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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Uncertainty quantification for high explosive reactant and product equations of state

Equations of state (EOSs) are typically represented as physics-informed models with tunable parameters that are adjusted to replicate calibration data as closely as possible. Uncertainty quantification (UQ) allows for the development of an ensemble of EOS parameters that are consistent with the calibration data instead of a single EOS. In this work, we perform UQ for the reactant and product EOSs for a variety of high explosives (HEs). In doing so, we demonstrate a strategy for dealing with heterogeneous (both experimental and calculated) data. We also use a statistical distance metric to quantify the differences between the various HEs using the UQ results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Neural network surrogate models for equations of state

Equation of state (EOS) data provide necessary information for accurate multiphysics modeling, which is necessary for fields such as inertial confinement fusion. Here, we suggest a neural network surrogate model of energy and entropy and use thermodynamic relationships to derive other necessary thermodynamic EOS quantities. We incorporate phase information into the model by training a phase classifier and using phase-specific regression models, which improves the modal prediction accuracy. Our model predicts energy values to 1% relative error and entropy to 3.5% relative error in a log-transformed space. Although sound speed predictions require further improvement, the derived pressure values are accurate within 10% relative error. Our results suggest that neural network models can effectively model EOS for inertial confinement fusion simulation applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Updated universal relations for tidal deformabilities of neutron stars from phenomenological equations of state

Equation of state (EOS) insensitive relations, so-called universal relations, between the neutron star (NS) compactness, its multipolar tidal deformability coefficients, and between the tidal parameters for binary systems are essential to break degeneracies in gravitational wave data analysis. Here, we validate and recalibrate these universal relations using a large set of almost 2 million phenomenological EOSs that are consistent with current observations. In doing so, we extend universal relations to a larger region of the EOS parameter space, most notably to softer EOSs and larger compactnesses. We show that waveform models that neglect higher-than-leading-order tidal deformations of the NSs accumulate as much as 3.5 radians of dephasing from 20Hz to merger. Further, we also perform a full Bayesian parameter estimation of the GW170817 data, and we compare the NS radius constraints produced using universal relations from the literature and the updated fits we propose here. We find that the new fits yield a NS radius that is smaller by about 500 meters. This difference is less than the statistical uncertainty on the radius at the signal-to-noise-ratio of GW170817, but it is significantly larger than the precision anticipated for next-generation detectors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Neural network representations of multiphase Equations of State

Abstract Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either “from scratch” to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, highlighting their advantages and shortcomings.

Science & Technology - Other Topics↗
DOE OSTI2023

Uncertain characterization of reservoir fluids due to brittleness of equation of state regression

Equations of state (EoS) play a central role in modeling the phase equilibrium of fluid mixtures. Their parameterization involves fitting a model to experimental data, i.e., solving a nonlinear, non-convex, multivariate optimization problem. The latter requires one to select design variables, domains of definition for each variable, and weights assigned to individual measurements. We demonstrate that subjective choices of an optimization algorithm and an initial guess also impact the regression process. Consequently, EoS predictions are fundamentally uncertain even after the EoS tuning to a limited set of experimental data points. We demonstrate this observation for two hydrocarbon reservoir fluids, in which five properties of the heaviest carbon fraction are treated as design variables. While all the optimization algorithms and initial guesses match experimental data for the gas and liquid properties, the resulting EoS parameterizations lead to dramatically different predictions of the fluid’s thermophysical behavior in the unsampled pressure and temperature regions. In conclusion, we propose the probabilistic treatment of design variables to quantify the predictive uncertainty of the resulting fluid models.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Black Box Equations of State: Creating Semi-analytic Solutions to the Noh Problem and Verifying Equation of State Interfaces

The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Chiral Effective Field Theory and the High-Density Nuclear Equation of State

Born in the aftermath of core-collapse supernovae, neutron stars contain matter under extraordinary conditions of density and temperature that are difficult to reproduce in the laboratory. In recent years, neutron star observations have begun to yield novel insights into the nature of strongly interacting matter in the high-density regime where current theoretical models are challenged. At the same time, chiral effective field theory has developed into a powerful framework to study nuclear matter properties with quantified uncertainties in the moderate-density regime for modeling neutron stars. In this article, we review recent developments in chiral effective field theory and focus on many-body perturbation theory as a computationally efficient tool for calculating the properties of hot and dense nuclear matter. We also demonstrate how effective field theory enables statistically meaningful comparisons among nuclear theory predictions, nuclear experiments, and observational constraints on the nuclear equation of state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Extending and Smoothing Two-dimension Equation of State Simulation Data

The Multiphase Equation of State (MEOS) project works to produce high quality equation of state tables which are used in computationally intensive simulations of materials in different conditions. An equation of state table describes the state of matter under certain physical conditions such as pressure, volume, temperature, or internal energy. MEOS uses many different models and combinations thereof to produce accurate tables consisting of continuous smooth data, derivatives, and higher-order derivatives. Accurate and smooth data are important factors in producing precise simulations. This report focuses on improving the electron tables produced from Purgatorio and Thomas-Fermi data. Purgatorio data is extremely accurate but often jagged and discontinuous in the lower temperature and density region. Thomas-Fermi is a model that provides smooth data throughout. Together, this produces an EOS data table that is both accurate and smooth. This report describes the implementation of a new feature that allows users to define more detailed regions in the Purgatorio table to be replaced with Thomas-Fermi. As a result, MEOS can generate a table that is both more smooth and still accurate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

High-Pressure Equation of State of 1,3,5-triamino-2,4,6-trinitrobenzene: Insights into the Monoclinic Phase Transition, Hydrogen Bonding, and Anharmonicity

The high-pressure equation of state (EOS) of energetic materials (EMs) is important for continuum and mesoscale models of detonation performance and initiation safety. Additionally, obtaining a high-fidelity EOS of the insensitive EM 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has proven to be difficult because of challenges in experimental characterization at high pressures (HPs). In this work, powder X-ray diffraction patterns were fitted using the recently discovered monoclinic I2/a phase above 4 GPa, which shows that TATB is less compressible than when indexed with the triclinic $P\bar{1}$ phase. First-principles calculations were performed with Perdew–Burke–Ernzerhof (PBE) and PBE0 functionals including thermal effects using the $P\bar{1}$ phase. PBE0 improves the description of hydrogen bonding and thus predicts accurate planar a and b lattice parameters under ambient conditions. However, discrepancies in the predicted lattice parameters above 4–10 GPa compared with experimental measurements indexed with $P\bar{1}$ are further evidence of a structural modification at high pressure. Layer sliding defects are formed during molecular dynamics simulations, which induces an anharmonic effect on the thermal expansion of the c lattice parameter. In short, the results provide several insights into determining high-fidelity EOS parameters for TATB and other molecular crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Automated Fitting of a Semi-empirical Multiphase Equation of State for Carbon

The equation of state (EOS) of carbon is important in high explosive, geophysical, and inertial confinement fusion applications. Within the semi-empirical Sesame framework, the EOS of each phase is represented by a sum of cold, vibrational, and thermal electronic Helmholtz free energy contributions. Each phase has ~5-10 independent parameters that are adjusted to reproduce single-phase data (e.g., thermal expansion, isothermal compression) as well as experimentally- and computationally- derived phase boundaries. Manual calibration of the full multiphase EOS is arduous. We present our progress in development of automated EOS parameterization based on minimization of an objective function. Here, this function encodes deviation of model EOS results from experimental/computational benchmarks. Optimization is implemented as a combination of global (particle swarm) and local optimization techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Uncertainty quantification for equations of state: copper as an example

Equations of state are essential for providing a fundamental description of materials properties in thermodynamic equilibrium and are used to provide closure relations for hydrodynamics simulations. Generally, equations of state rely on simple physics-based parameterized materials models to inform on the free energy of a material through out a given thermodynamic state space. Historically the parameters of these models have been tuned by hand to fit various experimental data. However, modern optimization and uncertainty quantification techniques allow us to quickly test thousands of parameter combinations and obtain meaningful uncertainty estimates on the parameters, opening opportunities for assessing systematic uncertainties in experiments, assessing model adequacy, and more. In this report, we use Bayesian inference to fit the solid (fcc) equation of state of copper. We focus on fitting five different experimental datasets, including the isobaric density, isobaric heat capacity, room temperature isotherm, principal isentrope, and principal Hugoniot. We fit all five data types simultaneously, and then explore the extent to which combinations of 2 subsets of the 5 datasets can constrain the EOS parameters, as compared to the fit to all 5. This information is useful for investigating the extent to which different datasets can con strain EOS models and thereby help guide experimental investigations in order to best constrain the EOS. We also discuss ways that the methodologies can be used to investigate systematic discrepancies between experiments, as well as how the methods can be used to assess model uncertainty. The framework we develop is general, in that it can be used with a variety of optimization or uncertainty quantification techniques and with a variety of data sources, including both experimental and ab-inito data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Ab initio equation of state for vanadium

Accurate materials’ equations of state (EOS) are essential for understanding materials properties as well as for use in multiphysics simulations. In particular, hydrodynamics simulations are based on three fundamental conservation laws (mass, momentum and energy) that form an under-determined system of equations. The equation of state serves as an additional closure relation between thermodynamic variables for a given material that enables numerical hydrodynamics simulation. In this report, we focus on the development of an ab initio EOS for the body centered cubic (BCC) phase of Vanadium (V) for eventual integration into a multiphase EOS in the OpenSesame EOS database.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Complete Equations of State for Cyclotetramethylene Tetranitramine

Complete equations of state for the volumetric deformation of the β-polymorph of cyclotetramethylene tetranitramine (β-HMX) have been derived from its Helmholtz free energy. Dispersion-corrected density functional theory calculations were used to compute the dependence of the frequencies of the vibrational normal modes on specific volume. Here, the normal mode frequencies were used directly to generate both a tabular equation of state and an approximate model where the sum over normal mode frequencies is replaced by a set of five Debye models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Gravitational waves from binary neutron star mergers with a spectral equation of state

In numerical simulations of binary neutron star systems, the equation of state of the dense neutron star matter is an important factor in determining both the physical realism and the numerical accuracy of the simulations. Some equations of state used in simulations are C 2 or smoother in the pressure/density relationship function, such as a polytropic equation of state, but may not have the flexibility to model stars or remnants of different masses while keeping their radii within known astrophysical constraints. Other equations of state, such as tabular or piece-wise polytropic, may be flexible enough to model additional physics and multiple stars' masses and radii within known constraints, but are not as smooth, resulting in additional numerical error. We will study in this paper a recently developed family of equation of state, using a spectral expansion with sufficient free parameters to allow for a larger flexibility than current polytropic equations of state, and with sufficient smoothness to reduce numerical errors compared to tabulated or piece-wise polytropic equations of state. We perform simulations at three mass ratios with a common chirp mass, using two distinct spectral equations of state, and at multiple numerical resolutions. We evaluate the gravitational waves produced from these simulations, comparing the phase error between resolutions and equations of state, as well as with respect to analytical models. From our simulations we estimate that the phase difference at merger for binaries with a dimensionless weighted tidal deformability difference greater than Δ$\tilde{Λ}$=55 can be captured by the SpEC code for these equations of state.

79 ASTRONOMY AND ASTROPHYSICS↗