Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

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

At least 1,207 records · Page 67

Illuminating Dark Matter Admixed in Neutron Stars with Simultaneous Mass–Radius Constraints

We investigate how simultaneous mass and radius measurements of massive neutron stars can help constrain the properties of dark matter possibly admixed in them. Within a fermionic dark matter model that interacts only through gravitation, along with a well-constrained nuclear matter equation of state, we show that the simultaneous mass and radius measurement of PSRJ0740+6620 reduces the uncertainty of dark matter central energy density by more than 50% compared to the results obtained from using the two observables independently, while other dark matter parameters remain unconstrained. Additionally, we find that the dark matter fraction fD should be smaller than 2% when constrained by the observed neutron star maximum mass alone, and it could be even smaller than 0.3% with the simultaneous measurement of mass and radius, supporting the conclusion that only a small amount of dark matter exists in dark matter admixed neutron stars (DANSs).

NICER↗

The steady global corona

The formation of the steady coronal structure which consists of coronal streamers and holes is seen in terms of a model employing numerical solutions of time-dependent, dissipationless, magnetohydrodynamic equations of motion applicable to the meridional plane. A coronal streamer consists of closed magnetic field lines near the solar surface with overlying and adjacent open field lines, and the atmosphere, which is stationary in the closed region, flows outward in the open region, or coronal hole. The steady coronal structure is obtained by starting the numerical calculation with a state comprising a polytropic, hydrodynamical solution to the steady-state radial equation of motion coupled with a dipole magnetic field. Global coronal configurations are calculated for values of the plasma beta which vary from 0.1 to 100. It is found that the height and lateral extension of the closed region are only weakly dependent on the data.

Steinolfson, R. S.↗

Orion Parachute Riser Cutter Development

This paper presents the tests and analytical approach used on the development of a steel riser cutter for the CEV Parachute Assembly System (CPAS) used on the Orion crew module. Figure 1 shows the riser cutter and the steel riser bundle which consists of six individual cables. Due to the highly compressed schedule, initial unavailability of the riser material and the Orion Forward Bay mechanical constraints, JSC primarily relied on a combination of internal ballistics analysis and LS-DYNA simulation for this project. Various one dimensional internal ballistics codes that use standard equation of state and conservation of energy have commonly used in the development of CAD devices for initial first order estimates and as an enhancement to the test program. While these codes are very accurate for propellant performance prediction, they usually lack a fully defined kinematic model for dynamic predictions. A simple piston device can easily and accurately be modeled using an equation of motion. However, the accuracy of analytical models is greatly reduced on more complicated devices with complex external loads, nonlinear trajectories or unique unlocking features. A 3D finite element model of CAD device with all critical features included can vastly improve the analytical ballistic predictions when it is used as a supplement to the ballistic code. During this project, LS-DYNA structural 3D model was used to predict the riser resisting load that was needed for the ballistic code. A Lagrangian model with eroding elements shown in Figure 2 was used for the blade, steel riser and the anvil. The riser material failure strain was fine tuned by matching the dent depth on the anvil with the actual test data. LS-DYNA model was also utilized to optimize the blade tip design for the most efficient cut. In parallel, the propellant type and the amount were determined by using CADPROG internal ballistics code. Initial test results showed a good match with LS-DYNA and CADPROG simulations. Final paper will present a detailed roadmap from initial ballistic modeling and LS-DYNA simulation to the performance testing. Blade shape optimization study will also be presented.

Oguz, Sirri↗

Stratospheric warmings diagnosed using the transformed Eulerian-mean equations and the effect of the mean state on wave propagation

Terms for the transformed Eulerian equations are calculated in order to characterize the phenomenom of sudden stratospheric warming. The transformed diagnostics are applied to data for warmings during Dec. and Jan. 1976-1977, as well as cross sections for the directions of the Eiliassen-Palm (EP) fluxes and residual mean meridional circulations. The convergence of the EP flux was determined to provide a strong approximation to the total effect of waves in forcing the zonal mean flow. The EP fluxes change from an upward and equatorward direction to an upward and poleward direction during the warmings, and indications are reported that the effect is due to a feedback on wave propagation of an evolving mean flow. Ray paths in the meridional plane are computed for different mean wind fields to determine the direction of wave propagation according to linear theory based on the WKB approximation.

Oneill, A.↗

Arctic Sea ice by passive microwave observations from the Nimbus-5 Satellite

The results of a dynamic/thermodynamic numerical model of Arctic sea ice are compared with satellite images from the Nimbus 5 electrically scanning microwave radiometer. The model combines aspects of two previous sea ice models those of Parkinson and Washington and Ling, Rasmussen, and Campbell. A solid/fluid model basically follows the formulation of the Parkinson and Washington model with the addition of the constitutive equation and equation of state from the Ling model. The Parkinson and Washington model simulates the seasonal cycle of sea ice thicknesses and concentrations with a horizontal resolution of roughly 200 km and a timestep of 8 hours. The thermodynamics are calculated through energy balances at the interfaces between ice and air, water and ice, and water and air. The ice dynamics are calculated through a momentum equation balancing air stress, water stress, dynamic topography, and Coriolis force, with an adjustment for internal ice resistance.

Campbell, W. J.↗

Estimating ionization states and continuum lowering from ab initio path integral Monte Carlo simulations for warm dense hydrogen

Warm dense matter (WDM) is an active field of research, with applications ranging from astrophysics to inertial confinement fusion. Ionization degree and continuum lowering are important quantities to understand how materials behave under these conditions, but can be difficult to diagnose since experimental campaigns are limited and often require model-dependent analysis. This is especially true for hydrogen, which has a comparably low scattering cross section, making high-quality data particularly difficult to obtain. Consequently, building equation of state tables often relies on simulations in combination with untested approximations to extract properties from experiments. Here, we investigate an approach for extracting the ionization potential depression and ionization degree—quantities which are otherwise not directly accessible from the physical model—from first-principles path integral Monte Carlo (PIMC) simulations utilizing a chemical model. In contrast to experimental measurements, where noise and nonequilibrium effects add to the uncertainty of the inferred parameters, PIMC simulations provide a clean signal with well-defined thermodynamic conditions. Comparisons against commonly used models show a qualitative agreement, but we find deviations primarily for the high-density and high-temperature cases. We also demonstrate the decreasing sensitivity of the dynamic structure factor with respect to both ionization and continuum lowering for increasing scattering angles in x-ray Thomson scattering experiments. Our work has important implications for the design of future experiments, but also offers qualitative understanding of structure factors and the imaginary-time correlation function obtained from first-principles quantum Monte Carlo simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

General relativistic hydrodynamic simulations of binary strange star mergers

We perform fully general-relativistic simulations of binary strange star mergers considering two different approaches for thermal effects. The first uses a cold equation of state (EOS) derived from a modified version of the MIT bag model which is then supplemented by a Γ-law correction. The second approach employs a microphysical description of the finite-temperature effects. We describe results obtained with the two treatments, highlighting the influence of thermal effects. We find that the postmerger dynamics differs significantly in the two cases, leading to quantitative differences in the postmerger gravitational-wave spectrum and ejecta mass. The peak frequency of the postmerger gravitational-wave emission is consistent with the established quasi-universal relations for binary neutron star mergers and as a result, our simulations cannot distinguish between mergers of neutron stars and those of strange stars. Our models with realistic treatment of finite-temperature effects produce a significant amount of ejecta ≳0.02 M ⊙ ​. Here, the resulting flux of strangelets near the Earth, computed assuming that all neutron star mergers are in fact strange-stars mergers and that the binary considered here is representative, is in tension with experimental upper limits. As such, our results tentatively disfavor a scenario in which strange-quark matter is the lowest energy state of matter.

79 ASTRONOMY AND ASTROPHYSICS↗

Helium emission from model flare layers

The emission of visible and UV He I and He II line radiation from a plane-parallel model flare layer characterized by electron temperatures of 10,000 to 50,000 K and electron densities of 10 to the 10th power to 10 to the 15th power per cu cm is analyzed by solving the statistical-equilibrium equations for a 30-level He I-II-III system, using parametric representations of the line and continuum radiation fields. The atomic model was chosen to provide accurate solutions for the first two resonance lines of He I and He II as well as for the D3 and 10,830-A lines of He I. Reaction rates are discussed, and sample solutions to the steady-state population equations are given for a generally optically thin gas assumed to be irradiated over 2pi sr by a blackbody spectrum at 6000 K. Specific results are examined for ionization equilibrium, level populations, approximate optical depths of a 1000-km-thick flare layer, line intensities, and upper-level population rates.

Kulander, J. I.↗

Modeling and optimization of steady flow of natural gas and hydrogen mixtures in pipeline networks

Here, we extend the canonical problems of simulation and optimization of steady-state gas flows in pipeline networks with compressors to the transport of mixtures of highly heterogeneous gases injected throughout a network. Our study is motivated by proposed projects to blend hydrogen generated using clean energy into existing natural gas pipeline systems as part of efforts to reduce the reliance of energy systems on fossil fuels. Flow in a pipe is related to endpoint pressures by a basic Weymouth equation model, with an ideal gas equation of state, where the wave speed depends on the hydrogen concentration. At vertices, in addition to mass balance, we also consider mixing of incoming flows of varying hydrogen concentrations. The problems of interest are the heterogeneous gas flow simulation (HGFS), which determines system pressures and flows given fixed boundary conditions and compressor settings, as well as the heterogeneous gas flow optimization (HGFO), which extremizes an objective by determining optimal boundary conditions and compressor settings. We examine conditions for uniqueness of solutions to the HGFS, as well as compare and contrast mixed-integer and continuous nonlinear programming formulations for the HGFO. We develop computational methods to solve both problems, and examine their performance using four test networks of increasing complexity.

08 HYDROGEN↗

In Situ Determination of Thermoelastic Properties of Magnesite at High Pressure and Temperature With Implications to Seismic Detectability of Moderately Carbonated Lithologies in the Earth's Mantle

Abstract Subduction of carbonate‐bearing oceanic plates into Earth's interior recycles carbon from the surface to the deep mantle. The subducted carbonates can significantly affect mantle properties and dynamics. Magnesite is recognized as one of the major potential carbon hosts in the deep mantle because of its stability up to deep lower mantle conditions. However, despite many previous studies on the equation of state and elastic properties of magnesite, large discrepancies still exist for its elastic moduli and their pressure and temperature derivatives. Here we report in situ density and elastic wave velocity measurements on a natural magnesite at simultaneous high pressure‐temperature conditions up to ∼8 GPa–1073 K in a multi‐anvil apparatus using ultrasonic and synchrotron X‐ray techniques. Global fitting of the data set to finite strain equations yieldsK S0 = 114.0 ± 1.2 GPa, = 4.9 ± 0.3, = (−0.019 ± 0.002) GPa/K,G 0 = 68.6 ± 0.4 GPa,G′ = 1.6 ± 0.1, and = (−0.018 ± 0.001) GPa/K. Compared to other major upper mantle and transition zone minerals, magnesite has intermediateV P , the lowestV S , and the lowest density. Thus, magnesite possesses higherV P /V S ratio than other mantle minerals in normal mantle regions, whereas this feature is less pronounced in subduction zone environments. Modeling of the velocity profiles of carbonated lithologies along different geotherms suggests that moderately‐enriched magnesite domains are unlikely to be detected seismically in the Earth's mantle.

Geochemistry & Geophysics↗

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Viscosities of the Baryon-Rich Quark-Gluon Plasma from Beam Energy Scan Data

Here, this work presents the first Bayesian inference study of the (3 + 1)D dynamics of relativistic heavy-ion collisions and quark-gluon plasma viscosities using an event-by-event (3 + 1)D hydrodynamics + hadronic transport theoretical framework and data from the Relativistic Heavy Ion Collider Beam energy scan program. Robust constraints on initial state nuclear stopping and the baryon chemical potential-dependent shear viscosity of the produced quantum chromodynamic (QCD) matter are obtained. The specific bulk viscosity of the QCD matter is found to exhibit a preferred maximum around $\sqrt{s_{NN}}$ = 19.6 GeV . This result allows for the alternative interpretation of a reduction (and/or increase) of the speed of sound relative to that of the employed lattice-QCD based equation of state for net baryon chemical potential μ B ~0.2(0.4) GeV .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Error quantification and comparison of binary neutron star gravitational waveforms from numerical relativity codes

Future gravitational wave detections of merging binary neutron star systems have the possibility to tightly constrain the equation of state of dense nuclear matter. In order to extract such constraints, gravitational waveform models need to be calibrated to accurate numerical relativity simulations of the late inspiral and merger. In this work, we take an essential step toward classifying the error and potential systematics in current generation numerical relativity simulations of merging binary neutron stars. To this end, we perform a direct comparison of two codes (fil, spec), which differ in many aspects, including the numerical methods and discretizations used and equations solved. We find that despite these different approaches, the codes are—within current numerical resolution bounds—fully consistent, and broadly comparable in cost for a given accuracy level. Our results indicate that the error in the waveforms is primarily dominated by the hydrodynamic evolution, consistent with earlier findings in the literature. Finally, we also discuss current limitations and cost estimates for numerical relativity simulations to reach the accuracies required in the era of next-generation gravitational detectors.

gravitational waves↗

Efficient and robust stability analysis in the internal energy, volume, and moles (UVN) space

Hydrodynamic simulation of fluids in vessels is often based on the internal energy (U), volume (V), and the number of moles of all components ( re N = N 1 , N 2 , ..., N n ) as the working variables to determine the thermodynamic state by finding the global maximum of entropy. The procedure of finding the equilibrium state may be divided into two steps: stability analysis and phase-split computations. Stability analysis is performed first, and the phase-split computation proceeds if the system is unstable. Most of the past work on UVN space has been based on phase-split computations, while the stability analysis is barely investigated. Furthermore, previous studies for the stability analysis use only Newton's method to solve the non-linear algebraic equations. We present an efficient and robust approach for stability analysis where UVN is specified. The successive substitution iteration (SSI) is used to provide good initial guesses for Newton's method. The proposed approach results in a reduced number of unknowns and does not require a large number of iterations to achieve convergence in Newton's method. Overall, our proposed formulation is compatible with different equations of state and is applicable to both pure component and multi-components. The robustness and efficiency of the algorithm for stability analysis are demonstrated in various examples.

02 PETROLEUM↗

Designing a quantum-accurate machine-learning potential to enable large-scale simulations of deuterium under shock

Large-scale molecular dynamics of deuterium under shock can elucidate kinetic processes vital to the target design in inertial confinement fusion and high-energy-density experiments. However, modeling the complex evolution of this material from an insulating molecular state at ambient pressure to an ionized, atomic fluid under strong shock is beyond the capability of simple pair and even bond order potentials. We thus train a quantum-accurate and broadly transferable machine-learning interatomic potential for deuterium using the Chebyshev Interaction Model for Efficient Simulations framework. We show that due to an improved description of the molecular-to-atomic transition, our model is able to better reproduce the ab initio equation of state, radial distribution functions, and principal Hugoniot than bond order potentials. This represents an important step toward large-scale quantum-accurate and nonequilibrium simulations of complicated systems under dynamic changes including phase transitions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Thermodynamics of hydrogen-helium mixtures at high pressure and finite temperature

A technique is reviewed for calculating thermodynamic quantities for mixtures of light elements at high pressure, in the metallic state. Ensemble averages are calculated with Monte Carlo techniques and periodic boundary conditions. Interparticle potentials are assumed to be coulombic, screened by the electrons in dielectric function theory. This method is quantitatively accurate for alloys at pressures above about 10 Mbar. An alloy of equal parts hydrogen and helium by mass appears to remain liquid and mixed for temperatures above about 3000 K, at pressures of about 15 Mbar. The additive volume law is satisfied to within about 10%, but the Gruneisen equation of state gives poor results. A calculation at 1300 K shows evidence of a hydrogen-helium phase separation.

Hubbard, W. B.↗

Comparison between the PISO algorithm and preconditioning methods for compressible flow

Two widely used family of algorithms, pressure-based and density-based methods, have been developed for computational fluid dynamics (CFD) problems over the years. Pressure-based methods (such as SIMPLE and PISO) use a Poisson-like equation for updating pressure instead of the continuity equation, while density-based methods use the continuity equation to update density (an equation of state is used to provide density in pressure based schemes and pressure in density based schemes). Pressure-based methods were developed originally for incompressible flows at low Reynolds numbers and were then extended to high Reynolds numbers and compressible applications. On the other hand, density based methods were originally developed for transonic flows and have been extended down to low Mach numbers through the use of preconditioning techniques. We compare these two very different approaches to solving the Navier-Stokes equations in order to gain an understanding of their similarities and differences. Specifically, we consider the PISO scheme as a representative pressure-based method and contrast it with a recently developed preconditioning scheme. We also compare the relative performance of the PISO algorithm with a Euler implicit algorithm that is employed to solve the preconditioned equations by means of a vector stability analysis.

Merkle, Charles L.↗

An analytical technique for the analysis of airplane spin entry and recovery

The dynamic equations of motion for a spinning airplane are simplified to facilitate the analysis of spin entry and recovery maneuvers. Solutions of a nonlinear, first order equation for spin rate enable calculation of spin entry and recovery times and control required for recovery. The analysis is applied to a light airplane for which both aerodynamic data, rotory balance wind tunnel tests, and spin flight test data have been obtained. A comparison of predicted and actual transient spin responses is made which supports the validity of the analytical approach taken but which also illustrates the difficulty in obtaining accurate aerodynamic data for spinning airplanes. Certain normalized parameters of the reduced state spin equation suggest criteria for assessing the transient spin characteristics of light airplanes.

Taylor, L. W., Jr.↗