New Equation Of State Research Articles

High-pressure equations of state and elastic properties of the hcp-Iron

The present study deals with the elastic properties at different pressure of hcp-iron have been carried out. By exerting pressure on the cubic body of n-th power of edge length, we have used a new equation of state based on Eulerian finite theory. We have computed the bulk modulus and their pressure derivative from this formulated equation of state. The results from the proposed equation of state (EOS) show the better agreement with available experimental data. Thus, the derived expressions are able to predict the elastic properties of hcp-iron under high pressures.

Thermodynamic properties of liquid bismuth under pressure: New regularities and an equation of state

A new regularity for internal pressure has been introduced based on the suggested potential energy function in liquid bismuth. Both the experimental data and the calculated quantities from the power law equation of state have been used to show the validity of the regularity. The quantity X3Z−1 is a linear function of ln(X) with crossing points for all isotherms at high temperature, where X=VVm0, V, Vm0, and Z are molar volume, the molar volume at melting point and zero pressure, and compressibility factor. For the reduced isothermal bulk modulus B*=BTVRT and the quantity Zint=PintVRT, where BT, R, T and Pint are isothermal bulk modulus, the gas constant, temperature and internal pressure, the new regularities have been introduced that both calculated X3B*−1 and X3Zint from the equation of state of a power law form versus ln(X) are nearly linear along each isotherm. However, those derived values from experiments become nonlinear functions of ln(X) at large pressure for all isotherms. Based on the new equation of state, analytical expression of thermodynamic properties of liquid bismuth can be obtained. The different extreme values exist along the isotherms for the calculated internal energy, isobaric heat capacity, and isochoric heat capacity for the new equation of state and the power law form equation of state.

On the equation of state for concrete-like materials

This paper presents a systematic study on the equation of state for concrete-like materials. A new method is first proposed to analyze plate impact test data by considering the effects of both wave structures and strength surface; plate impact tests are then performed on cement mortar with impact velocities ranging from 45 m/s to 3050 m/s and experimental results are analyzed by using the newly proposed method; Subsequently, the accuracy of the existing equations of state (i.e. the p∼α equation of state and the equation of state of HJC) is evaluated and similarities and differences are also discussed. Finally, a new equation of state is proposed based on the previous work and the newly acquired test data. The numerical results using the three equations of state are compared with plate impact test data in terms of particle velocity-time history, longitudinal wave velocity and HEL. It is found that the newly proposed equation of state is in good agreement with plate impact test data of concrete-like materials and is advantageous over the existing equations of state.

Study on the characteristics of blast loads due to two simultaneous detonated charges in real air

Most studies about the air blast loads due to a single explosion have been widely reported based on the assumption that the air is an ideal gas. However, this assumption is not applicable for investigating the blast load due to multiple charge explosions in a realistic environment. In this paper, according to the existing data, the mathematical relationship between the specific internal energy and adiabatic index under high pressure is determined, and a new equation of state(EOS) for the real gas is derived. Then, the new EOS is implemented in LS-DYNA to simulate the reflected procedure of blast waves near the ground, and the average errors of overpressure and positive impulse are less than 10% and 21%, respectively. Finally, the validated model is used to investigate the effects of the total charge weight, scaled distance, and distance between the charges on the characteristics of the blast load due to two simultaneous detonated charges. Numerical simulation results show that under the condition of real gas, the total mass and distances between charges will heavily affect the starting and optimal positions of overpressure and impulse enhancement, which lays a foundation for characterizing the closed flow field of multiple charge explosions.

An International Standard Formulation for trans-1-Chloro-3,3,3-trifluoroprop-1-ene [R1233zd(E)] Covering Temperatures from the Triple-Point Temperature to 450 K and Pressures up to 100 MPa

A new Helmholtz energy equation of state is presented for trans-1-chloro-3,3,3-trifluoroprop-1-ene [R1233zd(E)], which is expressed with temperature and density as independent variables. Experimental data in the range of temperatures from 215 to 444 K and pressures up to 35 MPa form the basis of the new equation. In this range, expected uncertainties (k = 2) of the new equation of state are 0.07% for vapor pressures at temperatures above the normal boiling point temperature (≈291K), 0.2% for vapor pressures at lower temperatures, 0.05% for liquid densities, 0.15% for vapor densities, 0.1% for saturated liquid densities, 0.05% for liquid-phase sound speeds, and 0.08% for vapor-phase sound speeds. The new equation is valid at temperatures from the triple-point temperature (165.75 K) to 450 K and pressures up to 100 MPa with reasonable uncertainties outside the available range of data because it fully extrapolates with correct physical behavior to higher temperatures and pressures as well as to lower temperatures. The equation of state presented here has been recommended as an international standard by the working group presently revising ISO 17584 (Refrigerant Properties).

A simple derivation of a new equation of state (EOS) based on Eulerian finite strain and its applicability

A simple derivation of a new equation of state (EOS) based on Eulerian finite strain and its applicability

The equation of state and shock-driven decomposition of polymethylmethacrylate (PMMA)

We present new equations of state (EOS) for polymethylmethacrylate and its shock-driven decomposition products, generated in both tabular form and as linear US−up fits to all previously available shock data. Different approaches are taken for materials shocked above and below the apparent threshold for chemical reactions at pressures P≈30 GPa. Both EOSs are calibrated to and compared with a broad array of experimental results, as well as new ab initio molecular dynamics simulations presented here. Comparisons are good in most cases, and we focus our particular attention on those observables that test the distinction between reactants and products.

State variable, entropy, should be negative

<p indent="0mm">The positive-and-negative property of a physical quantity is usually related to its physical meaning. The general convention is to use positive values to represent positive things and negative values to represent negative things. However, the state variable, entropy, is a strange physical quantity. From a macroscopic perspective, entropy represents the unavailable energy of the heat output of a thermodynamic system as it changes from an arbitrary state to a state in equilibrium with the environment, in short, the unavailable heat of the system. From a microscopic point of view, entropy represents the degree of disorder (chaos) in a system. Both the macroscopic and microscopic physical meanings of entropy indicate that it represents a negative thing. Therefore, entropy should be negative by its nature. However, historically, since Planck’s statement of Nernst’s heat theorem, entropy has always been taken for granted as a positive value. This is contrary to people’s cognitive habits, which adds to the mystery of entropy. Analyses indicate that Planck’s statement of Nernst’s heat theorem is not general and is valid only for single-component substances, such as perfect crystals. It is not an absolute fact that “entropy cannot be negative”. The Planck’s choice of a zero-temperature perfect crystal as the zero point of entropy is a non-physical operation and involves only a matter of convenience. Recently, based on the symmetry of reversible thermodynamics, a new equation of state for ideal solids has been established. Since entropy is explicitly included in the equation of state for ideal solids, the zero point of entropy cannot be chosen arbitrarily. The analysis from the thermodynamic stability and the verification of the property data show that entropy in the ideal solid equation of state must have a negative value. This physically specifies that the zero point of entropy should be the point of maximum entropy, i.e., the zero-pressure ideal gas limiting state. In fact, the ideal gas equation of state has a zero point of volume. That is the ideal solid limiting state (zero-volume state). At this zero point, the volume always takes a positive value. In brief, the zero point of volume of the ideal gas equation of state is the zero-temperature ideal solid, while the zero point of the entropy of the ideal solid equation of state is the zero-pressure ideal gas. The ideal solid equation of state is a creation of thermodynamic symmetry. The zero point of entropy, i.e., zero-pressure ideal gas is likewise a requirement of thermodynamic symmetry. The smaller the absolute value of negative entropy, the greater the unavailable energy of the system (the smaller the available energy) and the higher the degree of disorder of the system (the lower the degree of order). This is consistent with people’s cognitive habits. In addition, the zero-pressure ideal gas can be used as the zero point of entropy for both the ideal gas and the ideal solid equations of state, thus allowing a uniform orientation and division of the applicability of various practical equations of state between these two extreme equations of state. Unlike the choice of zero-temperature perfect crystal as the zero point of entropy, when zero-pressure ideal gas is used as the zero point of entropy, entropy takes a negative value, which is in accordance with the physical meaning of entropy and is also the requirement of thermodynamic symmetry. Taking a negative value for entropy is the physical, essential choice.

Thermalization of Light's Orbital Angular Momentum in Nonlinear Multimode Waveguide Systems.

We show that the orbital angular momentum (OAM) of a light field can be thermalized in a nonlinear cylindrical multimode optical waveguide. We find that upon thermal equilibrium, the maximization of the optical entropy leads to a generalized Rayleigh-Jeans distribution that governs the power modal occupancies with respect to the discrete OAM charge numbers. This distribution is characterized by a temperature that is by nature different from that associated with the longitudinal electromagnetic momentum flow of the optical field. Counterintuitively and in contrast to previous results, we demonstrate that even under positive temperatures, the ground state of the fiber is not always the most populated in terms of power. Instead, because of OAM, the thermalization processes may favor higher-order modes. A new equation of state is derived along with an extended Euler equation resulting from the extensivity of the entropy itself. By monitoring the nonlinear interaction between two multimode optical wave fronts with opposite spins, we show that the exchange of angular momentum is dictated by the difference in OAM temperatures, in full accord with the second law of thermodynamics. The theoretical analysis presented here is corroborated by numerical simulations that take into account the complex nonlinear dynamics of hundreds of modes. Our results may pave the way toward high-power optical sources with controllable orbital angular momenta, and at a more fundamental level, they may open up opportunities in drawing parallels with other complex multimode nonlinear systems like rotating atomic clouds.

Confronting a set of Skyrme and $$\chi _{EFT}$$ predictions for the crust of neutron stars

With the improved accuracy of neutron star observational data, it is necessary to derive new equation of state where the crust and the core are consistently calculated within a unified approach. For this purpose we describe non-uniform matter in the crust of neutron stars employing a compressible liquid-drop model, where the bulk and the neutron fluid terms are given from the same model as the one describing uniform matter present in the core. We then generate a set of fifteen unified equations of state for cold catalyzed neutron stars built on realistic modelings of the nuclear interaction, which belongs to two main groups: the first one derives from the phenomenological Skyrme interaction and the second one from $\chi_{EFT}$ Hamiltonians. The confrontation of these model predictions allows us to investigate the model dependence for the crust properties, and in particular the effect of neutron matter at low density. The new set of unified equations of state is available at the CompOSE repository.

A phase field model for compressible immiscible fluids with a new equation of state

In this paper, we propose a new compressible phase field model of two different immiscible fluid components, in which the density of each phase is variable. In order to establish the compressible phase field model, a new P-V-T equation of state is introduced to solve the pressure. The new model is derived by the physics law of conservation, and conforms to the second law of thermodynamics. The model adopts an innovative expression of Helmholtz free energy, taking into account the new state equation of pressure and the varying material properties of each phase. A high-order accurate numerical scheme is introduced to solve the model equations. The convection terms of the governing equations are discretized by the fifth-order WENO scheme, and the residual terms are discretized by the Lax–Friedrichs method. Finally, the reliability and validity of the compressible two-phase model are verified by numerical simulations.

New equations of state describing both the dynamic viscosity and self-diffusion coefficient for potassium and thallium in their fluid phases

Experimental data on the viscosity and self-diffusion coefficient of two metallic compounds in their fluid phases, that is, potassium and thallium, are modeled using the translational elastic mode theory, which has been successfully applied to the case of water. It is shown that this theory allows the experimental data to be accounted for in accordance with their uncertainties and, above all, it allows the different variations observed between the different authors to be explained. Particularly in the case of thallium, this theory makes it possible to represent viscosity data with much better precision than the so-called reference equation of state. The dilute-gas limit laws connecting various parameters of the theory obtained in the case of water are confirmed here and thus give them a universal character. The elastic mode theory is accompanied by the development of new equations of state, mainly to describe properties along the saturated vapor pressure curve, which greatly extend the temperature range of application of these equations compared to those found in the literature. The whole analysis thus makes it possible to propose precise values of various thermodynamic parameters at the melting and boiling temperature corresponding to atmospheric pressure.

Thermophysical properties of biodiesel fuels from modified perturbed hard trimer chain equation of state

In the present study, a modified version of the perturbed hard trimer chain equation of state was employed to predict thermophysical properties of fatty acid methyl ester (FAME) and fatty acid ethyl ester (FAEE) systems. The thermophysical properties in question are liquid density, vapor pressure, heat capacity, viscosity and thermal conductivity. The predictive power of the model has been assessed by calculating the aforementioned thermophysical properties and comparing with experimental ones as well as other models. Typically, the overall average absolute relative deviation (AARD in %) of the predicted densities for 1665 data points was found to be 2.57%. Simplicity and good agreement between the experimental data and those calculated from the present model, are the reasons for applicability of proposed model with sufficient accuracy for engineering applications. The capability of this new equation of state in predicting both thermodynamic and transport properties simultaneously with good accuracies is really prominent.

Acoustic cavitation characteristics of bubble in compressible liquid

The newly proposed Gilmore-NASG model is used to study the acoustic cavitation characteristics of bubble in compressible liquid under the boundary condition of considering the compressible effect of the liquid, and comparison is made between the results calculated by the Gilmore-NASG model and original KM-VdW model without considering the mass exchange, chemical reaction and heat exchange between the gas in the bubble and the surrounding liquid. The results suggest that, compared with the KM-VdW model, the Gilmore-NASG model which employs a new equation of state to describe the gas, liquid and variations of liquid density and sound velocity due to compressibility, can give a larger compression ratio of cavitation bubble, a deeper collapse depth, higher temperature and pressure peaks. This is mainly because that the co-volume of argon molecule in the NASG equation of state is smaller than that in the VdW equation of state and the effect of the co-volume of water molecule is considered in the NASG equation of state, that is, the Gilmore-NASG model gives more comprehensive consideration to the liquid compressibility. When the bubble collapses violently, the Gilmore-NASG model takes into account the changes of sound velocity caused by the compressibility of the liquid at the bubble wall, effectively avoid the possibility of abnormal increase in the Mach number of the liquid at the bubble wall. With the increase in the driving sound pressure amplitude, the difference between the results given by the two models more and more significantly and the temperature and pressure peaks in the bubble given by the Gilmore-NASG model increase more significantly. With the rise of driving frequency, the difference between the results given by the two models gradually decreases and tends to be consistent under the high-frequency excitation. This indicates that the temperature and pressure in the bubble may arrive at higher values considering the compressibility of the medium caused by the co-volume changes of gas and surrounding liquid at different temperatures and pressures. In the meantime, the Gilmore-NASG model can accurately predict the changes in density, pressure and temperature of the liquid at the bubble wall as well as sound velocity, so this model has advantages in the study of bubble cavitation characteristics under high pressure and the effect of surrounding liquid on bubble cavitation characteristics. There will be important applications for the research on specific issues such as high-intensity focused ultrasound, shock wave lithotripsy treatment and sonochemistry.

Thermodynamics of Helium-4 Dimerization and Trimerization.

A new equation of state (EOS) for helium-4 is used to obtain the equilibrium thermochemical properties of helium-4 dimerization (24He ⇌ 4He2) and trimerization (34He ⇌ 4He3) between 3.0 and 10.0 K. It is shown that at sufficiently low temperatures there are appreciable populations of dimer and trimer. The calculations account only for monomer, dimer, and trimer. At 3.0 K, the respective KPo values for dimerization and trimerization are 0.4832 and 0.4876, respectively. The standard enthalpy changes at 3.0 K are -54.53 and -110.0 J/mol, and standard entropy changes are -24.22 and -42.97 J/mol-K. Statistical thermodynamic calculations provide results that are qualitatively consistent with those obtained from the EOS calculations.

A Hybrid Real/Ideal Gas Mixture Computational Framework to Capture Wave Propagation in Liquid Rocket Combustion Chamber Conditions

The present work focuses on the development of new mathematical and numerical tools to deal with wave propagation problems in a realistic liquid rocket chamber environment. A simplified real fluid equation of state is here derived, starting from the literature. An approximate Riemann solver is then specifically derived for the selected conservation laws and primitive variables. Both the new equation of state and the new Riemann solver are embedded into an in-house one-dimensional CFD solver. The verification and validation of the new code against wave propagation problems are then performed, showing good behavior. Although such problems might be of interest for different applications, the present study is specifically oriented to the low order modeling of high-frequency combustion instability in liquid-propellant rocket engines.

Thermodynamic perturbation theory coefficients for ellipsoidal molecules

Perturbation theory has been the center of the development of the new generation of equations of state. First- and second-order perturbation theories are very common, but require approximations for obtaining an analytical form. Recently, a new equation of state has been proposed in which the reference fluid is based on the hard Gaussian overlap approach, and the perturbed potential is defined as a spherically symmetric square well. In such an approach, the first- and second-order coefficients were considered the same as the ones applied for a system in which the reference term is spherical. Using Monte Carlo simulations, we investigated the validity of such an approximation by calculating the first- and second-order coefficients of the high-temperature expansion series of the Helmholtz free energy. With our findings, this approximation seems to be quite reasonable for a certain range of anisotropies. We also present a calculation of the perturbed molar Helmholtz free energy using Monte Carlo simulations, which could in principle be used for improving the equation of state.

A New Equation of State for Dense Hydrogen–Helium Mixtures. II. Taking into Account Hydrogen–Helium Interactions

Abstract In a recent paper, we derived a new equation of state (EOS) for dense hydrogen/helium mixtures that covers the temperature–density domain from solar-type stars to brown dwarfs and gaseous planets. This EOS is based on the so-called additive volume law and thus does not take into account the interactions between the hydrogen and helium species. In the present paper, we go beyond these calculations by taking into account H/He interactions, derived from quantum molecular dynamics simulations. These interactions, which eventually lead to H/He phase separation, become important at low temperature and high density, in the domain of brown dwarfs and giant planets. The tables of this new EOS are made publicly available.

New International Formulation for the Viscosity of Heavy Water

The International Association for the Properties of Water and Steam has recently adopted a new formulation for the thermodynamic properties of heavy water. This manuscript describes the development of a new formulation for the viscosity of heavy water that is consistent with the new equation of state and is valid for fluid states up to 775 K and 960 MPa with uncertainties ranging from 1% to 5% depending on the state point. Comparisons with experimental data and with a previous viscosity formulation are presented. The new formulation contains terms for the enhancement of viscosity in a small region near the critical point that were not included in previous formulations. The new formulation is applicable over a wider range of conditions than previous correlations.

An equation of state based on the intermolecular potential and the radial distribution function to estimate the virial coefficients by using PvT chaotic data

We derive a new equation of state (EOS) for any non-polar, polar or quantum gas and any intermolecular potential through an approximation of the radial distribution function based on the Ornstein-Zernike equation. Such EOS is applied to estimate the virial coefficients B and C using two approaches. On one hand, B and C are directly computed from the proposed EOS considering the Mie potential for neon and water steam, which leads to values in very good agreement with the experimental data. On the other hand, the proposed EOS is applied in the context of a thermodynamic model to estimate B and C by fitting the simulated chaotic PvT data at an almost constant temperature. Such estimations of B and C are compared with the experimental values, which allows elucidating if B and C have a significant contribution on the virial equation at the considered pressures and temperatures. This methodology is applied to nitrogen and helium4 considering the intermolecular potentials of Mie, Morse, Kihara and Buckingham. For the considered gases and intermolecular potentials, the calculated values of B and C are in very good agreement with experimental data in a wide range of pressures and temperatures.