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Results for “equations 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.

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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Constraining the release of Sn to the ambient melting point following shock loading using time-resolved x-ray diffraction

The formation of liquid following release from a shocked state governs the transition from spall to cavitation and the formation of ejecta in metals. In order to build physics-based models of these processes, it is necessary to critically evaluate the relative importance of kinetics and entropy generation during the release along with the accuracy of multiphase equations of state. Tin (Sn) has served as a testbed for a variety of experiments examining strength and ejecta due to its accessible melt boundary and solid–solid phase transitions. This work presents experiments examining the phase evolution of high purity Sn following the shock and release to ambient stress near the melting point. Sn is found to release to states between its ambient solidus and liquidus from approximately 19 to 33 GPa under uniaxial loading, with the two-phase region being characterized by a reduction in the intensity of the (220), (211) β -Sn doublet. Jetting experiments performed at 27–28 GPa exhibit comparable diffraction patterns with what is observed following the uniaxial release. The solid fractions of β-Sn in the ambient mixed phase region are found to decrease linearly with increasing shock stress as increasing liquid Sn is formed. Here, the results provide much needed information for interpreting measurements of dynamic strength at a high strain rate and experiments examining cavitation and shallow bubble collapse in Sn.

, spall↗
NASA NTRS1987

Multigrid solution of the Euler equations on unstructured and adaptive meshes

A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structured multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

Mavriplis, Dimitri↗
DOE OSTI2025

Group Conductivity and Nonadiabatic Born Effective Charges of Disordered Metals, Warm Dense Matter, and Hot Dense Plasma

The average ionization state is a critical parameter in plasma models for charged particle transport, equations of state, and optical response. The dynamical or nonadiabatic Born effective charge (NBEC), calculated via first principles time-dependent density-functional theory, provides exact ionic partitioning of bulk electron response for both metallic and insulating materials. The NBEC can be transformed into a “group conductivity,” i.e., the electron conductivity ascribed to a subset of ions. We show that for disordered metallic systems, such as warm dense matter (WDM) and hot dense plasma, the static limit of the NBEC is different from the average ionization states, but that the ionization state can be extracted from the group conductivity even in mixed systems. Here we demonstrate this approach using a set of archetypical examples, including cold and warm aluminium, low- and high-density WDM carbon, and a WDM carbon-beryllium-hydrogen mixture.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1980

An artificial energy method for calculating flows with shocks

The artificial-viscosity method, first proposed by von Neumann and Richtmyer, introduces an artificial viscous pressure term in regions of compression such that an increase in entropy occurs in shock transition zones. The paper describes how dissipative flows can be induced by reducing the total energy available for adiabatic processes in shock zones. A class of inviscid fluid flows, called semiflows, is described in which the flows exhibit thermodynamic differences. Induced dissipative flows modify the pressure in regions of compression in a manner analogous to the artificial-viscosity method and for a gas, the effect is equivalent to suitably modifying the gas constant in the equation of state. By employing MacCormack's method and the usual non-adiabatic equations, numerical solutions of a Riemann problem are compared with the modified artificial energy method, showing that the dissipation effect predicted by the analytical formulation is reflected in the numerical method as well.

Rose, M. E.↗
NASA NTRS1989

Hypervelocity atmospheric flight: Real gas flow fields

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Howe, John T.↗
NASA NTRS1990

Relaxation processes in a turbulent compressible magnetofluid

The compressible extensions of time asymptotic relaxation states of incompressible two-dimensional magnetohydrodynamic turbulence are studied. A polytropic equation of state is used with viscous and resistive dissipation. The incompressible case is known to allow three distinct time asymptotic types of behavior: magnetic energy dominated relaxation, kinetic energy dominated relaxation, and cross helicity dominated relaxation. At low Mach numbers the incompressible scenario is reproducible from the compressible simulations, and compressibility plays only a secondary role. At moderate, but still subsonic, Mach numbers the distinct incompressible processes are still recognizable, but strong compressibility features dominate the high-wave-number regime of several simulations. In particular, the magnetic and kinetic energy dominated simulations display regions of strong acoustic turbulence near the dissipation scale.

Ghosh, S.↗
NASA NTRS1990

Hypervelocity atmospheric flight: Real gas flow fields

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that were reduced to a relatively compact set of equations of a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-averaged behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equation a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. For hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates, chemical nonequilibrium is considered and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Howe, John T.↗
NASA NTRS1995

Modeling of shallow and inefficient convection in the outer layers of the Sun using realistic physics

In an attempt to understand the properties of convective energy transport in the solar convective zone, a numerical model has been constructed for turbulent flows in a compressible, radiation-coupled, nonmagnetic, gravitationally stratified medium using a realistic equation of state and realistic opacities. The time-dependent, three-dimensional hydrodynamic equations are solved with minimal simplifications. The statistical information obtained from the present simulation provides an improved undserstanding of solar photospheric convection. The characteristics of solar convection in shallow regions is parameterized and compared with the results of Chan & Sofia's (1989) simulations of deep and efficient convection. We assess the importance of the zones of partial ionization in the simulation and confirm that the radiative energy transfer is negliglble throughout the region except in the uppermost scale heights of the convection zone, a region of very high superadiabaticity. When the effects of partial ionization are included, the dynamics of flows are altered significantly. However, we confirm the Chan & Sofia result that kinetic energy flux is nonnegligible and can have a negative value in the convection zone.

Kim, Yong-Cheol↗
NASA NTRS2006

Computing Isentropic Flow Properties of Air/R-134a Mixtures

MACHRK is a computer program that calculates isentropic flow properties of mixtures of air and refrigerant R-134a (tetrafluoroethane), which are used in transonic aerodynamic testing in a wind tunnel at Langley Research Center. Given the total temperature, total pressure, static pressure, and mole fraction of R-134a in a mixture, MACHRK calculates the Mach number and the following associated flow properties: dynamic pressure, velocity, density, static temperature, speed of sound, viscosity, ratio of specific heats, Reynolds number, and Prandtl number. Real-gas effects are taken into account by treating the gases comprising the mixture as both thermally and calorically imperfect. The Redlich-Kwong equation of state for mixtures and the constant-pressure ideal heat-capacity equation for the mixture are used in combination with the departure- function approach of thermodynamics to obtain the equations for computing the flow properties. In addition to the aforementioned calculations for air/R-134a mixtures, a research version of MACHRK can perform the corresponding calculations for mixtures of air and R-12 (dichlorodifluoromethane) and for air/SF6 mixtures. [R-12 was replaced by R-134a because of environmental concerns. SF6 has been considered for use in increasing the Reynolds-number range.]

Kvaternik, Ray↗
DOE OSTI2023

Central speed of sound, the trace anomaly, and observables of neutron stars from a perturbative analysis of scaled Tolman-Oppenheimer-Volkoff equations

The central speed of sound (SS) measures the stiffness of the equation of state (EOS) of superdense neutron star (NS) matter. Its variations with density and radial coordinate in NSs in conventional analyses often suffer from uncertainties of the specific nuclear EOS used. Using the central SS and NS mass/radius scaling obtained from solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations, we study the variations of SS, trace anomaly and several closely related properties of NSs in an EOSmodel- independent manner. We find that the SS increases with the reduced central pressure Pˆ c ≡ P c =ε c (scaled by the central energy density εc), and the conformal bound for SS tends to break down for NSs with masses higher than about 1.9M ⊙ . The ratio P=ε is upper bounded as P=ε ≲ 0.374 around the centers of stable NSs. We demonstrate that it is an intrinsic property of strong field gravity and is more relevant than the perturbative QCD bound on it. While a sharp phase transition at high densities characterized by a sudden vanishing of SS in cores of massive NSs are basically excluded, the probability for a continuous crossover signaled by a peaked radial profile of SS is found to be enhanced as Pˆ c decreases, implying it likely happens near the centers of massive NSs. Moreover, a new and more stringent causality boundary as R max =km ≳ 4.73$M$$^{max}_{NS}$ =M ⊙ þ 1.14 for the NS mass-radius curve is found to be excellently consistent with observational data on NS masses and radii. Here, new constraints on the ultimate energy density and pressure allowed in NSs before collapsing into black holes are obtained and compared with earlier predictions in the literature

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

New insights into supradense matter from dissecting scaled stellar structure equations

The strong-field gravity in general relativity (GR) realized in neutron stars (NSs) renders the equation of state (EOS) P(ε) of supradense neutron star matter to be essentially nonlinear and refines the upper bound for Φ ≡ P/ε to be much smaller than the special relativity (SR) requirement with linear EOSs, where P and ε are respectively the pressure and energy density of the system considered. Specifically, a tight bound Φ ≲ 0.374 is obtained by perturbatively anatomizing the intrinsic structures of the scaled Tolman–Oppenheimer–Volkoff (TOV) equations without using any input nuclear EOS. New insights gained from this novel analysis provide EOS-model-independent constraints on the properties (e.g., density profiles of the sound speed squared s 2 = dP/dε and trace anomaly Δ = 1/3 – Φ) of cold supradense matter in NS cores. Using the gravity-matter duality in theories describing NSs, we investigate the impact of gravity on supradense matter EOS in NSs. In particular, we show that the NS mass M NS , radius R, and compactness ξ ≡ M NS /R scale with certain combinations of its central pressure and energy density (encapsulating its central EOS). Thus, observational data on these properties of NSs can straightforwardly constrain NS central EOSs without relying on any specific nuclear EOS model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Isotope effects in supercooled H 2 O and D 2 O and a corresponding-states-like rescaling of the temperature and pressure

Water shows anomalous properties that are enhanced upon supercooling. The unusual behavior is observed in both H 2 O and D 2 O, however, with different temperature dependences for the two isotopes. It is often noted that comparing the properties of the isotopes at two different temperatures (i.e., a temperature shift) approximately accounts for many of the observations—with a temperature shift of 7.2 K in the temperature of maximum density being the most well-known example. However, the physical justification for such a shift is unclear. Motivated by recent work demonstrating a “corresponding-states-like” rescaling for water properties in three classical water models that all exhibit a liquid–liquid transition and critical point, the applicability of this approach for reconciling the differences in the temperature- and pressure-dependent thermodynamic properties of H 2 O and D 2 O is investigated here. Utilizing previously published data and equations-of-state for H 2 O and D 2 O, we show that the available data and models for these isotopes are consistent with such a low temperature correspondence. These observations provide support for the hypothesis that a liquid–liquid critical point, which is predicted to occur at low temperatures and high pressures, is the origin of many of water’s anomalies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Simultaneous compression and opacity data from time-series radiography with a Lagrangian marker

Time-resolved radiography can be used to obtain absolute shock Hugoniot states by simultaneously measuring at least two mechanical parameters of the shock, and this technique is particularly suitable for one-dimensional converging shocks where a single experiment probes a range of pressures as the converging shock strengthens. However, at sufficiently high pressures, the shocked material becomes hot enough that the x-ray opacity falls significantly. Additionally, if the system includes a Lagrangian marker such that the mass within the marker is known, this additional information can be used to constrain the opacity as well as the Hugoniot state. In the limit that the opacity changes only on shock heating, and not significantly on subsequent isentropic compression, the opacity of the shocked material can be determined uniquely. More generally, it is necessary to assume the form of the variation of opacity with isentropic compression or to introduce multiple marker layers. Alternatively, assuming either the equation of state or the opacity, the presence of a marker layer in such experiments enables the non-assumed property to be deduced more accurately than from the radiographic density reconstruction alone. An example analysis is shown for measurements of a converging shock wave in polystyrene at the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Current challenges in the physics of white dwarf stars

White dwarfs are a class of stars with unique physical properties. They present many challenging problems whose solution requires advanced theories of dense matter, state-of-the-art experimental techniques, and extensive computing efforts. New ground- and space-based observatories will soon provide an increasingly detailed view of white dwarf stars and reveal new phenomena that will challenge our models. This review is an introduction to the nature of white dwarfs, the physical processes that determine their structure and evolution, and the physical conditions they span. Here we discuss a wide variety of currently unsolved or partially resolved problems in their constitutive physics that are broadly related to equations of state, transport processes and opacities.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1972

Quantum statistical mechanics of dense partially ionized hydrogen.

The theory of dense hydrogenic 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. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.

Dewitt, H. E.↗
DOE OSTI2025

Black hole-neutron star binaries near neutron star disruption limit in the mass regime of event GW230529

In May 2023, the LIGO-Virgo-KAGRA (LVK) Collaboration reported the likely black hole-neutron star (BHNS) merger GW230529_181500. The signal was observed with high significance in only one detector, limiting constraints on the black hole spin and motivating our study of disruption in this mass regime. That event is expected to be the merger of a 2.5–4.5 M ⊙ primary with a secondary compact object of mass between 1.2–2.0 M ⊙ . This makes it the first BHNS merger with a significant potential for the production of electromagnetic (EM) counterparts, and provides further evidence for compact objects existing within the suspected lower mass gap. To produce post-merger EM transients, the component of the black hole spin aligned with the orbital angular momentum must be sufficiently high, allowing the neutron star to be tidally disrupted. The disrupting BHNS binary may then eject a few percent of a solar mass of matter, leading to an observable kilonova driven by radioactive decays in ejecta, and/or a compact-binary gamma-ray burst (cbGRB) resulting from the formation of an accretion disk and relativistic jet. Determining which mergers lead to disruption of the neutron star is necessary to predict the prevalence of EM signals from BHNS mergers, yet most BHNS simulations so far have been performed far from the minimum spin required for tidal disruption. Here, we use the Spectral Einstein Code to explore the behavior of BHNS mergers in a mass range consistent with GW230529_181500 close to that critical spin, and compare our results against the mass remnant model currently used by the LVK Collaboration to predict the probability of tidal disruption. Furthermore, our numerical results reveal the emergence of non-zero accretion disks even below the predicted NS disruption limit, of low mass but capable of powering cbGRBs. Our results also demonstrate that the remnant mass model underpredicts the disk mass for the DD2 equation of state, while they are within expected modeling errors for SFHo. The disruption limit itself, however, is not found to significantly differ from the predictions of the analytical model, unless remnant masses M rem ≲ 0.001 M ⊙ prove interesting observationally. In all of our simulations, any kilonova signal would be dim and most likely dominated by post-merger disk outflows.

GW230529_181500↗
DOE OSTI2025

Signature of hadron-quark crossover in binary-neutron-star mergers

Here, we study observational signatures of the hadron-quark crossover in binary-neutron-star mergers by numerical-relativity simulations with various mass configurations. We employ two equations of state (EoSs) for matter consistent with inference from the observational data. In the crossover scenario the EoS is softened in a density realized in binary-neutron-star mergers and is smoothly continued to quark matter. In the phase transition scenario without crossover, the EoS remains stiff and a first-order phase transition takes place in a density out of reach of mergers. A GW170817-like system forms a remnant massive neutron star in both scenarios, and it collapses into a black hole only in the crossover scenario due to the softening while gravitational-wave emission is strong. This difference is clearly reflected in the sudden shutdown of gravitational waves. For a given EoS, the lifetime of the merger remnant is determined primarily by the total mass of the system. Identifying these features in a variety of future events with the next generation of ground-based gravitational-wave detectors will enable us to clarify details of hadron-quark transition. The mass of the accretion disk surrounding the remnant black hole is affected not only by the lifetime of the remnant but also by the mass ratio of the system. Electromagnetic emission associated with the disk outflow will also be useful for detailed investigation of the hadron-quark transition.

QCD phase transitions↗