Different Equations Of State Research Articles

Comparison of different equations of state in a model based on VdW–P for prediction of CO2 hydrate formation pressure in Lw-H-V phase and a new correlation to degrade error of the model

Carbon dioxide plays a significant role in global warming. Formation of carbon dioxide hydrate is one of the several ways to remove this gas from the atmosphere. In order to attain a proper process design, pressure and temperature of the hydrate formation should be estimated.The empirical correlations, charts and thermodynamic model scan be used to predict these conditions.In this work, a model based on van der Waals–Platteeuw for prediction of hydrate formation conditions of CO2which uses four different equations of state, PR, RK, PT and ALS in Lw-H-V phase and in temperature range of 271.6 K–283.2 K is used and the results are brought out in order to compare with each other and with experimental data reported in the literature.Among PR, PT, RK and ALS equations of state, PR with total AADP of 2.52% shows better results than other equations of state.For the model based on VdW–P which uses PR as an equation of state a correlation is presented in order to reduce the amount of error which appears at high temperatures. This correlation reduces the amount of AADP for temperatures of hydrate formation higher than 280.44 K from 4.42 % to 1.04%.

Modelling solubility of phenolics of mango ginger extract in supercritical carbon dioxide using equation of state and empirical models.

Solubility of phenolics of mango ginger extract in supercritical carbon dioxide was studied at 40-60°C and 100-350bar. Critical temperature, critical pressure and critical volume of caffeic acid, the principal component of the extract were calculated using group contribution methods and compared with the values obtained by CHEMDRAW®. Vapor pressure of caffeic acid was predicted by Reidel method. Solubility prediction in supercritical carbon dioxide was studied using two different equation of states (EOS) models and eight empirical models. Peng-Robinson EOS predicted the solubility very well with average deviation of 0.68% from the experimental solubility. Empirical equations based on the simple error minimization using non-linear regression method which do not require complex physiochemical properties was also found suitable to predict the solubility at different extraction conditions. Jouyban et al. model showed very less deviation (2.25%) for predicted solubility values from the experiment.

Viscous driving of global oscillations in accretion discs around black holes

We examine the role played by viscosity in the excitation of global oscillation modes (both axisymmetric and non-axisymmetric) in accretion discs around black holes using two-dimensional hydrodynamic simulations. The turbulent viscosity is modeled by the $\alpha$-ansatz, with different equations of state. We consider both discs with transonic radial inflows across the innermost stable circular orbit, and stationary discs truncated by a reflecting wall at their inner edge, representing a magnetosphere. In transonic discs, viscosity can excite several types of global oscillation modes. These modes are either axisymmetric with frequencies close to multiples of the maximum radial epicyclic frequency $\kappa_\mathrm{max}$, non-axisymmetric with frequencies close to multiples of of the innermost stable orbit frequency $\Omega_\mathrm{ISCO}$, or hybrid modes whose frequencies are linear combinations of these two frequencies. Small values of the viscosity parameter $\alpha$ primarily produce non-axisymmetric modes, while axisymmetric modes become dominant for large $\alpha$. The excitation of these modes may be related to an instability of the sonic point, at which the radial infall speed is equal to the sound speed of the gas. In discs with a reflective inner boundary, we explore the effect of viscosity on trapped $p$-modes which are intrinsically overstable due to the corotation resonance effect. The effect of viscosity is either to reduce the growth rates of these modes, or to completely suppress them and excite a new class of higher frequency modes. The latter requires that the dynamic viscosity scales positively with the disc surface density, indicating that it is a result of the classic viscous overstability effect.

Bianchi Type I Cosmological Models in Eddington-inspired Born–Infeld Gravity

We consider the dynamics of a barotropic cosmological fluid in an anisotropic, Bianchi type I space-time in Eddington-inspired Born–Infeld (EiBI) gravity. By assuming isotropic pressure distribution, we obtain the general solution of the field equations in an exact parametric form. The behavior of the geometric and thermodynamic parameters of the Bianchi type I Universe is studied, by using both analytical and numerical methods, for some classes of high density matter, described by the stiff causal, radiation, and pressureless fluid equations of state. In all cases the study of the models with different equations of state can be reduced to the integration of a highly nonlinear second order ordinary differential equation for the energy density. The time evolution of the anisotropic Bianchi type I Universe strongly depends on the initial values of the energy density and of the Hubble function. An important observational parameter, the mean anisotropy parameter, is also studied in detail, and we show that for the dust filled Universe the cosmological evolution always ends into isotropic phase, while for high density matter filled universes the isotropization of Bianchi type I universes is essentially determined by the initial conditions of the energy density.

Information theoretical methods as discerning quantifiers of the equations of state of neutron stars

Abstract In this work we use the statistical measures of information entropy, disequilibrium and complexity to discriminate different approaches and parametrizations for different equations of state for quark stars. We confirm the usefulness of such quantities to quantify the role of interactions in such stars. We find that within this approach, a quark matter equation of state such as SU(2) NJL with vectorial coupling and phase transition is slightly favoured and deserves deeper studies.

A new limiting procedure for discontinuous Galerkin methods applied to compressible multiphase flows with shocks and interfaces

Although the Discontinuous Galerkin (dg) method has seen widespread use for compressible flow problems in a single fluid with constant material properties, it has yet to be implemented in a consistent fashion for compressible multiphase flows with shocks and interfaces. Specifically, it is challenging to design a scheme that meets the following requirements: conservation, high-order accuracy in smooth regions and non-oscillatory behavior at discontinuities (in particular, material interfaces). Following the interface-capturing approach of Abgrall [1], we model flows of multiple fluid components or phases using a single equation of state with variable material properties; discontinuities in these properties correspond to interfaces. To represent compressible phenomena in solids, liquids, and gases, we present our analysis for equations of state belonging to the Mie–Grüneisen family. Within the dg framework, we propose a conservative, high-order accurate, and non-oscillatory limiting procedure, verified with simple multifluid and multiphase problems. We show analytically that two key elements are required to prevent spurious pressure oscillations at interfaces and maintain conservation: (i) the transport equation(s) describing the material properties must be solved in a non-conservative weak form, and (ii) the suitable variables must be limited (density, momentum, pressure, and appropriate properties entering the equation of state), coupled with a consistent reconstruction of the energy. Further, we introduce a physics-based discontinuity sensor to apply limiting in a solution-adaptive fashion. We verify this approach with one- and two-dimensional problems with shocks and interfaces, including high pressure and density ratios, for fluids obeying different equations of state to illustrate the robustness and versatility of the method. The algorithm is implemented on parallel graphics processing units (gpu) to achieve high speedup.

Effects of shear and rotation on the spherical collapse model for clustering dark energy

In the framework of the spherical collapse model we study the influence of shear and rotation terms for dark matter fluid in clustering dark energy models. We evaluate, for different equations of state, the effects of these terms on the linear overdensity threshold parameter, $\delta_{\rm c}$, and on the virial overdensity, $\Delta_{\rm V}$. The evaluation of their effects on $\delta_{\rm c}$ allows us to infer the modifications occurring on the mass function. Due to ambiguities in the definition of the halo mass in the case of clustering dark energy, we consider two different situations: the first is the classical one where the mass is of the dark matter halo only, while the second one is given by the sum of the mass of dark matter and dark energy. As previously found, the spherical collapse model becomes mass dependant and the two additional terms oppose to the collapse of the perturbations, especially on galactic scales, with respect to the spherical non-rotating model, while on clusters scales the effects of shear and rotation become negligible. The values for $\delta_{\rm c}$ and $\Delta_{\rm V}$ are higher than the standard spherical model. Regarding the effects of the additional non-linear terms on the mass function, we evaluate the number density of halos. As expected, major differences appear at high masses and redshifts. In particular, quintessence (phantom) models predict more (less) objects with respect to the $\Lambda$CDM model and the mass correction due to the contribution of the dark energy component has negligible effects on the overall number of structures.

Higher dimensional charged gravastar admitting conformal motion

In the present paper we have discussed about the higher dimensional charged gravastar admitting conformal motion. The gravastar, gravitationally vacuum condense star is generally considered as the alternative to black hole which has three regions with three different equation of state. (i) In interior region p=−ρ, (ii) in shell p=ρ, (iii) in exterior region p=ρ=0. p=−ρ is generally called the ‘false vacuum’ or ‘degenerate vacuum’ or ρ vacuum. We match our interior spacetime to the R-N higher dimensional spacetime in presence of thin shell.

Numerical simulation of rapid expansion of supercritical carbon dioxide

Axisymmetric rapid expansion of supercritical carbon dioxide is investigated in this article. The extended generalized Bender equation of state is used to give a good description of the fluids over a wide range of pressure and temperature conditions. The locations of Mach disks are analyzed and compared with an experimental correlation for the case where there is no plate positioned in front of the nozzle exit. It is found that the disagreement between our numerical results and the experimental formula is very small when the pressure ratio is small, and increases as the pressure ratio increases. It is also found that with different equations of state, the predicted positions of Mach disks do not differ a lot, but the temperature profiles in the chamber differ a lot. The case where there is a plate positioned in front of the nozzle exit is also studied in this article. A universal similarity solution is obtained. © 2014 American Institute of Chemical Engineers AIChE J, 61: 317–332, 2015

Studying equilibrium values of moduli of elasticity, using models of the mechanics of finite deformations of a continuous medium

The physical content of an equation of state in the form of σ = σ(υ) is discussed as it applies to the theory of the elastic properties of crystals. Here, σ is pressure and υ is a change in the volume of the crystal under the effect of pressure. We assume that the energy of a deformed state is determined using an elastic modulus no higher than the third order. The forms of the analytical dependences of σ = σ(υ) for the eight most popular equations of state in the mechanics of finite deformations of a continuous medium then coincide, and with the same equation of the state predicted by the Mott model. As an example, differences between the values of the elastic moduli of Cu and Al, calculated using different equations of state for the mechanics of finite deformations of continuous media in the Mott model, are discussed.

Modelling a Liquid Material in Drop Test Simulations of a Cask for Liquid Radioactive Waste

The aim of this paper is the comparison of different material models for the simulation of fluid impact on a cask for transport of radioactive liquid material. Simulated is a 9 m drop test performed according to International Atomic Energy Agency regulations. In order to reduce computational time, proposed is to model the transported fluid as a hypothetic linearly elastic material. This enables us to use less time demanding FE explicit dynamic analysis based on Lagrange formulation only instead of combination of Lagrange and Euler formulations. Compared are the results obtained for three elastic material and three fluid models based on different equations of state.

Thermodynamic analysis of hydrogen tank filling. Effects of heat losses and filling rate optimization

A thermodynamic analysis of the refueling of a gaseous fuel tank and a thermal analysis of heat losses through tank walls is presented. The objective of the thermodynamic analysis is to compare the temperature and pressure evolutions coming from different equations of state and from thermodynamic tables. This comparison is performed with nitrogen and hydrogen and the compression is assumed adiabatic. It is shown that the ideal-gas assumption results in under-prediction of the tank temperature and pressure for hydrogen but in over-prediction for nitrogen. An approximate analytical expression of the Redlich–Kwong equation of state is given which is in very good agreement with thermodynamic tables. To handle heat losses, different approaches are used and compared. First, a global thermal conductance is introduced which allows deriving analytical expressions. Then, a thermal nodal modeling of tank walls is proposed to take into account thermal capacity effects. Finally a 1D semi-infinite modeling of the tank walls is presented. Finally, this model is used to optimize mass flow rate in order to limit the temperature rise during the filling process.

The Higher Dimensional Gravastars

A new model of gravastar is obtained in $D$-dimensional Einstein gravity. This class of solutions includes the gravastar as an alternative to D-dimensional versions of the Schwarzschild-Tangherlini black hole. The configuration of this new gravastar consists of three different regions with different equations of state: [I] Interior: 0 \leq r < r_1, \rho = -p; [II] Shell: r_1 \leq r < r_2, \rho = p; [III] Exterior: r_2 < r, \rho = p =0. The outer region of this gravastar corresponds to a higher dimensional Schwarzschild-Tangherlini black hole.

Investigation of equation of state and in-mediumNNcross sections through nuclear stopping

By using an antisymmetrized molecular dynamics model (AMD), the data of kinematically complete events are compared with the experimental INDRA data through nuclear stopping in $\text{Xe}+\text{Sn}$ collisions at 10 to $100A$ MeV. The sensitivity of the nuclear stopping is studied through interactions with different equations of state (EOSs) (soft and stiff) and in-medium $NN$ cross sections in different energy domains. Above $25A$ MeV, both EOSs and different $NN$ cross sections can affect the nuclear stopping, but none of these parameters used in the AMD model can reproduce the experimental data at 20 to $30A$ MeV. On the other hand, below $25A$ MeV, nuclear stopping is not sensitive to both of the EOSs and the $NN$ cross sections because of complete nuclear stopping. This indicates that some important mechanisms may be missing in AMD or that the selection of central collision events may be significantly different between the experiments and the simulations at this energy range.

A pressure-based treatment for the direct numerical simulation of compressible multi-phase flow using multiple pressure variables

In this paper we present a pressure-based numerical scheme for the direct numerical simulation of compressible two-phase flows using the stiffened gas equation of state. While for many technical applications, two-phase flows can be treated as incompressible, this assumption fails in cases with high pressure and temperature as they can be found in rocket combustion chambers, for example. Our interest is in the development of a pressure-based method that aims at the extension of an incompressible two-phase code to the compressible regime. The development builds upon an asymptotic pressure decomposition using multiple pressure variables and has originally been designed for single-phase flows. Its adaptation to compressible two-phase flows is presented. This includes the possibility to resolve and track the interface as well as the description of the two phases by different equations of state. It is shown that the pressure-based scheme does not necessitate a cumbersome interface treatment in order to avoid spurious oscillations in the vicinity of the material interface. We do not yet take into account phase changes whose approximation requires a careful thermodynamic consistent procedure. Numerical examples are shown ranging from the one-dimensional transport of a multi-material contact discontinuity to the three-dimensional simulation of shock-droplet interactions. The scheme proves to be able to accurately simulate the propagation of pressure waves in gaseous and liquid phases.

Polar quasi-normal modes of neutron stars with equations of state satisfying the2 M⊙constraint

In this paper we analyze the quasi-normal mode spectrum of realistic neutron stars by studying the polar modes. In particular we study the spatial wI mode, the f mode, and the fundamental p mode. The study has been done for 15 different equations of state containing exotic matter and satisfying the $2 M_{\odot}$ constraint. Since f and p modes couple to matter perturbations, the influence of the presence of hyperons and quarks in the core of the neutron stars is more significant than for the axial component. We present phenomenological relations for the frequency and damping time with the compactness of the neutron star. We also consider new phenomenological relations between the frequency and damping time of the w mode and the f mode. These new relations are independent of the equation of state, and could be used to estimate the central pressure, mass or radius, and eventually constrain the equation of state of neutron stars. To obtain these results we have developed a new method based on the Exterior Complex Scaling technique with variable angle.

Alternative scenarios of relativistic heavy-ion collisions. III. Transverse momentum spectra

Transverse-mass spectra, their inverse slopes and mean transverse masses in relativistic collisions of heavy nuclei are analyzed in a wide range of incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is performed within the three-fluid model employing three different equations of state (EoS's): a purely hadronic EoS, an EoS with the first-order phase transition and that with a smooth crossover transition into deconfined state. Calculations show that inverse slopes and mean transverse masses of all the species (with the exception of antibaryons within the hadronic scenario) exhibit a step-like behavior similar to that observed for mesons and protons in available experimental data. This step-like behavior takes place for all considered EoS's and results from the freeze-out dynamics rather than is a signal of the deconfinement transition. A good reproduction of experimental inverse slopes and mean transverse masses for light species (up to proton) is achieved within all the considered scenarios. The freeze-out parameters are precisely the same as those used for reproduction of particles yields in previous papers of this series. This became possible because the freeze-out stage is not completely equilibrium.

Electron screening effects on crustal torsional oscillations

We systematically examine the crustal torsional oscillations as varying the stellar mass and radius, where we take into account the effect of electron screening due to the inhomogeneity of electron distribution. In the examinations, we adopt two different equations of state (EOSs) for the inner crust region of neutron stars. As a result, we find that the frequencies depend obviously on the EOS, even if the neutron star models are almost independent of the EOS. That is, one could solve the degeneracy of the stellar models with different EOS via the observations of shear oscillations frequencies. Additionally, we find that the fundamental frequencies of the ℓ-th order torsional oscillations can reduce 6% due to the effect of electron screening, which is independent of the adopted EOS and stellar models. This reduction of frequencies can be crucial to make constraints on the density dependence of the nuclear symmetry energy, L, i.e., the constraint on L can reduce ∼15% by the electron screening effect.

Calculation of Energies and Entropies from Isochoric and Isothermal Experimental Data

This paper presents residual values of Helmholtz energy (Ar/(RT)), entropy (Sr/R), and internal energy (Ur/(RT)) for a ternary mixture that resembles a distribution natural gas between 223.15 K and 303.15 K up to 20 MPa. The methodology uses isochoric and isothermal density measurements to apply corrections to the residuals for Helmholtz energy (δAr/(RT)), entropy (δSr/R), and internal energy (δUr/(RT)) calculated using an equation of state. The method is demonstrated for three representative equations of state: REFPROP, Peng–Robinson, and Redlich–Kwong. Accurate (p−ρ–T) isochoric and isothermal data provide experimental values of the compression factor (Z) and the derivative of pressure with respect to temperature at constant density (∂p/∂T)ρ which are used to calculate residual entropies and energies. The results obtained by using different equations of state at the same conditions have slight differences in the residual values. It is possible to represent those differences by equivalent changes in temperature for entropy (δTS) and internal energy (δTU) that are ≤ 0.5 K for temperatures above 225 K. For this mixture, the values of δAr/(RT), δSr/R, and δUr/(RT) determined from REFPROP are sufficiently small that no corrections are required. For the Peng–Robinson and Redlich–Kwong equations of state, a global fit describing the residual corrections presents a practical application. The residual deviations of the plots lie within ± 0.0005, ± 0.001, and ± 0.002 in the residuals for δAr/(RT), δSr/(RT), and δUr/(RT), respectively.

Role of model ingredients on the directed flow and its disappearance using isospin dependent quantum molecular dynamics model

We study the effect of different equations of state, momentum dependence of nuclear forces and in-medium nucleon-nucleon cross-sections on the directed flow and its disappearance. Our findings reveal that soft momentum-dependent equation of state along with reduced cross-section shows good agreement with the experimentally observed mass dependence of balance energy.