Equation Of State In Form Research Articles

Validation of a detonation product equation of state for an insensitive high explosive via slab geometry expansion tests

Slab expansion (SLABEX) tests are conducted to validate a process for calibrating the detonation products equation of state (EOS) of a high explosive (HE). The SLABEX tests use rectangular slabs of PBX 9502, a polymer-bonded HE formulation consisting of 95 wt.% 1,3,5-triamino-2,4,6-trinitrobenzene bound with Kel F-800, a co-polymer of chlorotrifluoroethylene and vinylidene-fluoride. Three PBX 9502 slab thicknesses are examined, each confined symmetrically by two rectangular copper (Cu) plates approximately one-tenth the thickness of the HE slab. For the duration of each experiment, the detonation flow along the central axis of the PBX 9502 slab remains two-dimensional. The lateral flow velocity component of the outer surfaces of the expanding Cu plates is measured, along with the steady axial detonation speed along the central axis of the SLABEX. Hydrodynamic simulations of the Cu plate expansion in the SLABEX geometry, driven by the energy stored in the detonation products by the detonation combustion event, are conducted using a Jones–Wilkins–Lee EOS for the detonation products. This EOS form was recently parameterized for PBX 9502 in the cylinder expansion test geometry using a newly developed calibration technique [Voelkel et al., Combust. Flame 246, 112373 (2022)]. Good agreement between the experiment and prediction is found in each SLABEX test, demonstrating that the detonation product EOS calibration technique produces EOSs that are predictive when applied to other geometries.

Equation of state of MgO up to 345 GPa and 8500 K

The accurate equation of state (EOS) of MgO can be used as a pressure scale, but the EOS currently used has too much uncertainty to serve as a pressure scale, especially at high-pressure and high-temperature conditions. Here we present a complete EOS of solid MgO up to 345 GPa, 8500 K, and its derived pressure-volume-temperature (P-V-T) EOS form, which can be used as a pressure scale. In this EOS, the free energy is expressed as a three-parameter function based on a quasi-Debye thermodynamic model, which establishes a relatively accurate phonon thermodynamic description by determining the phonon dispersion relation and phonon density of states from the volume-dependent sound velocity. The three parameters are determined by a global optimization method, which minimizes the sum of the weighted variances between the physical quantities calculated by the thermodynamic model and the relevant experimental values within the unified EOS framework. To improve the accuracy of the EOS, the parameters are constrained by room-temperature sound velocities and shock compression data, including P-V-T data and sound velocities up to 265 GPa along the principal Hugoniot of MgO measured by us, the P-V-T data at 174--203 GPa, and partial P-V-T data of MgO preheated to 1850 K by others. The derived EOS of MgO can well reproduce not only the above data used to define the parameters, but also the shock compression data and the measured isobaric specific heat not used in the parameter optimization.

Towards mitigation of apparent tension between nuclear physics and astrophysical observations by improved modeling of neutron star matter

Observations of neutron stars (NSs) by the LIGO-Virgo and NICER collaborations have provided reasonably precise measurements of their various macroscopic properties. In this paper, we employ a Bayesian framework to combine them and place improved joint constraints on the properties of the NS equation of state (EOS). We use a hybrid EOS formulation that employs a parabolic expansion-based nuclear empirical parametrization around the nuclear saturation density augmented by a generic 3-segment piecewise polytrope model at higher densities. Within the 90% credible level this parametrization predicts ${R}_{1.4}={12.57}_{\ensuremath{-}0.92}^{+0.73}\text{ }\text{ }\mathrm{km}$ and ${\mathrm{\ensuremath{\Lambda}}}_{1.4}={550}_{\ensuremath{-}225}^{+223}$ for the radius and dimensionless tidal deformability, respectively, of a $1.4\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ NS. Finally, we show how the construction of the full NS EOS based solely on the nuclear empirical parameters at saturation density leads to certain tension with the astrophysical data, and how the hybrid approach provides a resolution to it.

GW190814: on the properties of the secondary component of the binary

ABSTRACT We show that the odds of the mass-gap (secondary) object in GW190814 being a neutron star (NS) improve if one allows for a stiff high-density equation of state (EoS) or a large spin. Since its mass is $\in (2.50,2.67) \, \mathrm{M}_{\odot }$, establishing its true nature will make it either the heaviest NS or the lightest black hole (BH), and can have far-reaching implications on NS EoS and compact object formation channels. When limiting oneself to the NS hypothesis, we deduce the secondary’s properties by using a Bayesian framework with a hybrid EoS formulation that employs a parabolic expansion-based nuclear empirical parametrization around the nuclear saturation density augmented by a generic 3-segment piecewise polytrope (PP) model at higher densities and combining a variety of astrophysical observations. For the slow-rotation scenario, GW190814 implies a very stiff EoS and a stringent constraint on the EoS specially in the high-density region. On the other hand assuming the secondary object is a rapidly rotating NS, we constrain its rotational frequency to be $f=1170^{+389}_{-495}$ Hz, within a 90 per cent confidence interval (CI). In this scenario, the secondary object in GW190814 would qualify as the fastest rotating NS ever observed. However, for this scenario to be viable, rotational instabilities would have to be suppressed both during formation and the subsequent evolution until merger, otherwise the secondary of GW190814 is more likely to be a BH.

An engineering application of Prosperetti and Lezzi equation to solve underwater explosion bubbles

The dynamic behaviors of underwater explosion bubbles differ for different explosives. The explosive characteristic parameters will result in a greater impact on the motion characteristics of the bubbles. Based on the bubble dynamics equation established by Prosperetti and Lezzi [“Bubble dynamics in a compressible liquid. Part 1. First-order theory,” J. Fluid Mech. 168, 457âĂŞ-478 (1986); “Bubble dynamics in a compressible liquid. Part 2. Second-order theory,” J. Fluid Mech. 185, 289âĂŞ-321 (1987)], we proposed an initial condition and an equation of state (EOS) form applicable for calculating the underwater explosion bubble dynamics of different explosives. With the assumption of instantaneous detonation and initial shock wave formation at the gas–liquid boundary, we calculated the initial state of the bubble boundary and established the initial condition for calculating explosion bubbles. Using the Jones–Wilkins–Lee EOS for different explosives, we constructed an isentropic EOS with a polytropic exponent that varied with density. We calculated and analyzed the differences in the initial expansions and the subsequent oscillations of underwater explosion bubbles with different explosives as well as the effects of different explosive parameters on the explosion bubble dynamics. This study showed that the proposed initial condition and the EOS form with a polytropic exponent that varied with density yielded good calculation accuracy and achieve close association of the underwater explosion bubbles with the properties of the explosive detonation and the characteristics of the detonation products. In addition, the explosion bubbles differed in the initial expansion, where the bubbles produced by explosives with higher densities and greater detonation velocities expanded more rapidly.

Optimal control of an abstract evolution variational inequality with application to homogenized plasticity

The paper is concerned with an optimal control problem governed by a state equation in form of a generalized abstract operator differential equation involving a maximal monotone operator. The state equation is uniquely solvable, but the associated solution operator is in general not G\^ateaux-differentiable. In order to derive optimality conditions, we therefore regularize the state equation and its solution operator, respectively, by means of a (smoothed) Yosida approximation. We show convergence of global minimizers for regularization parameter tending to zero and derive necessary and sufficient optimality conditions for the regularized problems. The paper ends with an application of the abstract theory to optimal control of homogenized quasi-static elastoplasticity.

New parametrized equation of state for dark energy surveys

We present a new parameterization for the equation of state (EoS) $\omega_X=P_X/\rho_X$, which can reproduce a $f(R)$-like evolution with a precision between $[0.5\%-0.8\%]$ over the numerical solutions. Also, our proposal can render a variety of popular $f(R)$ models that are considered as viable candidates for the cosmic late time acceleration. By using observational data from baryonic acoustic oscillations, supernovae and cosmic chronometers we investigate the constraints on the new EoS parameters. This proposal set a EoS formulation which can be used in an efficient way and makes a good candidate to be implemented in a variety of surveys in order to test the $f(R)$ generic behaviour.

Converging shock flows for a Mie-Grüneisen equation of state

Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. The remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analytical Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.

Homogeneous two-phase flow models and accurate steam-water table look-up method for fast transient simulations

The accurate simulation of fast steam-water transients requires precise algorithms for calculating fluid properties. The system of the governing flow equations must be closed with an Equation of State (EoS) to calculate the pressure as a function of the system conservative variables. For water, accurate analytical EoS for this purpose are not available yet. The aim of this paper is to show an efficient and very accurate algorithm to calculate water properties when the independent variables of the EoS are the density and the specific internal energy. Our algorithm uses a new table look-up method with bicubic interpolation based on the IAPWS-IF97 EoS formulation, and it is able to account for metastable states. The liquid metastability domain is extended until the spinodal curve, here determined and compared with other formulations.The EoS algorithm is coupled to two classical homogeneous two-phase flow models, namely the Homogeneous Equilibrium Model (HEM) and the Homogeneous Relaxation Model (HRM). HEM and HRM are used to simulate fast depressurization, waterhammer and steam explosion problems. Comparison of the numerical results with available experimental data shows the good performance of the proposed algorithms.

AN EOS-BASED NUMERICAL SIMULATION OF THERMAL RECOVERY PROCESS USING UNSTRUCTURED MESHES

In the past thirty years, the development of compositional reservoir simulators using an equation of state (EOS) has been addressed in the literature. However, the development of compositional thermal simulators in conjunction with the EOS formulation, in particular, has not been addressed extensively. In this work, a fully implicit, thermal, compositional EOS-based simulator in conjunction with unstructured meshes has been developed. In this model, an equation of state is used for equilibrium calculations among phases. Also, the physical properties are calculated based on an EOS, hence obviating the need for using steam tables for calculation of water/steam properties. The governing equations for the model comprise fugacity equations, material balance, pore volume constraint and energy equation. The governing partial differential equations are solved using the EbFVM (Element based Finite Volume Method). Results for several case studies consisting of 2D and 3D reservoirs are presented in order to demonstrate the applicability of the method.

TESTING UNIVERSAL RELATIONS OF NEUTRON STARS WITH A NONLINEAR MATTER-GRAVITY COUPLING THEORY

Due to our ignorance of the equation of state (EOS) beyond nuclear density, there is still no unique theoretical model for neutron stars (NSs). It is therefore surprising that universal EOS-independent relations connecting different physical quantities of neutron stars can exist. Lau et al. [ApJ, 714, 1234 (2010)] found that the frequency of the $f$-mode oscillation, the mass, and the moment of inertia are connected by universal relations. More recently, Yagi and Yunes [Science, 341, 365 (2013)] discovered the I-Love-Q universal relations among the mass, the moment of inertia, the Love number, and the quadrupole moment. In this paper, we study these universal relations in the Eddington-inspired Born-Infeld (EiBI) gravity. This theory differs from general relativity (GR) significantly only at high densities due to the nonlinear coupling between matter and gravity. It thus provides us an ideal case to test how robust the universal relations of NSs are with respect to the change of the gravity theory. Thanks to the apparent EOS formulation of EiBI gravity developed recently by Delsate and Steinhoff [Phys. Rev. Lett., 109, 021101 (2012)], we are able to study the universal relations in EiBI gravity using the same techniques as those in GR. We find that the universal relations in EiBI gravity are essentially the same as those in GR. Our work shows that, within the currently viable coupling constant, there exists at least one modified gravity theory that is indistinguishable from GR in view of the unexpected universal relations.

The relativistic equation of state in accretion and wind flows

In the present study we derive a 4-velocity distribution function for the relativistic ideal gas following the original approach of Maxwell–Boltzmann (MB). Using this distribution function, the relativistic equation of state (EOS): ρ-ρ0=(γ-1)-1p, is expressed in the parametric form: ρ=ρ0f(λ),and p=ρ0g(λ), where λ is a parameter related to the kinetic energy, and hence, to the temperature of the gas. In the nonrelativistic limit, this distribution function perfectly reduces to original MB distribution and the EOS reduces to ρ-ρ0=32p, whereas in the extreme ultra-relativistic limit, the EOS becomes ρ=3p correctly. Using these parametric equations the adiabatic index γ=cpcv and the sound speed as are calculated as a function of λ. They also satisfy the inequalities: 43⩽γ⩽53 and as⩽13 perfectly. The computed distribution function, adiabatic index γ, and the sound speed as are compared with the results obtained from the canonical ensemble theory which nicely match with the standard results (Synge, 1957 and Chandrasekhar, 1939). The main advantage in using the EOS is that the probability distribution function can be factorized and therefore, may be helpful to solve complex dynamics of the astrophysical system. Interestingly, in one of the astrophysical application revels that shocks in accretion flows become unlikely and except for the region very nearby the compact object, the EOS remains non-relativistic (Mondal and Basu, 2011). We therefore, conclude that the new form of EOS will be helpful to verify many conventional ideas in many astrophysical problems.

A new probabilistic tool for the determination and optimization of multiphase equation of state parameters: Application to tin

A thermodynamically consistent Equation Of State (EOS) was developed to predict and analyse the behaviour of multiphase metals under shock wave loading. Assuming the Mie-Gruneisen hypothesis together with the Birch (for example) formulation, the EOS gives the relation between pressure P, temperature T and atomic volume V. Experimental data (P,V,T) for each phase are provided mainly by X-ray diffraction measurements with diamond anvil cells. In this work, mathematical tools are designed to optimize the determination of the EOS parameters and evaluate uncertainty. The general EOS form is y = f ϑ (x ) where y = P, x = (V,T) and ϑ is the parameter vector to calibrate. Using experimental data (x i ,y i ), the least square (non-linear) regression provides an optimal value ϑ∗ for the fit parameters. The measurement errors on y and x give biased estimation of ϑ∗ with the standard method. Assuming centered and known variance laws for the errors, a statistical procedure is proposed to estimate ϑ∗ and determine confidence intervals. Thanks to a Bayesian approach it is possible to introduce physical interval knowledge of the parameters in this procedure. Moreover, various EOS f ϑ∗ formulations are evaluated with a chi-squared type statistical test. The present method is applied on experimental data for multi phase tin (β and γ phases and liquid state) in order to provide an optimized multi-phase model. Furthermore, the method is used to design further experimental campaign and to evaluate the gain of new experimental data with the corresponding estimated errors.

Analysis of equation of state for nanomaterials

An equation of state (EOS) recently proposed for nanomaterials is discussed critically. Different possible forms of the EOS are discussed with their correlations. We have considered 20 nanomaterials for this purpose, viz. CdSe, Rb 3C 60, carbon nanotube, γ-Fe 2O 3, ε-Fe (hexagonal iron), MgO, γ-Al 2O 3 (67 nm), α-Fe 2O 3, α-Fe (filled nanotube), TiO 2 (anatase ), 3C–SiC (30 nm), TiO 2 (rutile phase), Zr 0.1Ti 0.9O 2, γ-Si 3N 4, Ni-filled MWCNT, Fe-filled MWCNT, CeO 2 (cubic fluorite phase and orthorhombic phase), germanium (49 nm), GaN (wurtzite phase) and SnO 2 (rutile phase) (14 nm). It is found that the change in the form of EOS does not improve the results. This demonstrates the validity of the EOS proposed for nanomaterials. The EOS is also used to study the effect of temperature on compression of Ni (20 nm). It is found that there is small shift in isotherm due to increase in the temperature. The results have been found to present a good agreement with the available experimental data.

Equation of state in form which relates mol fraction and molarity of two (or more) component thermodynamic system consisted of ideal gases, and it’s applications

Most people would face a problem if there is a need to calculate the mole fraction of a substance A in a gaseous solution (a thermodynamic system containing two or more ideal gases) knowing its molarity at a given temperature and pressure. For most it would take a lot of time and calculations to find the answer, especially because the quantities of other substances in the system aren?t given. An even greater problem arises when we try to understand how special relativity affects gaseous systems, especially solutions and systems in equilibrium. In this paper formulas are suggested that greatly shorten the process of conversion from molarity to mole fraction and give us a better insight into the relativistic effects on a gaseous system.

EOS calculations for hydrothermal diamond anvil cell operation

The hydrothermal diamond anvil cell (HDAC) is an excellent tool for high-temperature, high-pressure (hydrothermal) experiments. For an accurate determination of pressure induced by a certain temperature in an isochoric sample chamber volume, an equation of state (EOS) of water can be used instead of direct measurement. This paper reviews the theoretic background and provides all needed equations for the application of EOS of water to HDAC experiments summarizing state-of-the-art knowledge and incorporating up-to-date thermodynamic data. The p-T conditions determined using the IAPWS-95 formulation for the thermodynamic properties of ordinary water are in agreement with values obtained from direct methods or other established EOS formulations. In particular, (1) the calculation of density through the (a) melting point or (b) homogenization method along with determining (2) pressure as a function of density and temperature or (3) density as a function of pressure and temperature is explained. As a new aspect in the context of HDAC operations, the critical influence of nucleation and a strategy to overcome this problem are discussed. Furthermore, we have derived new polynomial equations, which allow the direct calculation of the fluid phase's density from the melting temperature. These are implemented in a spreadsheet program, which is freely available for interested users.

ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept. 2. Equations of State on Demand and Dynamic Updates over the Web

ThermoData Engine (TDE) is the first full-scale software implementation of the dynamic data evaluation concept, as reported recently in this journal. The present paper describes two major software enhancements to TDE: (1) generation of equation of state (EOS) representations on demand and (2) establishment of a dynamically updated experimental data resource for use in the critical evaluation process. Four EOS formulations have been implemented in TDE for on-demand evaluation: the volume translated Peng-Robinson, modified Sanchez-Lacombe, PC-SAFT, and Span Wagner EOS. The equations are fully described with their general application. The class structure of the program is described with particular emphasis on special features required to implement an equation, such as an EOS, that represents multiple properties simultaneously. Full implementation of the dynamic data evaluation concept requires that evaluations be based on an up-to-date "body of knowledge" or, in the case of TDE, an up-to-date collection of experimental results. A method to provide updates through the World Wide Web is described that meets the challenges of maintenance of data integrity with full traceability. Directions for future enhancements are outlined.

A new equation of state for rubidium vapors at temperatures up to 1600 K and pressures up to 4 MPa

Statistical matching is performed of a wide range of diverse experimental data on the thermodynamic properties of saturated and superheated rubidium vapors at temperatures up to 1650 K. The parametric models used in the matching of data include the equation of state in the virial form and equations in the form of group expansions in terms of degrees of activity. Values of the second virial and group coefficients are obtained using new spectroscopic data on the singlet potential of rubidium atoms in the ground electron state. The equation of state in the form of expansion of density in terms of degrees of activity is used to calculate the tables of thermodynamic functions and estimate their confidence errors at temperatures up to 1600 K and pressures up to 4 MPa.

Equation of state of liquid Fe‐10 wt % S: Implications for the metallic cores of planetary bodies

The equation of state (EOS) of molten Fe‐10 wt % S was investigated by means of static high‐pressure density measurements using a newly developed variation of the sink/float technique. The method involves the use of tailored density composite spheres made of Pt or WC cores and an Al2O3 (ruby/sapphire) mantle as bracketing markers for comparative density measurements of liquid Fe‐10 wt % S at pressures (P) up to 20 GPa and at temperatures (T) up to 2123 K. The results of isothermal compression data confirm the validity of extrapolating to 20 GPa an EOS for pressures up to 6 GPa obtained earlier by Sanloup et al. [2000] using an X‐ray absorption technique. The analysis of new data obtained in the 1773–2123 K interval up to 20 GPa resulted in new EOS parameters and also revealed the need for a well‐determined melt density value at 1 atm. Application of our results to the identification of composition of liquid metallic cores of Ganymede, Io, and Mars showed Fe‐10 wt % S to be a possible candidate. We used different EOS formulations to extrapolate our results to the P‐T conditions of the Earth's interior. For temperatures between 4773 K at the core‐mantle boundary and 5973 K at the inner core boundary the extrapolation made using the Vinet EOS resulted in density values closest to the density of the core suggested by the preliminary reference Earth model.

Thermodynamic properties of ozone-friendly substances: individual and combined refrigerants

Experimental thermodynamic data of individual substances and some mixtures were selected for a statistical treatment. The substances selected are the ozone-layer-friendly cooling liquids (HFC-134a, HFC-152a, HC-290, HC-600a, etc, and their mixtures). As a result of the treatment the equations of state (EOS) were produced in the form of the Carnahan-Starling-De Santis (CSD) EOS. The same form of EOS was accepted for the blends including HFC-134a/HFC-152a, HC-600a/HFC-152a, HC-600a/HFC-134a, and HC-290/HC-600a. Software programs combined in a data base were produced in order to evaluate coefficients of EOS with experimental data, to calculate thermodynamic properties of cooling liquids, and to determine the characteristics of refrigerating cycles which use the liquids. The modelling of several types of cycle was carried out for pure substances and the mixtures. The characteristics of the cycles were compared with those of CFC-12. The results of the cycle modelling show that the blends HFC-134a/HFC-152a and HC-600a/HFC-152a have some advantages relative to HFC-134a. These blends can be used as effective alternative refrigerants.