Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Equation of State”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties

Here, we introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (𝜒⁢EFT ). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as 𝜒⁢EFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the 𝜒⁢EFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

The extended Vinet analytical equations of state

When testing new materials models, it is often not possible to use tabulated Equations of States (EOS) since the model might only be available in a smaller specialized research code without capability to read in tables. In such cases a versatile and easy to implement analytical EOS is needed. In this report I derive, give, and discuss all formulas necessary for implementing the thermodynamically complete extended Vinet EOS 3 into codes. While similar to a Mie-Grüneisen (MG) EOS, this Vinet EOS is based on an isotherm and substantially easier to correctly implement than a MG EOS. In the extended Vinet the isotherm’s density dependence is given as a power series in density to accommodate for higher density behavior which normally requires the Hugoniot based MG.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Perturbative QCD and the neutron star equation of state

Here, we construct a physics-agnostic approach to the neutron star (NS) equation of state (EoS) based on a sound speed model, which connects both low-density information from nuclear theory and high-density constraints from perturbative quantum chromodynamics (pQCD). Using this approach, we study the impact of pQCD calculations on NS EoS that have been constrained by astrophysical observations. We find that pQCD affects the EoS mainly beyond the densities realized in NS. Furthermore, we observe an interesting interplay between pQCD and astrophysical constraints, with pQCD preferring softer EoS for the heaviest NS while recent NICER observations suggest the EoS to be stiffer. We explore the sensitivity of our findings to pQCD uncertainties and study the constraining power of pQCD if future observations of heavy NS were to suggest radii larger than 13 km.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

First-principles equation of state database for warm dense matter computation

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds LiF , B 4 C , BN , CH 4 , CH 2 , C 2 H 3 , CH , C 2 H , MgO , and MgSiO 3 . For all these materials, we provide the pressure and internal energy over a density-temperature range from ~ 0.5 to 50 g cm - 3 and from ~ 10 4 to 10 9 K, which are based on ~ 5000 different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of L - and K -shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. Furthermore, we derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of H 2 O , H 2 O 2 , Al 2 O 3 , CO , and CO 2 to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Development of uncertainty-aware equation-of-state models: Application to copper

Sophisticated hydrodynamic codes are commonly used to understand and predict events relevant to natural and applied sciences. The degree to which these simulations reflect reality, however, is dependent on how well we understand the materials and underlying physics involved. These research communities need material models that communicate the uncertainty in the physical properties, which at their basest form comes from the uncertainty in the underlying experimental measurements. Additionally, we have constructed a new framework for using both experimental measurements and the associated experimental uncertainties to build equation-of-state models that reflect not only current best measurements but also the accuracy of those measurements. This method had been used to construct an ensemble of equation-of-state models for copper that communicates the experimental uncertainties in the data through the equation-of-state model, which is available for application in any simulation metric of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Strength, deformation, and equation of state of tungsten carbide to 66 GPa

Here, strength, texture, and equation of state of hexagonal tungsten monocarbide (WC) have been determined under quasi-hydrostatic and non-hydrostatic compression to 66 GPa using angle-dispersive X-ray diffraction in the diamond anvil cell. Quasi-hydrostatic compression in a Ne pressure medium demonstrates that nanocrystalline WC is slightly less incompressible than bulk-scale WC, with respective bulk moduli of K 0 = 377 ± 7 and 397 ± 7 GPa and pressure derivatives K 0 ’ = 3.8 ± 0.3 and 3.7 ±0.3. This decrease in incompressibility with grain size is similar to behavior observed in other ceramics. Under nonhydrostatic compression, WC supports a mean differential stress of ~12-15 GPa at plastic yielding, which occurs at ~30 GPa. Strength in WC is anisotropic, with the (001) plane supporting 29-42% higher stress than stresses calculated from mean strain. Simulations using an Elasto-ViscoPlastic Self-Consistent model indicate that strength inferred from lattice strain theory may be overestimated due to effects of plastic deformation. Plastic deformation generates a texture maximum near $\langle\bar{2}110\rangle$ in the compression orientation, initially through prismatic slip on the {$10\bar{1}0$}$\langle\bar{1}2\bar{1}0\rangle$ and {$10\bar{1}0$}$\langle0001\rangle$ slip systems, followed by activation of pyramidal slip on {$10\bar{1}1$}$\langle\bar{2}113\rangle$ at ~40-50 GPa.

36 MATERIALS SCIENCE↗
NASA NTRS1984

Conservative streamtube solution of steady-state Euler equations

This paper presents a new method for solving the steady state Euler equations. The method is similar to streamline curvature methods but has a conserative finite volume formulation which ensures correct shock capturing. Either wall position or wall pressure may be prescribed as boundary conditions, permitting both direct and inverse calculations. In supersonic applications the solution is obtained by space-marching while in subsonic and transonic applications iterative relaxation methods are used. Numerical results are given for: (1) supersonic diffuser with oblique shocks (direct calculation); (2) supersonic jet entering still reservoir (inverse calculation); (3) subsonic bump in a channel with 25 percent blockage (direct and inverse); (4) subsonic high-work turbine cascade (direct); and (5) transonic bump in a channel with 12 percent blockage (direct calculation).

Drela, M.↗
DOE OSTI2021

Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory

We present predictions for the neutron matter equation of state, from leading to fourth order of chiral effective field theory, using recently developed, accurate chiral nucleon-nucleon potentials. For the many-body method, we employ the nonperturbative particle-particle ladder approximation, that is, we solve the G-matrix equation. Furthermore, we find the impact of subleading three-neutron forces to be mild and attractive. We also show order-by-order predictions for the symmetry energy, and discuss its density dependence in relation to empirical constraints. For the nuclear matter equation of state, in this work we adopt an empirical parametrization with good saturation properties. This is to highlight, specifically, the energy and pressure in neutron matter, particularly when comparing with empirical constraints.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Stability of expanding accretion shocks for an arbitrary equation of state

We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

Huete, César (ORCID:0000000232278520)↗
NASA NTRS1991

Shock wave equation of state of serpentine to 150 GPa - Implications for the occurrence of water in the earth's lower mantle

The shock wave equation of state of Mg end-member serpentine was determined to 150 GPa by examining the shock properties of three polycrystalline serpentines: (1) a lizardite serpentine found near Globe (Arizona), (2) an antigorite serpentine from Thurman (New York), and (3) a chrysotile serpentine from Quebec (Canada). The shock wave experiments were carried out using either a two-stage light gas gun or a 40-mm bore propellant. The shock equation of state that was obtained is shown to exhibit four distinct regions: a low-pressure phase, a mixed phase region, a high-pressure phase, and a very high-pressure phase. The high-pressure density and sound speed of an H2O-rich magnesium silicate determined from these experiments indicate that the observed seismic properties of the lower mantle allow the existence of several weight percent of water in the lower mantle.

Tyburczy, James A.↗
DOE OSTI2020

Multidimensional Tests of a Finite-Volume Solver for MHD With a Real-Gas Equation of State

This work considers two algorithms of a finite-volume solver for the MHD equations with a real-gas equation of state (EOS). Both algorithms use a multistate form of Harten-Lax-Van Leer approximate Riemann solver as formulated for MHD discontinuities. This solver is modified to use the generalized sound speed from the real-gas EOS. Two methods are tested: EOS evaluation at cell centers and at flux interfaces where the former is more computationally efficient. A battery of 1D and 2D tests are employed: convergence of 1D and 2D linearized waves, shock tube Riemann problems, a 2D nonlinear circularly polarized Alfvén wave, and a 2D magneto-Rayleigh-Taylor instability test. The cell-centered EOS evaluation algorithm produces unresolvable thermodynamic inconsistencies in the intermediate states leading to spurious solutions while the flux-interface EOS evaluation algorithm robustly produces the correct solution. The linearized wave tests show this inconsistency is associated with the magnetosonic waves and the magneto-Rayleigh-Taylor instability test demonstrates simulation findings where the spurious solution leads to an unphysical simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1971

Ride comfort control in large flexible aircraft

The problem of ameliorating the discomfort of passengers on a large air transport subject to flight disturbances is examined. The longitudinal dynamics of the aircraft, including effects of body flexing, are developed in terms of linear, constant coefficient differential equations in state variables. A cost functional, penalizing the rigid body displacements and flexure accelerations over the surface of the aircraft is formulated as a quadratic form. The resulting control problem, to minimize the cost subject to the state equation constraints, is of a class whose solutions are well known. The feedback gains for the optimal controller are calculated digitally, and the resulting autopilot is simulated on an analog computer and its performance evaluated.

Warren, M. E.↗
NASA NTRS1987

Control of SCOLE

A relatively low order model is used to control SCOLE. Drastic truncation of the discretized model is proposed by means of a modal expansion. An open loop eigenvalue problem is illustrated as is truncated modal equations, modal state equations, actual output vector and modal Kalman filter. Also illustrated is independent modal-space control.

Meirovitch, L.↗
NASA NTRS1989

Flux-split algorithms for the multi-dimensional Euler equations with real gases

Upwind algorithms are developed for the numerical solution of the multidimensional Euler equations for real gases. Flux-splitting methods are derived which account for a general equation of state. Approximations to the state equation based on physical arguments result in simplified algorithms which may be implemented into existing perfect-gas codes. Applications of the method to several high-Mach-number high-temperature flows are presented for two and three space dimensions.

Grossman, B.↗
DOE OSTI2024

Equation of State and Thermometry of the 2D SU ( N ) Fermi-Hubbard Model

We characterize the equation of state (EoS) of the SU ( N > 2 ) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N = 3 , 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU ( N ) FHM. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Empirical radius formulas for canonical neutron stars from bidirectionally selecting features of equations of state in extended Bayesian analyses of observational data

Significant advancement in Bayesian inference of nuclear equation of state (EOS) from gravitational wave and x-ray observations of neutron stars (NSs) has been made by the nuclear astrophysics community especially since GW170817. By extending the traditional Bayesian analysis which normally ends at presenting the marginalized posterior probability distribution functions (PDFs) of individual EOS parameters and their correlations (or sometimes only the Pearson correlation coefficients which are only reliably useful when the variables are linearly correlated while they are actually often not), we search for a data-driven and robust empirical formula for the radius 𝑅 1.4 of canonical NSs in terms of the characteristic EOS parameters (features). We also identify the single most important but currently poorly known EOS parameter for determining the 𝑅 1.4 . Using three regression-model-building methodologies: bidirectional stepwise feature selection, least absolute shrinkage selection operator (LASSO) regression, and neural network regression on a large set of posterior EOSs and the corresponding 𝑅 1.4 values inferred from earlier comprehensive Bayesian analyses of NS observational data, we systematically and rigorously develop the most probable 𝑅 1.4 formulas with varying statistical accuracy and technical complexity. Here, the most important EOS parameters for determining 𝑅 1.4 are found consistently in each of the feature selection processes to be (in order of decreasing importance): curvature 𝐾 sym , slope 𝐿, skewness 𝐽 sym of nuclear symmetry energy, skewness 𝐽 0 , incompressibility 𝐾 0 of symmetric nuclear matter, and the magnitude 𝐸 sym ⁡(𝜌 0 ) of symmetry energy at the saturation density 𝜌 0 of nuclear matter.

Bayesian methods↗