such systems is poorly understood because the necessary extreme conditions make observation difficult and data scarce. To meet this need, experiments combining ultrafast synchrotron-based radiography with plate impact loading were performed at the dynamic compression sector at the advanced photon source. Metal microspheres of several densities and strengths (Au, Ta, and W) were placed inside a polymer matrix. A planar shock wave was then produced in the polymer by the impact of a gun-launched flyer plate. X-ray images of the resulting flow were collected at ~150ns intervals. These images document the progression of particle deformation across a range of flow conditions and particle materials. They show that the extent of deformation is sensitive to the ratio of drag stress to particle strength. The deforming particle's shape is determined by the initial shock–particle interaction, fluid stagnation pressure, and vorticity, each acting on its own timescale. A set of scaling relationships is presented to capture these observations and enable comparison with prior hydrodynamic data. The result is a framework for predicting the conditions under which strong particles are severely deformed by a shock-driven flow.
Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.
ABSTRACT Characterization of the interface between explosive product gases and ambient air in an explosion is a complicated task due to the turbulent mixing and inherently three‐dimensional expansion of the interface. This study aims to quantify the evolution of the interface as a temporally varying Hausdorff dimension. Two test series were conducted with Composition C‐4 charges with masses of 105 and 880 g. Imaging data were collected from the time of detonation until shock wave detachment using ultra‐high‐speed cameras. Gas cloud profiles were extracted using automated image processing algorithms, and the Hausdorff dimension of these two‐dimensional slices of the gas cloud was then estimated using boxcounting algorithms. When scaled with standard gas dynamic nondimensional scalings, the Hausdorff dimension of all explosive events appears to collapse towards a single curve. The fireball was initially nonfractal and began to develop fractal properties as the shock wave separated from the detonation products. Artificial perturbation of the charged surface had no detectable impact on the evolution of the Hausdorff dimension in the early development of the fireball outside of error, despite visible phenomenological differences in the early development of mixing on the fireball surface.
Experimental benchmarking of transport coefficients under extreme conditions is required for validation of differing theoretical models. To date, measurement of transport properties of dynamically compressed samples remains a challenge with only a limited number of studies able to quantify transport in high pressure and temperature matter. x-ray photon correlation spectroscopy utilizes coherent x-ray sources to measure time correlations of density fluctuations, thus providing measurements of length and timescale-dependent transport properties. Here, we present a first-of-a-kind experiment to conduct x-ray photon correlation spectroscopy in laser shock compression experiments. We report measurement of the turbulent velocity in the wake of a laser driven supersonic shock and place an upper bound on thermal diffusivity in a solid density plasma on nanosecond timescales.
In high-energy-density shock compression experiments, the desired state of compression is typically achieved by passing shock waves through a sequence of different materials. Here, a theoretical approach for transiently strengthening such shocks passing through interfaces of experimentally relevant impedance ratios is examined. A semi-analytical method based on characteristics analysis is used to solve the problem of a shock passing from one material to another through an intermediate region of non-uniform impedance; by appropriately designing this region, a greater shock strength can be achieved in the second material for a finite duration than in the absence of this region. When a shock passes into a material of higher impedance, the shock strengthening increases to a maximum before decreasing to an asymptotic value as the strength of the incident shock is increased. For shocks passing into materials of decreasing impedance, the shock strengthening increases monotonically as the strength of the incident shock is increased when the impedance ratio is above a critical threshold. Incorporating multiple intermediate materials can further increase the strength of the transmitted shock, with an exponential discretization of intermediate material impedances being the most effective distribution for strengthening strong shocks. The results suggest that up to 25% and 9% increases in pressure behind the leading shock can be achieved for materials of increasing and decreasing impedance, respectively. The technique is applied to the design of laser-driven dynamic compression experiments, and the results of the analysis are verified via comparison to simulations performed with the HYADES hydrodynamics code.
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.
Here we present a crystal plasticity model tailored for high-pressure, high-strain-rate conditions that uses a multiscale treatment of dislocation-based slip kinetics. We use this model to analyze the pronounced plasticity-induced lattice rotations observed in shock-compressed polycrystalline tantalum via in situ x-ray diffraction. By making direct comparisons between experimentally measured and simulated texture evolution, we can explain how the details of the underlying slip kinetics control the degree of lattice rotation that ensues. Specifically, we show that only the highly nonlinear kinetics caused by dislocation nucleation can explain the magnitude of the rotation observed under shock compression. We demonstrate a good fit between our crystal plasticity model and x-ray diffraction data and exploit the data to quantify the dislocation nucleation rates that are otherwise poorly constrained by experiment in the dynamic compression regime.
The MARBLE project is a novel inertial confinement fusion platform for studying the development of atomic mixing and temperature equilibration in inertial confinement fusion implosions and their impact on thermonuclear burn. Experiments involve the laser-driven implosion of capsules filled with deuterated engineered foams whose pores are filled with a gaseous mixture of hydrogen and tritium. By varying the size of the foam pores, we can study the timescale of the development of atomic mix relative to the development of thermal equilibrium between species. In contrast, previous separated reactant experiments have only provided information on the total amount of mix mass. Additionally, we report on the series of MARBLE experiments [first reported in Haines et al., Nat. Commun. 11, 544 (2020)] performed on the University of Rochester's OMEGA laser facility and detailed and highly resolved three-dimensional radiation-hydrodynamic simulations of the implosions. In both the experimental and simulation results, we observe that the reactants do not achieve thermal equilibrium during the course of the implosion except in atomically mixed regions—i.e., that atomic mixing develops faster than thermal equilibration between species. The results suggest that ion temperature variations in the mixture are at least as important as reactant concentration variations for determining the fusion reaction rates.
To date, temperature and conductivity have many outstanding implications in extreme environments but are yet to be fully understood under high pressure and temperature dynamic conditions. Here, we introduce an approach to provide high quality electrical conductivity results under dynamic loading conditions. Emphasis is given to address the skin depth effect's influence in a dynamic loading experiment by using thin films. The thin film samples in this study were at least 100 times thinner than previous samples in dynamic electrical conductivity experiments, increasing the current density to its full potential across the sample's entire cross section. Consideration of the skin depth accounts for at minimum a 4× scaling factor to the final electrical conductivity result that has been neglected in previous dynamic electrical conductivity studies. We also obtained improved signal-to-noise ratio with custom diagnostics optimized for better electrical impedance matching. Furthermore, these considerations were applied to Sn to assess electrical conductivity at elevated pressure and temperature. The high signal-to-noise ratio with reduced skin depth influence results in Sn allowing observation of the conductivity changes related to solid-to-solid and solid-to-liquid phase transitions. Additionally, we calculate the Sn thermal conductivity using the Wiedemann-Franz law for our experiments and compare against thermal transport dependent temperature measurements from previous work.
The spin state of Fe can alter the key physical properties of silicate melts, affecting the early differentiation and the dynamic stability of the melts in the deep rocky planets. The low-spin state of Fe can increase the affinity of Fe for the melt over the solid phases and the electrical conductivity of melt at high pressures. However, the spin state of Fe has never been measured in dense silicate melts due to experimental challenges. We report detection of dominantly low-spin Fe in dynamically compressed olivine melt at 150 to 256 gigapascals and 3000 to 6000 kelvin using laser-driven shock wave compression combined with femtosecond x-ray diffraction and x-ray emission spectroscopy using an x-ray free electron laser. The observation of dominantly low-spin Fe supports gravitationally stable melt in the deep mantle and generation of a dynamo from the silicate melt portion of rocky planets.
The purpose of this research was to measure the equation of state for additively manufactured (AM) and forged 304L stainless steel using a novel experimental technique. An understanding of the dynamic behavior of AM metals is integral to their timely adoption into various applications. The Hugoniot of the AM 304L was compared to that of the forged 304L at particle velocities where the material retains a two-wave structure. This comparison enabled us to determine the sensitivity of the equation of state to microstructure as varied due to processing. Our results showed that there was a measurable difference in the measured shock velocity between the AM and forged 304L. The shock wave velocities for the AM 304L were found to be ~3% slower than those for the forged 304L at similar particle velocities. To understand these differences, properties such as densities, sound speeds, and texture were measured and compared between the forged and AM materials. Our results showed that no measurable difference was found in these properties. Additionally, it is possible that differing elastic wave amplitudes may influence shock velocity.
The dynamic-shell concept for inertial confinement fusion (ICF) uses an initially homogeneous target and a carefully shaped laser pulse to form a shell and implode it. The laser pulse consists of a series of pickets that drive shocks into the target. The first few shocks converge inwards and rebound from the center of the target, creating an expanding, low-density plasma. Subsequent shocks are launched into the expanding plasma and eventually coalesce to form a shell, which is then imploded with a traditional ICF laser pulse. This study describes radiation-hydrodynamic simulations that investigate the sensitivity of dynamic-shell targets to imperfections in the laser drive. A one-dimensional (1D) study looks at mistiming and power variations in the pickets and a two-dimensional (2D) study examines irradiation perturbations imposed by the laser-beam geometry. Simulations show that less than ~2% power imbalance or 200 ps timing variation in the pickets is sufficient to keep the yield above 90% of the maximum. Additionally, the 2D simulations show that 72 or more beams are required to keep irradiation nonuniformities low enough to obtain fusion yields close to that of 1D simulations.
Titanium alloys are used in a large array of applications. In this work we focus our attention on the most used alloy, Ti-6Al-4V (Ti64), which has excellent mechanical and biocompatibility properties with applications in aerospace, defense, biomedical, and other fields. Here we present high-fidelity experimental shock compression data measured on Sandia’s Z machine. We extend the principal shock Hugoniot for Ti64 to more than threefold compression, up to over 1.2 TPa. We use the data to validate our ab initio molecular dynamics simulations and to develop a highly reliable, multiphase equation of state (EOS) for Ti64, spanning a broad range of temperature and pressures. The first-principles simulations show very good agreement with Z data and with previous three-stage gas gun data from Sandia’s STAR facility. The resulting principal Hugoniot and the broad-range EOS and phase diagram up to 10 TPa and 10 5 K are suitable for use in shock experiments and in hydrodynamic simulations. The high-precision experimental results and high-fidelity simulations demonstrate that the Hugoniot of the Ti64 alloy is stiffer than that of pure Ti and reveal that Ti64 melts on the Hugoniot at a significantly lower pressure and temperature than previously modeled.
Here, the effect of ionic disorder on the principal Hugoniot is investigated using multiple scattering theory to very high pressure (Gbar). Calculations using molecular dynamics to simulate ionic disorder are compared to those with a fixed crystal lattice, for both carbon and aluminum. For the range of conditions considered here we find that ionic disorder has a relatively minor influence. It is most important at the onset of shell ionization and we find that, at higher pressures, the subtle effect of the ionic environment is overwhelmed by the larger number of ionized electrons with higher thermal energies.
Heterojunction Si solar cells exhibit notable performance degradation. Here, we modeled this degradation by electronic defects getting generated by thermal activation across energy barriers over time. To analyze the physics of this degradation, we developed the SolDeg platform to simulate the dynamics of electronic defect generation. First, femtosecond molecular dynamics simulations were performed to create a-Si/c-Si stacks, using the machine learning-based Gaussian approximation potential. Second, we created shocked clusters by a cluster blaster method. Third, the shocked clusters were analyzed to identify which of them supported electronic defects. Fourth, the distribution of energy barriers that control the generation of these electronic defects was determined. Fifth, an accelerated Monte Carlo method was developed to simulate the thermally activated time-dependent defect generation across the barriers. Our main conclusions are as follows. (1) The degradation of a-Si/c-Si heterojunction solar cells via defect generation is controlled by a broad distribution of energy barriers. (2) We developed the SolDeg platform to track the microscopic dynamics of defect generation across this wide barrier distribution and determined the time-dependent defect density N(t) from femtoseconds to gigaseconds, over 24 orders of magnitude in time. (3) We have shown that a stretched exponential analytical form can successfully describe the defect generation N(t) over at least 10 orders of magnitude in time. (4) We found that in relative terms, Voc degrades at a rate of 0.2%/year over the first year, slowing with advancing time. (5) We developed the time correspondence curve to calibrate and validate the accelerated testing of solar cells. We found a compellingly simple scaling relationship between accelerated and normal times t normal ∝ t accel T(accel)/T(normal) . (6) We also carried out experimental studies of defect generation in a-Si:H/c-Si stacks. We found a relatively high degradation rate at early times that slowed considerably at longer time scales.
The aim of the proposed research was to provide a multi-scale study of the properties of warm dense hydrocarbons, by studying the thermodynamic properties through the equation of state and the microscopic properties by x-ray scattering. Understanding the fundamental properties of warm dense mixtures is an intellectual challenge due to the complexity of the system. Unlike liquids or gases, where constituent particle interactions occur through collisions or bonding between valence electrons, in these strongly coupled systems the atoms will be partially ionized and compressed so tightly together that interactions between the inner core electrons can play a role in the systems chemistry. Advances in computational capabilities and development of new theoretical models have been used to predict the properties of mixtures but there is currently no experimental data of the fundamental interaction between the particles in mixtures to test these predictions against. The proposed research was to experimentally investigate the interaction of the different species in hydrocarbons by measuring the compressibility of substances with different carbon and hydrogen ratios and the complexity of the microscopic interactions through elastic and inelastic x-ray scattering. To study the bulk properties of warm dense hydrocarbons we established the Warm Dense Matter Research Laboratory (WDMRL) in the Institute for Shock Physics at Washington State University. The goal was for experiments in the WDMRL to determine shock loading conditions of interest in the hydrocarbon mixtures. We planned on using Hugoniot EOS measurements and a range of carbon and hydrogen concentrations to determine conditions when the EOS of the mixture varied significantly from that of the classical mixing model. Even though shock transit measurements through aluminum foils suggested pressures upto 400GPa, the experiments in the WDMRL were unsuccessful in getting usable shockwave compression data above 100GPa in polystyrene which was below the pressure of interest for hydrocarbon mixtures (>200GPa). To complete the project, we tested a technique using x-ray phase contrast imaging to map the location of tracer layers in a test sample of polycarbonate to record the material motion in dynamically compressed samples. A technique that will be useful for future warm dense matter experiments. These experiments used <200nm gold layers in polycarbonate samples to measure the material velocity and shock speed using x-ray phase contrast imaging. These results were compared to continuum surface measurements performed at ISP and show that the tracer layer technique can measure hydrodynamic properties accurately in dynamically compressed materials.