Different Equations Of State Research Articles

On the evaluation of accretion process near a quantum-improved charged black hole

This paper deals with astrophysical accretion onto the quantum-improved charged black hole. An accretion process does not depend on time; it is a stationary process. In this analysis, we explore the physical quantities like energy density, radial velocity, sonic speed, and accretion mass rate for quantum-improved charged black holes and compare them with the existing outcomes corresponding to the Schwarzschild black hole. Following the Michel and Babichev approaches, we investigate the quantities mentioned above by taking into account different equations of state. These fundamental approaches and black hole parameters are responsible for decreasing the fluid's radial infalling velocity during the accretion process and, for others, as a gravitational enhancer, increasing the fluid flow into the black hole horizon. The polytropic fluid's accretion process is also discussed. All the quantities are analyzed graphically with a contour structure. It is observed that the maximum accretion rate is achieved for different values of the considered black hole parameters. From this analysis, we may be able to understand the physical mechanism of accretion onto a quantum-improved charged black hole.

Predictive modeling of flow characteristics in supersonic separators using machine learning

In the pursuit of cleaner energy sources, pre-processing fuel streams is crucial before distribution. Challenges arise during this process, leading to operational issues and diminished transmission efficiency. Among different technologies, supersonic separators are the ones that separate undesired components from the main gas stream more effectively. Precise forecasting of nozzle flow rate and shockwave location at a low cost can markedly enhance the efficiency of manufacturing and rating. In this research, the one-dimensional method has been developed to solve flow equations simultaneously by implementing equations of state. CFD has been used for the verification of the developed model, and the effect of different equations of state is investigated. Results show that the one-dimensional model significantly reduces the calculation time. Different EOSs result in up to 2.0 % and 3.5 % variation in the prediction of shock location and the mass flow rate, respectively.A machine learning methodology is employed to predict the location of shockwaves and the choked flow rate at an even lower cost. A dataset of 160 entries, generated using Peng Robinson's EOS, serves as the basis for this analysis. Prediction tasks are executed using Random Forest, k-nearest Neighbors, and Multilayer Perceptron models. While all three models demonstrate proficiency in data interpolation with R2 scores up to 0.9962 and 0.9951 for the shockwave location and mass flow rate, respectively, discerning their performance in extrapolation appears contingent on the specific case. In the case of extrapolation, Multilayer Perceptron and k-Nearest Neighbors show better match to one-dimensional results.

QPOs and circular orbits around black holes in Chaplygin-like cold dark matter

Understanding the nature of dark energy in the universe is an actual issue in theoretical astrophysics and cosmology. One way to do it is by probing dark fluids with different equations of states (EoS). In the present work, we consider a Schwarzschild black hole (BH) surrounded by a dark fluid with a Chaplygin-like EoS as a generalized version of the Chaplygin EoS. We first investigate the effects of the dark fluid parameters on the horizon properties of the BH. The effective mass of the spacetime is calculated and analyzed under the dark fluid parameters. The scalar invariants of the BH spacetime are also calculated, and it is shown that the spacetime curvature increases as the dark fluid parameter increases. Next, we studied the circular motion of the test particle around the BH. As standard particle motion investigations, we analyze the effective potential of the particles for circular motion, specific energy, and angular corresponding to circular orbits with zero and nonvanishing values of the dark fluid intensity. In addition, we study the innermost stable circular orbits (ISCO). It is observed that there is an outermost stable circular orbit (OSCO) due to the presence of the dark fluid. It also shows that at a critical value of the dark fluid intensity parameter, ISCO and OSCO take the same radius. We calculate the frequency of Keplerian orbits and radial and vertical oscillations of the particles along stable circular orbits. We also applied orbital data from hotspots observed near Sgr A* to obtain upper and lower values for the EoS parameter. Finally, we investigate quasiperiodic oscillations and obtain the mass-to-EoS parameter relations for GRS J1915-105 and XTE 1550-564.

X-ray emission spectrum for axion–photon conversion in magnetospheres of strongly magnetized neutron stars

Detecting axionic dark matter (DM) could be possible in an X-ray spectrum from strongly magnetized neutron stars (NSs). We examine the possibility of axion–photon conversion in the magnetospheres of strongly magnetized NSs. In the current work, we investigate how the modified Tolman–Oppenheimer–Volkoff (TOV) system of equations (in the presence of a magnetic field) affects the energy spectrum of axions and axions-converted-photon flux. We have considered the distance-dependent magnetic field in the modified TOV system of equations. We employ three different equations of states (EoSs), namely APR, FPS, and SLY, to solve these equations. We obtain the axions emission rate by including the Cooper-pair-breaking formation process and Bremsstrahlung process in the core of NSs using the NSCool code. We primarily focus on Magnificient seven (M7) star RXJ 1856.5-3754. We further investigate the impact of the magnetic field on the actual observables, such as axion energy spectrum and axion-converted-photon flux at an axion mass in meV range by assuming mass MNS∼1.4M⊙.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_{NS} \\sim 1.4M_{\\odot }.$$\\end{document} We compare our calculated axion-converted-photon flux from all available archival data sets from PN+MOS+Chandra. We also study the variation of the energy spectrum at a fixed energy with varying central magnetic fields. Our predicted axion-converted-photon flux values as a function of axion energy closely follow the experimentally archival data, which allows us to put bounds on the axion mass for the three EoS.

Numerical characterization of high-pressure hydrogen jets for compression–ignition engines applying real gas thermodynamics

The development of hydrogen-fueled direct-injection compression–ignition engines requires adequate models that can accurately predict the spatial development and heat release rate of a jet at high pressure. It is found in literature that the combustion process benefits from minimizing flame–wall interaction, but it is unresearched how to achieve this. Jet theory can greatly reduce research efforts, only its validity is uncertain for hydrogen injections at relevant conditions. This work checks the validity via a parametric study performed with Computational Fluid Dynamics simulations. Sonic conditions are imposed at the nozzle exit, using different equations of state. It is found that real gas behavior needs to be used to compute these conditions and to model the jet dynamics. Furthermore, jet theory shows qualitative agreement with the simulation results. Finally, the heat release rate of a multi-hole injector appears insensitive to injection properties, but jet penetration can be controlled.

Impact of energy–momentum conservation violation on the configuration of compact stars and their GW echoes

This work investigates the impacts of energy–momentum conservation violation on the configuration of strange stars constraint with gravitational wave (GW) event GW190814 as well as eight recent observations of compact objects. The GW echoes from these interesting classes of compact objects are also calculated. To describe the matter of strange stars, we have used two different equations of state (EoSs): first an ad-hoc exotic EoS, the stiffer MIT Bag model and next realistic CFL phase of quark matter EoS. We choose Rastall gravity as a simple model with energy–momentum conservation violation with a set of model parameter values. Our results show that this gravity theory permits stable solutions of strange stars and the resulting structures can foster GW echoes. We illustrate the implication of the gravity theory and found that the negative values of the Rastall parameter result in more compact stellar configurations and lower GW echo frequency. With an increase in the Rastall parameter, both the compactness of the stellar configurations and echo time decrease. It is worth mentioning here that with the chosen set of some probable strange star candidates from observational data and also in light of GW 190814, we have evaluated the radii of stellar models. Also, the GW echo frequencies associated with strange stars are found to be in the range of ≈ 9–27 kHz for both cases. From this work, it is also inferred that the assumption regarding the equivalence of Rastall’s theory to Einstein’s theory is refuted as we have noticed many deviations in the physical properties of the considered compact stars.

Damping of density oscillations from bulk viscosity in quark matter

We study the damping of density oscillations in the quark matter phase that might occur in compact stars. To this end we compute the bulk viscosity and the associated damping time in three-flavor quark matter, considering both nonleptonic and semileptonic electroweak processes. We use two different equations of state of quark matter, more precisely, the MIT bag model and perturbative QCD, including the leading-order corrections in the strong coupling constant. We analyze the dependence of our results on the density, temperature and value of strange quark mass in each case. We then find that the maximum of the bulk viscosity is in the range of temperature from 0.01 to 0.1 MeV for frequencies around 1 kHz, while the associated minimal damping times of the density oscillations at those temperatures might be in the range of few to hundreds milliseconds. Our results suggest that bulk viscous damping might be relevant in the postmerger phase after the collision of two neutron stars if deconfined matter is achieved in the process. Published by the American Physical Society 2024

Detection of Simultaneous Quasiperiodic Oscillation Triplets in 4U 1728-34 and Constraining the Neutron Star Mass and Moment of Inertia

We report simultaneous detection of twin kHz and ∼40 Hz quasiperiodic oscillations (QPOs) in the time-resolved analysis of the AstroSat/LAXPC observation of the neutron star low-mass X-ray binary, 4U 1728-34. The frequencies of the multiple sets of triplets are correlated with each other and are consistent with their identification as the orbital, periastron precession, and twice the nodal precession frequencies. The observed relations, along with the known spin of the neutron star, put constraints on the mass and the ratio of the moment of inertia to the mass of the neutron star to be M⊙*=1.92±0.01 and I45/M⊙*=1.07±0.01 under the simplistic assumption that the metric is a Kerr one. We crudely estimate that the mass and moment of inertia values obtained may differ by about 1% and 5%, respectively, if a self-consistent metric is invoked. Using the Tolman–Oppenheimer–Volkoff equations for computing the moment of inertia of a neutron star in slow rotation approximation, having different equations of state, we find that the predicted values of neutron star parameters favor stiffer equations of state. We expect more stringent constraints would be obtained using a more detailed treatment, where the equation of state–dependent metric is used to compute the expected frequencies rather than the Kerr metric used here. The results provide insight into both the nature of these QPOs and the neutron star interior.

On the sound velocity bound in neutron stars

It has been suggested in the literature that the sound velocity of the nuclear matter vs exceeds the so-called sound velocity bound vs≤c/3 at high density, where c is the speed of light. In this paper, we revisit the issue of neutron star properties, comparing current measurements of mass, radius, and tidal deformability with 105 different equations of state. These equations are parametrized at low density and saturate the sound velocity bound beyond twice the saturation density. This allows us to conservatively determine the maximum mass compatible with observed neutron star properties and the sound velocity bound. We find that majority of the models are eliminated by the incompatibility with the observations and, especially, the recently detected massive pulsar (2.35±0.17M⊙) is hardly realized by our simulations. Our study strongly supports that the sound velocity bound is not satisfied in nature.

Research on the State Equation of High-Pressure Expansion Process of Liquid Hydrogen

Liquid hydrogen, characterized by high purity, efficient storage and transportation, and renewable clean energy, has become a crucial component in the efficient utilization of energy. A profound understanding of the thermodynamic properties of the high-pressure expansion process of liquid hydrogen plays a significant role in the utilization of hydrogen energy, the development of liquid hydrogen booster pumps, and the implementation of liquid hydrogen-related projects. In this paper, starting from the perspective of the state equation, we conduct research on the large-scale high-pressure expansion process of liquid hydrogen. Several commonly used state equations are employed to calculate the PVT (Pressure-Volume-Temperature) values of this process, and appropriate modifications and combinations are made to improve the accuracy of the state equations. The advantages and disadvantages of the different equations of state for each pressure range and the causes of errors are further discussed based on the standard values given in the NIST database, and some suggestions are made for the improvement of the equations of state and the design of liquid hydrogen-related equipment.

Comparative study on the equation of state of detonation products

The equation of state (EOS) for detonation products can predict explosive performance with basic information about density, enthalpy of formation, and elemental composition. However, to achieve higher prediction accuracy, it is necessary to select an appropriate EOS for the specific detonation parameters being calculated. To study the applicability of different equations of states for explosive products, five EOSs, Becker–Kistiakowsky–Wilson, Kihara–Hikita–Tanaka, Virial-Wu (VLW), Lennard-Jones–Devonshire (LJD), and Jacobs–Cowperthwaite–Zwisler (JCZ), were used to calculate the Hugoniot curve of nitrogen and the detonation performance of typical explosives. The calculation results show that all five EOSs can provide reasonably accurate predictions of the Hugoniot curve of nitrogen on the relative volume-pressure plane. Moreover, the EOSs can accurately predict the detonation velocity and pressure of explosives within a wide range of initial densities. When it comes to temperature calculations, LJD and JCZ demonstrate higher prediction accuracy. Additionally, the results indicate that VLW may not be suitable for calculating the overdriven detonation of explosives, particularly at higher pressures.

Thermal evolution and axion emission properties of strongly magnetized neutron stars

Emission properties of compact astrophysical objects such as Neutron stars (NSs) are associated with crucial astronomical observables. In the current work, we obtain the mass, pressure profiles of the non-rotating NSs using the modified Tolman Oppenheimer Volkoff (TOV) system of equations in the presence of intense magnetic field. We obtain the profiles by using a specific distance-dependent magnetic field in the modified TOV equations. We employ three different equations of states (EoS) to solve the TOV equations by assuming the core of NSs comprises a hadronic matter. Employing the above profiles, we determine the cooling rates of spherically symmetric NSs as a function of time with and without including the magnetic field using the NSCool code. We have also determined the cooling rates as a function of radius for three different NSs. Furthermore, we determine the luminosity of neutrinos, axions, and photons emitting from the NSs in the presence and absence of a magnetic field for an axion mass 16 meV and three different EoS. Our comparative study indicates that the cooling rate and luminosities of neutrinos, axions, and photons change significantly due to the impact of the strong magnetic field. We also find that due to the magnetic field, the axion mass bound increases slightly compared to without a magnetic field.

Constraints on Neutron Star Structure from the Clocked X-Ray Burster 1RXS J180408.9−342058

Type I X-ray bursts are rapid-brightening transient phenomena on the surfaces of accreting neutron stars (NSs). Some X-ray bursts, called clocked bursters, exhibit regular behavior with similar light-curve profiles in their burst sequences. The periodic nature of clocked bursters has the advantage of constraining X-ray binary parameters and physics inside the NS. In the present study, we compute numerical models, based on different equations of state and NS masses, which are compared with the observations of a recently identified clocked burster, 1RXS J180408.9−342058. We find that the relation between the accretion rate and the recurrence time is highly sensitive to the NS mass and radius. We determine, in particular, that 1RXS J180408.9−342058 appears to possess a mass less than 1.7M ⊙ and favors a stiffer nuclear equation of state (with an NS radius ≳12.7 km). Consequently, the observations of this new clocked burster may provide additional constraints for probing the structure of NSs.

Evaluation of different equations of state and free-volume approaches for unified modeling of diffusion and thermodiffusion coefficients

This article is a development and testing of the previously suggested theoretical approach for simultaneous thermodynamic modeling of diffusion and thermodiffusion coefficients. The new theoretical framework allows for the calculation of transport properties with the aid of the concepts of penetration distances and emission functions, which are fully determined from thermodynamic equations that relate functions of state variables, that is, equations of state (EoS). Four underlying EoS were tested in this work, 3 different cubic EoS and PC-SAFT, with the aim of investigating the effect of the thermodynamic model on the description of experimental data. We also investigated the impact of different approaches to estimating the free volume, which is an essential part of the model. The results indicate that the application of the effective co-volume provides a superior representation of the diffusion and thermodiffusion coefficients, which should be included in the parameterization procedure for the selection of the unified model parameters. We evaluated the use of infinite dilution diffusion coefficient data and molecular dynamics simulation to validate model parameters, and discussed the possible ways to improve the model, including predicting diffusion data as a function of temperature.

Modeling Thermodynamic Properties of Mixtures of CO2 + O2 in the Allam Cycle by Equations of State

Different equations of state (EOS) were applied for describing thermodynamic properties of the system CO2+O2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {CO}_{2} + \ ext {O}_{2},$$\\end{document} which is important for the Allam cycle: cubic EOS (Soave–Redlich–Kwong, Peng–Robinson), molecular-based EOS (PC-SAFT, PCP-SAFT, SAFT-VR Mie, polar soft-SAFT, BACKONE, sCPA), and multiparameter EOS (GERG-2008, EOS-CG). The pure component models were taken from the literature. The results for the mixture were compared to experimental data from the literature for two cases: (i) the thermodynamic properties of the mixture were modeled using predictive mixing and combination rules; (ii) additional binary interaction parameters were fitted to experimental data for improving the performance. In the predictive mode (i), the best results were obtained with molecular-based EOS. In the adjusted mode (ii) the best results were obtained with the multi-parameter GERG-2008 EOS and EOS-CG.

An investigation comparing various numerical approaches for simulating the behaviour of condensing flows in steam nozzles and turbine cascades

The process of condensation takes place within the low-pressure stages of the steam turbine when undergoing rapid expansion. The dry supercooled steam turns into very tiny liquid droplets, and the resulting wet steam mixture causes additional losses and maintenance problems. Accurate simulation of steam condensing flows helps to obtain accurate information about the thermodynamics of such flows and use this information in the design of highly efficient steam turbine stages. In this study, by using the available numerical models in commercial CFD codes, seven cases are considered for simulating steam condensing flows. The important difference between these cases is the use of different condensation models and different equations of state to calculate the thermodynamic properties of wet steam. The objective of this research is to identify an appropriate model that can be used to simulate the flow of steam condensation effectively. In recent studies, it is still necessary for further improvement of the modelling methods because the numerical results did not fully match the experimental findings, underscoring the persisting uncertainties within this domain. The current study explores various condensation models and equations of state for calculating the thermodynamic properties of wet steam. This diversity of approaches is novel and allows for the comparison of different models to determine the most suitable one for effective flow simulation. The geometries of the IWSEP nozzle (International Wet Steam Experimental Project) and linear cascade of the last-stage rotor blades were considered. To identify the most appropriate model for the simulation of steam condensing flows, the numerical results are validated against in-house experiments. The results indicate that combining the Young droplet growth model with the Vukalovich and Young equations in cases 1 and 2 is not a suitable method for modelling steam condensing flows. However, cases 3 & 4, which are the combination of Gyarmathy and Fuchs-Sutugin droplet growth models with NIST real gas models, are the most appropriate ones. The findings of this research confirm the high sensitivity of the modelling of such flows, and emphasize that the necessary care should be taken in choosing the appropriate numerical model.

Coupled total- and semi-Lagrangian peridynamics for modelling fluid-driven fracturing in solids

This paper presents a novel computational approach for modelling fluid-driven fracturing in quasi-brittle solids using peridynamics. The approach leverages a rigorous coupling of the total- and semi-Lagrangian formulations of peridynamics. Specifically, the total-Lagrangian formulation, whch is based on classical peridynamics theory used for modelling fractures in solids, is combined with the semi-Lagrangian formulation to solve the Navier-Stokes equation using a non-local differential operator for weakly compressible fluid flow. The proposed approach offers a unified peridynamics-based framework that enables simulations of a wide range of fluid-driven fracturing problems in solids. The framework can model the solid as either an ordinary or non-ordinary material and quantify the fluid with different equations of state. To prevent unphysical inter-penetration, a fluid-solid interaction scheme that assumes fictitious fluid points in the solid domain is proposed to quantify the forces at the fluid-solid interface. The proposed computational approach is validated through simulations of several classic problems, including the dam break and the Kristianovich-Geertsma-de Klerk (KGD) problem. The predictive capability of the proposed approach is further demonstrated by numerical examples of fractures induced by fluid injection in sandstone, which reasonably capture the fracture patterns compared to experimental results. The presented approach offers an alternative to explicit modelling of fluid-driven fracturing processes and may find wide and useful applications to a variety of industrial and geophysical processes.

A Numerical Algorithm for Calculating Critical Points and Its Application to Predictive Mixture Models and Binary CO_2 Mixtures

The use of supercritical fluids in technical applications requires an accurate knowledge of their critical points. For mixtures, these can deviate significantly and without a linear dependency from the critical points of its individual pure components. Since even small amounts of admixture can have noticeable effects, this not only concerns blends of targeted compositions, but also unintentional mixtures for example caused by impurities. Within this work, a method for the calculation of critical points is presented which focuses on numerical robustness promoting a fast and reliable generation of results. Implemented into the thermodynamic property software TREND, with its mixture modeling capabilities, the method allows a flexible combination of different equations of state and mixture models which also includes predictive approaches. Against the background of an increasing relevance of mixtures based on supercritical CO_2 (sCO_2) for energy applications, critical lines are calculated and compared against experimental results for selected sCO_2-based mixtures recently considered for power plant applications. Herein, several combinations of equations of state (EoS) and mixture models are compared. Critical lines are calculated for the first time in this work with the combination of the multi-fluid mixture model with excess Gibbs energy (g^text {E}) models. It was found that the critical lines calculated with the combination of the multi-fluid mixture model with the g^text {E}-model COSMO-SAC yields good predictive results for the investigated CO_2 mixtures.

Physical characteristics of wormhole geometries under different EoS in the context of Rastall gravity

This paper investigates the characteristics of wormhole solutions within the framework of Rastall gravity. First, we derived the shape functions using two different equations of state (EoS). Then we examined the essential characteristics of the shape function for wormholes and the behavior of energy conditions. The present investigation based on the EoS produces wormhole solutions valid for negative values of μ or Υ, where μ=κΥ is a dimensionless parameter and Υ denotes a Rastall parameter. Furthermore, the Rastall parameter Υ plays a vital role in the stability conditions and geometric properties of a wormhole. The volume integral quantifier (V IQ) is also discussed, which gives the idea of the amount of exotic matter required near the wormhole throat. The conclusion shows that our solutions derived using both EoS in Rastall gravity are physically feasible.

Modeling of the Gas Dynamic Processes with Different Equations of State

The work is devoted to the study of the features of gas-dynamic processes at the high pressures. The flows of air, hydrogen and water vapor are considered. The results obtained using the ideal gas equation and two real gas equations - van der Waals and Soave-Redlich-Kwong are analyzed. The comparison has been done on the numerical simulation results for the safety valve operation problem. The problem was solved in a three-dimensional non-stationary formulation using the finite volume method. Numerical solution method was built on the basis of the Godunov’s method. The results of a comparison of isotherms for each media are presented. Those are obtained using the considered equations of state in the regions when the gases thermodynamic parameters are changed. The influence of the gas model on the processes in the safety valve has been studied in detailsfor hydrogen. A detailed comparison of the local distributions of pressure, temperature, density, and flow velocity has been made. The complex impact of the flow parameters was studied using the integral characteristics - the gas-dynamic force acting on the disk and the gas flow rate. It has been found the gas-dynamic forces obtained within the framework of ideal gas model and the Soave-Redlich-Kwong gas are close to each other in magnitude and exceed the force for the van-der-Waals gas. However, the flow rate of ideal gas significantly exceeded that for both real gases. It is due to a twofold increase in density, which is not compensated by a decrease in the flow velocity. Thus, to obtain accurate data on the dynamic and velocity effects of gas flows on technical devices at high pressures it is necessary to use the real gas equations of state.