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NASA NTRS1972

The thermodynamic properties of oxygen and nitrogen. Part 2: Thermodynamic properties of oxygen from 100 R to 600 R with pressure to 5000 psia

An equation of state is presented for liquid and gaseous oxygen for temperatures from 100 R to 600 R and pressures to 5000 psia. The pressure-density-temperature data available from the published literature have been reviewed, and appropriate corrections have been applied to bring experimental temperatures into accord with the International Practical Temperature Scale of 1968. Representative comparisons of property values calculated from the equation of state to measured values are included to illustrate the accuracy of the equation of state. The coefficients of the equation of state were determined by a weighted least squares fit to selected published data, and simultaneously to isochoric heat capacity data, and to data which define the phase equilibrium for the saturated liquid and saturated vapor. The equation of state is estimated to be accurate for the liquid to within 0.1 percent in density, to within 0.2 percent for the vapor below the critical temperature and for states above the critical temperatures to 250 K, and within 0.1 percent for supercritical states at temperatures from 250 K to 300 K. The vapor pressure equation is accurate to within + or - 0.01 K between the triple point and the critical point.

Stewart, R. B.↗

NASA NTRS1975

Input guide for computer programs to generate thermodynamic data for air and Freon CF4

FORTRAN computer programs were developed to calculate the thermodynamic properties of Freon 14 and air for isentropic expansion from given plenum conditions. Thermodynamic properties for air are calculated with equations derived from the Beattie-Bridgeman nonstandard equation of state and, for Freon 14, with equations derived from the Redlich-Quang nonstandard equation of state. These two gases are used in scale model testing of model rocket nozzle flow fields which requires simulation of the prototype plume shape with a cold flow test approach. Utility of the computer programs for use in analytical prediction of flow fields is enhanced by arranging card or tape output of the data in a format compatible with a method-of-characteristics computer program.

Tevepaugh, J. A.↗

DOE OSTI2022

QCD Equilibrium and Dynamical Properties from Holographic Black Holes

By using gravity/gauge correspondence, we employ an Einstein-Maxwell-Dilaton model to compute the equilibrium and out-of-equilibrium properties of a hot and baryon rich strongly coupled quark-gluon plasma. The family of 5-dimensional holographic black holes, which are constrained to mimic the lattice QCD equation of state at zero density, is used to investigate the temperature and baryon chemical potential dependence of the equation of state. We also obtained the baryon charge conductivity, and the bulk and shear viscosities with a particular focus on the behavior of these observables on top of the critical end point and the line of first order phase transition predicted by the model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1985

On the use of internal state variables in thermoviscoplastic constitutive equations

The general theory of internal state variables are reviewed to apply it to inelastic metals in use in high temperature environments. In this process, certain constraints and clarifications will be made regarding internal state variables. It is shown that the Helmholtz free energy can be utilized to construct constitutive equations which are appropriate for metallic superalloys. Internal state variables are shown to represent locally averaged measures of dislocation arrangement, dislocation density, and intergranular fracture. The internal state variable model is demonstrated to be a suitable framework for comparison of several currently proposed models for metals and can therefore be used to exhibit history dependence, nonlinearity, and rate as well as temperature sensitivity.

Allen, D. H.↗

DOE OSTI2024

IDAES-PSE 2.4.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost, most environmentally sustainable solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications.. Deprecations • Convergence Analysis tool (idaes/core/util/convergence): deprecated in favor of new Parameter Sweep tools. To be removed in v3.0.0. New Beta Capabilities • Parameter Sweep Tool (idaes.core.util.parameter_sweep) o A new API for defining and performing parameter sweep studies on IDAES models has been developed • Diagnostics Tools (idaes.core.util.model_diagnostics) o New methods for identifying duplicate variables and constraints have been added to the diagnostics toolbox o New tools for detecting ill conditioning in Jacobians have been developed and are available in the model_diagnostics module. These provide alternatives to the existing DegeneracyHunter toolbox, and will eventually be merged with this capability, but initial working versions have been provided as beta capabilities for interested users o IpoptConvergenceAnalysis (replaces deprecated Convergence Analysis tool):  A new tool for performing convergence analysis studies that leverages the new Parameter Sweep tools has been developed. This tool allows users to define the input parameters to their model and sampling methods for these (leveraging Pysmo's sampling tools) and to then solve their model across the sampled domains and return a summary of the solver performance (IPOPT only) Improved Models • Thickener model (idaes.models.unit_models.solid_liquid.thickener) o Improved model to include predictive correlations for unit sizing based on settling velocity measurements (steady-state only) • Modular Property Packages o Added general support for calculating critical properties of mixtures using defined Equation of State modules. New API defined for Equation of State modules in order to define the necessary constraints for calculating critical properties (most EoS modules DO NOT support calculation of critical properties (yet)) o Added new methods to Cubic Equation of State module to support calculation of critical properties

DiagnosticsToolbox↗

DOE OSTI2024

A second-order-in-time, explicit approach addressing the redundancy in the low-Mach, variable-density Navier-Stokes equations

A novel algorithm for explicit temporal discretization of the variable-density, low-Mach Navier-Stokes equations is presented here in this study. Recognizing there is a redundancy between the mass conservation equation, the equation of state, and the transport equation(s) for the scalar(s) which characterize the thermochemical state, and that it destabilizes explicit methods, we demonstrate how to analytically eliminate the redundancy and propose an iterative scheme to solve the resulting transformed scalar equations. The method obtains second-order accuracy in time regardless of the number of iterations, so one can terminate this subproblem once stability is achieved. Hence, flows with larger density ratios can be simulated while still retaining the efficiency, low cost, and parallelizability of an explicit scheme. The temporal discretization algorithm is used within a pseudospectral direct numerical simulation which extends the method of Kim, Moin, and Moser for incompressible flow to the variable-density, low-Mach setting, where we demonstrate stability for density ratios up to ~25.7.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Core States of Neutron Stars from Anatomizing Their Scaled Structure Equations

Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass–radius sequence characterized by a maximum mass ${M}_{\mathrm{NS}}^{\max}$ at radius $R$ max . We first show analytically that the ${M}_{\mathrm{NS}}^{\max}$ and $R$ max scale linearly with two different combinations of the NS central pressure $P$ $c$ and energy density $ε$ $c$ , by dissecting perturbatively the dimensionless Tolman–Oppenheimer–Volkoff (TOV) equations governing NS internal variables. The scaling relations are then verified via 87 widely used and rather diverse phenomenological as well as 17 microscopic NS EOSs with/without considering hadron–quark phase transitions and hyperons, by solving numerically the original TOV equations. The EOS of the densest NS matter allowed before it collapses into a black hole is then obtained. Using the universal ${M}_{\mathrm{NS}}^{\max}$ and $R$ max scalings and Neutron Star Interior Composition Explorer and XMM-Newton mass–radius observational data for PSR J0740+6620, a very narrow constraining band on the NS central EOS is extracted directly from the data for the first time, without using any specific input EOS model.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Influence of Real Gas Effects on Chemical Kinetics in Oxycombustion in Supercritical Carbon Dioxide

Oxycombustion in supercritical carbon dioxide is an integral part of the Allam Cycle, a technology that enables carbon-neutral use of fossil-fuels and carbon-negative use of biofuels. We simulate oxycombustion in a realistic combustor geometry for two sets of fuel conditions: pure methane, and a 40 percent methane/60 percent carbon dioxide blend, both at 343.15 K. The fuel jet mixes with a preheated swirler of 20 percent oxygen and 80 percent carbon dioxide at 1005.35 K, with a 100 percent carbon dioxide coflow at 783.15 K. The entire system operates at a pressure of 300 bar, putting the entire system above the critical temperature and pressure of carbon dioxide. Simulations are performed using PeleC, a compressible block-structured adaptive-mesh refinement (AMR) reacting flow code. Direct comparison of results using thermodynamically self-consistent implementations of the ideal gas equation of state and the Soave-Redlich-Kwong (SRK) equation of state allow quantification of the real gas impacts on combustion kinetics, flow temperatures, and pollutant formation.

carbon dioxide↗

NASA NTRS1985

Evolution of the innermost stable orbits around accreting neutron stars

The surface of most neutron stars with 'soft' equations of state lies within the innermost stable circular orbit predicted by general relativity. In disk accretion onto a weakly magnetized neutron star, the disk will reach the stellar surface for 'stiff' equations of state, but for soft equations of state the matter will hit the surface in free fall at an angle of about 0.001 to 0.1 radians. All calculations are carried out through first order in the angular momentum of the star.

Kluzniak, W.↗

DOE OSTI2023

Cosmological measurements from void-galaxy and galaxy-galaxy clustering in the Sloan Digital Sky Survey

We present the cosmological implications of measurements of void-galaxy and galaxy-galaxy clustering from the Sloan Digital Sky Survey (SDSS) Main Galaxy Sample (MGS), Baryon Oscillation Spectroscopic Survey (BOSS), and extended BOSS (eBOSS) luminous red galaxy catalogues from SDSS Data Release 7, 12, and 16, covering the redshift range 0.07 < $z$ < 1.0. We fit a standard ΛCDM cosmological model as well as various extensions, including a constant dark energy equation of state not equal to −1, a time-varying dark energy equation of state, and these same models allowing for spatial curvature. Results on key parameters of these models are reported for void-galaxy and galaxy-galaxy clustering alone, both of these combined, and all these combined with measurements from the cosmic microwave background (CMB) and supernovae (SN). For the combination of void-galaxy and galaxy-galaxy clustering, we find tight constraints of Ω m = 0.356 ± 0.024 for a base ΛCDM cosmology, Ω m = $0.391^{+0.028}_{-0.021}$, w = $-1.50^{+0.43}_{-0.28}$ additionally allowing the dark energy equation of state $w$ to vary, and Ω m = $0.331^{+0.067}_{-0.094}$, $w=-1.41^{+0.70}_{-0.31}$, and Ω k = $0.06^{+0.18}_{-0.13}$ further extending to non-flat models. The combined SDSS results from void-galaxy and galaxy-galaxy clustering in combination with CMB+SN provide a 30 per cent improvement in parameter Ω m over CMB+SN for ΛCDM, a 5 per cent improvement in parameter Ω m when $w$ is allowed to vary, and a 32 per cent and 68 per cent improvement in parameters Ω m and Ω k when allowing for spatial curvature.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm↗

NASA NTRS1972

Quantum statistical mechanics of dense partially ionized hydrogen

The theory of dense hydrogen plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. The statistical mechanical calculation of the plasma equation of state is intended for stellar interiors. The general approach is extended to the calculation of the equation of state of the outer layers of large planets.

Dewitt, H. E.↗

DOE OSTI2020

Simulations of Sweeping Wave Propagation in a Boron Carbide Plate

In February 2020, experiments were conducted at Los Alamos National Laboratory measuring the propagation of a sweeping wave through a plate of boron carbide which was induced by detonating an adjacent charge of high explosive. Six such shots were red and in each case progress of the wave along the exposed surface of the plate was tracked using photon doppler velocimetry (PDV). In this report we discuss calculations performed using the Lagrangian hydrocode FLAG to model data taken from these experiments. We discuss the models chosen for the different experimental components, the choice of mesh (focusing on, both, two- and three-dimensional geometries), and compare the results from these calculations to experimentally-extracted PDV traces. Notably, we find that the PDV traces for this experiment are most faithfully reproduced using the full three-dimensional geometry, even when the mesh resolution for the three-dimensional calculations was significantly lower than the resolution for the corresponding two-dimensional calculations. We attribute this to the geometry of the experimental setup. Moreover, we find only negligible differences for the PDV traces obtained using the sesame table equation of state for boron carbide and the Gruneisen equation of state.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Thermodynamic modeling of aqueous acetic acid, butyric acid, and lactic acid solutions

Based on the activity coefficient – fugacity coefficient approach, a rigorous thermodynamic modeling study is presented for accurate correlation of vapor-liquid equilibrium data of aqueous solutions of acetic acid (293 to 391 K), butyric acid (325 to 436 K), lactic acid (378 to 409 K), and acetic acid + butyric acid binary mixture (358 to 421 K). In addition, the pH data of the three aqueous, single carboxylic acid solutions were measured at 298 to 328 K and successfully correlated. Given that these aqueous carboxylic acid solutions exhibit various degrees of association behavior in both vapor and liquid phases, the thermodynamic models considered for this study include the Redlich-Kwong equation of state (RK-EoS) and the Hayden-O’Connell equation of state (HOC-EoS) for the vapor phase fugacity coefficients and the electrolyte non-random two-liquid model (eNRTL) and the association electrolyte non-random two-liquid model (AeNRTL) for the liquid phase activity coefficients. The combination of the HOC-EoS for the vapor phase and the AeNRTL model for the liquid phase is found to provide the best correlation results, consistent with the fact that the HOC-EoS and the AeNRTL model explicitly account for association behaviors in the vapor phase and the liquid phase, respectively.

09 BIOMASS FUELS↗

DOE OSTI2021

High-Order Multipole and Binary Love Number Universal Relations

Using a data set of approximately 2 million phenomenological equations of state consistent with observational constraints, we construct new equation-of-state-insensitive universal relations that exist between the multipolar tidal deformability parameters of neutron stars, Λ l , for several high-order multipoles (l = 5,6,7,8), and we consider finite-size effects of these high-order multipoles in waveform modeling. We also confirm the existence of a universal relation between the radius of the 1.4M ⊙ NS, R 1.4 and the reduced tidal parameter of the binary, Λ˜, and the chirp mass. We extend this relation to a large number of chirp masses and to the radii of isolated NSs of different mass M, R M . We find that there is an optimal value of M for every M such that the uncertainty in the estimate of R M is minimized when using the relation. We discuss the utility and implications of these relations for the upcoming LIGO O4 run and third-generation detectors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

The Symmetry Energy: Current Status of Ab Initio Predictions vs. Empirical Constraints

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Validity of a finite temperature expansion for dense nuclear matter

In this work we provide a new, well-controlled expansion of the equation of state of dense matter from zero to finite temperatures (𝑇) while covering a wide range of charge fractions (𝑌 𝑄 ), from pure neutron to isospin symmetric nuclear matter. Our expansion can be used to describe neutron star mergers using the equation of state inferred from neutron star observations. We discuss how knowledge from low-energy nuclear experiments and heavy-ion collisions can be directly incorporated into the expansion. We also suggest new thermodynamic quantities of interest that can be calculated from theoretical models or directly inferred by experimental data that can be used to infer the finite temperature equation of state. With our new method, we can quantify the uncertainty in our finite 𝑇 and 𝑌 𝑄 expansions without making assumptions about the underlying degrees of freedom. We can reproduce results from a microscopic equation of state up to 𝑇 = 100 MeV for baryon chemical potential 𝜇 𝐵 ≳ 1100 MeV [≈(1–2)⁢𝑛 sat ] within 5% error, with even better results for larger 𝜇 𝐵 and/or lower 𝑇. We investigate the sources of numerical and theoretical uncertainty and discuss future directions of study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Impact of composition and symmetry energy on the temperature of quasiprojectiles simulated with antisymmetrized molecular dynamics

The equation of state describes the emergent physical properties of matter. Experimental data is needed to help constrain the equation of state for nuclear matter. These constraints can help distinguish between an “asy-stiff” and an “asy-soft” equation of state, which has astrophysical implications. One path to help constrain the models is to analyze the nuclear caloric curve; some experiments have shown dependence on neutron excess, and may thus be sensitive to the asymmetry. A difference in the caloric curve based on the asymmetry of the reconstructed quasiprojectile (QP) had been observed using 70 Zn on 70 Zn at 35 MeV/nucleon taken with the NIMROD array. Antisymmetrized molecular dynamics calculations were performed for the same system and deexcited with gemini++. Both Gogny (asy-soft) and Gogny-as (asy-stiff) data sets were generated. The particles were then filtered based on detector geometric acceptance and thresholds. From the accepted particles, the excitation energy and temperature were calculated in the same way as for experimental data. Additionally, filter effects on the observed nuclear caloric curves were investigated. A tendency for the asy-stiff nuclear caloric curves to have higher temperatures than their asy-soft counterparts was observed for a number of probes. In addition, some probes may show sensitivity to the reconstructed composition of the QP, but this is inconclusive due to high statistical fluctuations and a large dependence on the exact method of event selection.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗