scholarly journals An anisotropic equation of state for high pressure, high temperature applications

2021 ◽  
Author(s):  
Robert Myhill
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Deformation Gradient ◽  
Seismic Velocities ◽  
San Carlos Olivine ◽  
High Pressure High Temperature ◽  
Wide Range ◽  
Anisotropic Equation ◽  
Scalar Properties ◽  
San Carlos

This paper presents a strategy for consistently extending isotropic equations of state to model anisotropic materials over a wide range of pressures and temperatures under nearly hydrostatic conditions. The method can be applied to materials of arbitrary symmetry. The paper provides expressions for the deformation gradient tensor, the lattice parameters, the isothermal elastic compliance tensor and thermal expansivity tensor. Scalar properties including the Gibbs energy, volume and heat capacities are inherited from the isotropic equation of state. Other physical properties including the isothermal and isentropic stiffness tensors, the Grueneisen tensor and anisotropic seismic velocities can be derived from these properties.The equation of state is demonstrated using periclase (cubic) and San Carlos olivine (orthorhombic) as examples.

scholarly journals Axial Compressibility and Thermal Equation of State of Hcp Fe–5wt% Ni–5wt% Si

Minerals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 98
Author(s):  
Eric Edmund ◽  
Francesca Miozzi ◽  
Guillaume Morard ◽  
Eglantine Boulard ◽  
Alisha Clark ◽  
...  
Keyword(s):  
Equation Of State ◽  
Ambient Temperature ◽  
Inner Core ◽  
Equations Of State ◽  
Axial Ratio ◽  
Seismic Velocities ◽  
X Ray Diffraction ◽  
Thermal Equation ◽  
Planetary Cores ◽  
Ni Addition

Knowledge of the elastic properties and equations of state of iron and iron alloys are of fundamental interest in Earth and planetary sciences as they are the main constituents of telluric planetary cores. Here, we present results of X-ray diffraction measurements on a ternary Fe–Ni–Si alloy with 5 wt% Ni and 5 wt% Si, quasi-hydrostatically compressed at ambient temperature up to 56 GPa, and under simultaneous high pressure and high temperature conditions, up to 74 GPa and 1750 K. The established pressure dependence of the c/a axial ratio at ambient temperature and the pressure–volume–temperature (P–V–T) equation of state are compared with previous work and literature studies. Our results show that Ni addition does not affect the compressibility and axial compressibility of Fe–Si alloys at ambient temperature, but we suggest that ternary Fe–Ni–Si alloys might have a reduced thermal expansion in respect to pure Fe and binary Fe–Si alloys. In particular, once the thermal equations of state are considered together with velocity measurements, we conclude that elements other than Si and Ni have to be present in the Earth’s inner core to account for both density and seismic velocities.

scholarly journals Development and Experimental Validation of Real Fluid Models for CFD Calculation of ORC and Steam Turbine Flows

Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 6879
Author(s):  
Andrii Rusanov ◽  
Roman Rusanov ◽  
Piotr Klonowicz ◽  
Piotr Lampart ◽  
Grzegorz Żywica ◽  
...  
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Steam Turbine ◽  
Thermodynamic Parameters ◽  
Equations Of State ◽  
Computational Cost ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Large Power ◽  
Wide Range

The article describes an interpolation–analytical method of reconstruction of the IAPWS-95 equations of state and the modified Benedict–Webb–Rubin equations of state with 32 terms (mBWR32). The method enables us to provide the thermodynamic closure in 3D computational fluid dynamics (CFD) calculations of turbomachinery flows with real working media, such as steam and Organic Rankine Cycle (ORC) fluids. The described approach allows for the sufficient accuracy of 3D flow calculations and does not require a significant increase in computational cost over perfect gas calculations. The method is validated against experimental data from measurements and compared with computational results from the model using the Tammann equation of state. Three turbine blading systems are considered—a multi-stage configuration from a low-pressure cylinder of a large-power steam turbine and two ORC microturbines working with organic media HFE7100 and R227ea. The calculation results obtained using the described method of approximation of the IAPWS-95 and mBWR32 equations exhibit satisfactory agreement with the experimental data, considering pressures, temperatures and enthalpies in key sections, as well as turbine power and efficiency in a wide range of changing thermodynamic parameters. In contrast, the Tammann equation of state provides acceptable results only for relatively small changes of thermodynamic parameters.

THERMAL AND CALORIC EQUATIONS OF STATE FOR NITROGEN: APPLICATION TO CRYOGENIC INJECTION CONDITIONS

2020 ◽  
Author(s):  
N. M. KUZNETSOV ◽  
◽  
S. N. MEDVEDEV ◽  
S. M. FROLOV ◽  
F. S. FROLOV ◽  
...  
Keyword(s):  
Equation Of State ◽  
Triple Point ◽  
Equations Of State ◽  
Applicability Domain ◽  
Analytical Equation ◽  
Nitrogen Application ◽  
Real Gas ◽  
The Real ◽  
Turbulent Reactive Flows ◽  
Wide Range

The real-gas analytical equation of state (EoS) for nitrogen is developed. The applicability domain of the EoS is verified in a wide range of density (from 0 to the value at the triple point, 0.867 g/cm3) and temperature (from 100 to 5000 K). The obtained EoS is introduced into the gasdynamic code for calculating multidimensional turbulent reactive flows.

scholarly journals Ab initio based equation of state of dense water for planetary and exoplanetary modeling

2019 ◽  
Vol 621 ◽  
pp. A128 ◽  
Author(s):  
S. Mazevet ◽  
A. Licari ◽  
G. Chabrier ◽  
A. Y. Potekhin
Keyword(s):  
Equation Of State ◽  
First Principles ◽  
Equations Of State ◽  
Pure Water ◽  
Analytical Form ◽  
Quantum Molecular Dynamics ◽  
Dense Water ◽  
Wide Range ◽  
Dynamical Simulations ◽  
Dynamics Simulations

Context. The modeling of planetary interiors requires accurate equations of state (EOSs) for the basic constituents with proven validity in the difficult pressure–temperature regime extending up to 50 000 K and hundreds of megabars. While EOSs based on first-principles simulations are now available for the two most abundant elements, hydrogen and helium, the situation is less satisfactory for water where no wide-range EOS is available despite its requirement for interior modeling of planets ranging from super-Earths to planets several times the size of Jupiter. Aims. As a first step toward a multi-phase EOS for dense water, we develop a temperature-dependent EOS for dense water covering the liquid and plasma regimes and extending to the super-ionic and gas regimes. This equation of state covers the complete range of conditions encountered in planetary modeling. Methods. We use first-principles quantum molecular dynamics simulations and the Thomas-Fermi extension to reach the highest pressures encountered in giant planets several times the size of Jupiter. Using these results, as well as the data available at lower pressures, we obtain a parametrization of the Helmholtz free energy adjusted over this extended temperature and pressure domain. The parametrization ignores the entropy and density jumps at phase boundaries but we show that it is sufficiently accurate to model interior properties of most planets and exoplanets. Results. We produce an EOS given in analytical form that is readily usable in planetary modeling codes and dynamical simulations (a fortran implementation is provided). The EOS produced is valid for the entire density range relevant to planetary modeling, for densities where quantum effects for the ions can be neglected, and for temperatures below 50 000K. We use this EOS to calculate the mass-radius relationship of exoplanets up to 5000 MEarth, explore temperature effects in the wet Earth-like, ocean planets and pure water planets, and quantify the influence of the water EOS for the core on the gravitational moments of Jupiter.

scholarly journals AQUA: a collection of H2O equations of state for planetary models

2020 ◽  
Vol 643 ◽  
pp. A105 ◽  
Author(s):  
Jonas Haldemann ◽  
Yann Alibert ◽  
Christoph Mordasini ◽  
Willy Benz
Keyword(s):  
Equation Of State ◽  
Internal Energy ◽  
High Pressures ◽  
Equations Of State ◽  
Chemical Elements ◽  
Thermodynamic Quantities ◽  
Calculated Density ◽  
Temperature Range ◽  
Wide Range ◽  
The Impact

Context. Water is one of the key chemical elements in planetary structure modelling. Due to its complex phase diagram, equations of state often only cover parts of the pressure-temperature space needed in planetary modelling. Aims. We aim to construct an equation of state of H2O spanning a very wide range, from 0.1 Pa to 400 TPa and 150 to 105 K, which can be used to model the interior of planets. Methods. We combined equations of state valid in localised regions to form a continuous equation of state spanning over the above-mentioned pressure and temperature range. Results. We provide tabulated values for the most important thermodynamic quantities: the density, adiabatic temperature gradient, entropy, internal energy, and bulk speed of sound of water over this pressure and temperature range. For better usability we also calculated density-temperature and density-internal energy grids. We discuss further the impact of this equation of state on the mass radius relation of planets compared to other popular equations of state like ANEOS and QEOS. Conclusions. AQUA is a combination of existing equations of state useful for planetary models. We show that, in most regions, AQUA is a thermodynamic consistent description of water. At pressures above 10 GPa, AQUA predicts systematic larger densities than ANEOS or QEOS. This is a feature that was already present in a previously proposed equation of state, which is the main underlying equation of this work. We show that the choice of the equation of state can have a large impact on the mass-radius relation, which highlights the importance of future developments in the field of equations of state and regarding experimental data of water at high pressures.

Reference correlations for the viscosity and thermal conductivity of fluids over an extended range of conditions: hexane in the vapor, liquid, and supercritical regions (IUPAC Technical Report)

2015 ◽  
Vol 87 (3) ◽  
pp. 321-337
Author(s):  
Richard A. Perkins ◽  
Marcia L. Huber ◽  
Marc J. Assael ◽  
Efthimia K. Mihailidou ◽  
Sofia K. Mylona ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Equation Of State ◽  
Thermodynamic Properties ◽  
Equations Of State ◽  
Reliable Data ◽  
Theoretical Knowledge ◽  
Technical Report ◽  
Wide Range ◽  
Extended Range ◽  
Vapor Liquid

AbstractThis article summarizes the correlation procedures developed for IUPAC Project 2012-040-1-100 [Reference correlations for the thermal conductivity and viscosity of fluids over extended range of conditions (vapor, liquid and supercritical regions)]. This project is focused on the development of wide-range reference correlations for the thermal conductivity and viscosity of fluids that incorporate as much theoretical knowledge of these properties as possible. The thermal conductivity and viscosity correlations developed here for pure fluids are functions of temperature and density. The best available equations of state for a given fluid are used to calculate the thermodynamic properties required for these correlations, often from measured temperatures and pressures. The correlation methodology developed during this project has been applied to hexane in this report but can be applied to any pure fluid with a reliable equation of state and reliable data for the thermal conductivity and viscosity over a significant range of temperatures and densities.

scholarly journals Supermassive neutron stars in axion F(R) gravity

2020 ◽  
Vol 493 (1) ◽  
pp. 78-86 ◽  
Author(s):  
Artyom V Astashenok ◽  
Sergey D Odintsov
Keyword(s):  
Equation Of State ◽  
Neutron Stars ◽  
Scalar Curvature ◽  
Equations Of State ◽  
Compact Stars ◽  
Axion Mass ◽  
Axion Field ◽  
Wide Range ◽  
Star Surface ◽  
Effective Contribution

ABSTRACT We investigated realistic neutron stars in axion R2 gravity. The coupling between curvature and axion field ϕ is assumed in the simple form ∼R2ϕ. For the axion mass in the range ma ∼ 10−11–10−10 eV the solitonic core within neutron star and corresponding halo with size ∼100 km can exist. Therefore the effective contribution of R2 term grows inside the star and it leads to change of star parameters (namely, mass, and radius). We obtained the increase of star mass independent from central density for wide range of masses. Therefore, maximal possible mass for given equation of state grows. At the same time, the star radius increases not so considerably in comparison with GR. Hence, our model may predict possible existence of supermassive compact stars with masses $M\sim 2.2\!-\!2.3\, \mathrm{M}_\odot$ and radii Rs ∼ 11 km for realistic equation of state (we considered APR equation of state). In general relativity one can obtain neutron stars with such characteristics only for unrealistic, extremely stiff equations of state. Note that this increase of mass occurs due to change of solution for scalar curvature outside the star. In GR curvature drops to zero on star surface where ρ = p = 0. In the model underconsideration the scalar curvature dumps more slowly in comparison with vacuum R2 gravity due to axion ‘galo’ around the star.

SITE-SPECIFIC EQUATIONS OF STATE FOR COASTAL SEA AREAS AND INLAND WATER BODIES

2017 ◽  
Author(s):  
Natalia Andrulionis ◽  
Natalia Andrulionis ◽  
Ivan Zavialov ◽  
Ivan Zavialov ◽  
Elena Kovaleva ◽  
...  
Keyword(s):  
Equation Of State ◽  
Black Sea ◽  
Water Samples ◽  
Equations Of State ◽  
Sea Water ◽  
Ionic Composition ◽  
Water Bodies ◽  
Aral Sea ◽  
The Black Sea ◽  
Coastal Sea

This article presents a new method of laboratory density determination and construction equations of state for marine waters with various ionic compositions and salinities was developed. The validation of the method was performed using the Ocean Standard Seawater and the UNESCO thermodynamic equation of state (EOS-80). Density measurements of water samples from the Aral Sea, the Black Sea and the Issyk-Kul Lake were performed using a high-precision laboratory density meter. The obtained results were compared with the density values calculated for the considered water samples by the EOS-80 equation. It was shown that difference in ionic composition between Standard Seawater and the considered water bodies results in significant inaccuracies in determination of water density using the EOS-80 equation. Basing on the laboratory measurements of density under various salinity and temperature values we constructed a new equation of state for the Aral Sea and the Black Sea water samples and estimated errors for their coefficients.

Wide-range equations of state for organic liquids

2007 ◽  
Vol 5 ◽  
pp. 113-120 ◽  
Author(s):  
R.Kh. Bolotnova
Keyword(s):  
High Pressures ◽  
Equations Of State ◽  
Organic Liquids ◽  
Liquid Phases ◽  
Wide Range ◽  
High Pressures And Temperatures

The method of construction the wide-range equations of state for organic liquids, describing the gas and liquid phases including dissociation and ionization which occurs during an intense collapse of steam bubbles and accompanied by ultra-high pressures and temperatures, is proposed.

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