Ideal Equation Of State Research Articles

Feasibility and performance of the staged Z-pinch: A one-dimensional study with FLASH and MACH2

Z-pinch platforms constitute a promising pathway to fusion energy research. Here, we present a one-dimensional numerical study of the staged Z-pinch (SZP) concept using the FLASH and MACH2 codes. We discuss the verification of the codes using two analytical benchmarks that include Z-pinch-relevant physics, building confidence on the codes' ability to model such experiments. Then, FLASH is used to simulate two different SZP configurations: a xenon gas-puff liner (SZP1*) and a silver solid liner (SZP2). The SZP2 results are compared against previously published MACH2 results, and a new code-to-code comparison on SZP1* is presented. Using an ideal equation of state and analytical transport coefficients, FLASH yields a fuel convergence ratio (CR) of approximately 39 and a mass-averaged fuel ion temperature slightly below 1 keV for the SZP2 scheme, significantly lower than the full-physics MACH2 prediction. For the new SZP1* configuration, full-physics FLASH simulations furnish large and inherently unstable CRs (>300) but achieve fuel ion temperatures of many kilo-electron volts. While MACH2 also predicts high temperatures, the fuel stagnates at a smaller CR. The integrated code-to-code comparison reveals how magnetic insulation, heat conduction, and radiation transport affect platform performance and the feasibility of the SZP concept.

Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations

This article presents entropy stable discontinuous Galerkin numerical schemes for equations of special relativistic hydrodynamics with the ideal equation of state. The numerical schemes use the summation by parts (SBP) property of the Gauss-Lobatto quadrature rules. To achieve entropy stability for the scheme, we use two-point entropy conservative numerical flux inside the cells and a suitable entropy stable numerical flux at the cell interfaces. The resulting semi-discrete scheme is then shown to be entropy stable. Time discretization is performed using SSP Runge-Kutta methods. Several numerical test cases are presented to validate the accuracy and stability of the proposed schemes.

Maximum baryon masses for static neutron stars in f(R) gravity

We investigate the upper mass limit predictions of the baryonic mass for static neutron stars in the context of f(R) gravity. We use the most popular f(R) gravity model, namely the R 2 gravity, and calculate the maximum baryon mass of static neutron stars adopting several realistic equations of state and one ideal equation of state, namely that of causal limit. Our motivation is based on the fact that neutron stars with baryon masses larger than the maximum mass for static neutron star configurations inevitably collapse to black holes. Thus with our analysis, we want further to enlighten the predictions for the maximum baryon masses of static neutron stars in R 2 gravity, which, in turn, further strengthens our understanding of the mysterious mass gap region. As we show, the baryon masses of most of the equations of states studied in this paper lie in the lower limits of the mass gap region –, but intriguingly enough, the highest value of the maximum baryon masses we found is of the order of . This upper mass limit also appears as a maximum static neutron star gravitational mass limit in other contexts. Combining the two results which refer to baryon and gravitational masses, we point out that the gravitational mass of static neutron stars cannot be larger than three solar masses, while based on maximum baryon masses results of the present work, we can conspicuously state that it is highly likely the lower mass limits of astrophysical black holes in the range of –. This, in turn, implies that maximum neutron star masses in the context of R 2 gravity are likely to be in the lower limits of the range of –. Hence our work further supports the General Relativity claim that neutron stars cannot have gravitational masses larger than and then, to explain observations comparable or over this limit, we need alternative extensions of General Relativity, other than f(R) gravity.

Refinements of the algorithms needed to retrieve atmospheric vertical thermodynamic profiles from GNSS radio occultations

Abstract In this work we consider some refinements to the Boundary Profile eValuation (BPV) method, developed by Vespe et al. (2004), Vespe and Persia (2006), Vespe (2016), Andrisani and Vespe (2020) in order to retrieve atmospheric thermodynamic profiles from Radio Occultation (RO) observations. Former BPV models solved typical rank deficiencies in treating RO data by applying parametric dry refractivity models for the atmosphere, such as the CIRA86aQ or Hopfield (1969). The involved parameters were selected by fitting those dry models with the refractivity observed in the stratosphere, where water vapor concentrations are negligible, with the usual Least Square Error (LSE) method. Dry refractivity is then extrapolated down to the Earth surface. Nevertheless, unphysical occurrence of negative values of humidity concentrations, typical for the so called “simple models” (Kursinski and Kursinski, 2013) can occur in the lower troposphere. This problem is solved with a non-negative residuals constrained fitting for the total refractivity, obtained with different mathematical methodologies. Other refinements include the departure from the ideal state equation for a more realistic state equation concerning compressibility factors for the dry and wet components of the atmosphere. An application to 848 RO observations from COSMIC_1 space mission, covering tropical and middle latitudes during the months of January, March and May 2009, together with a statistical comparison with other atmospheric models and experimental data, was made in order to estimate the accuracy of the BPV method. The results show a description about the thermodynamic state of the atmosphere in line with other recognized atmospheric models, in particular for what concerns the tropics and the southern middle latitudes.

Wiedemann-Franz law for hot QCD matter in a color string percolation scenario

Transport coefficients serve as important probes in characterizing the QCD matter created in high-energy heavy-ion collisions. Thermal and electrical conductivities as transport coefficients have got special significance in studying the time evolution of the created matter. We have adopted color string percolation approach for the estimation of thermal conductivity ($\kappa$), electrical conductivity ($\sigma_{el}$) and their ratio, which is popularly known as Wiedemann-Franz law in condensed matter physics. The ratio $\kappa/\sigma_{el}T$, which is also known as Lorenz number ($\mathbb{L}$) is studied as a function of temperature and is compared with various theoretical calculations. We observe that the thermal conductivity for hot QCD medium is almost temperature independent in the present formalism and matches with the results obtained in ideal equation of state (EOS) for quark-gluon plasma with fixed coupling constant ($\alpha_s$). The obtained Lorenz number is compared with the Stefan-Boltzmann limit for an ideal gas. We observe that a hot QCD medium with color degrees of freedom behaves like a free electron gas.

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

The paper studies the physical-constraints-preserving (PCP) schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state (EOS) on more general meshes. It is an extension of the work [Math. Models Methods Appl. Sci., 27:1871-1928, 2017] which focuses on the ideal EOS and uniform Cartesian meshes. The general EOS without a special expression poses some additional difficulties in discussing the mathematical properties of admissible state set with the physical constraints on the fluid velocity, density and pressure. Rigorous analyses are provided for the PCP property of finite volume or discontinuous Galerkin schemes with the Lax-Friedrichs (LxF) type flux on a general mesh with non-self-intersecting polytopes. Those are built on a more general form of generalized LxF splitting property and a different convex decomposition technique. It is shown in theory that the PCP property is closely connected with a discrete divergence-free condition, which is proposed on the general mesh and milder than that in [Math. Models Methods Appl. Sci., 27:1871-1928, 2017].

A new equation of state to predict S-CO2 flow with real gas effects

The accuracy of the thermodynamic properties prediction from the different Equation of state (EOS) varies upon the range of temperature and pressure. Despite the variety of EOS available, there is no de facto for selecting an EOS for particular computational modeling. The EOS model recently developed by Kumar and Kim (K-K EOS) determines more accurately the thermodynamic properties of CO2 than earlier models. In this present study, K-K EOS is successfully implemented in the computational analysis of compressible supercritical CO2 flow (S-CO2) in the thermodynamic region near and away from the vapour-liquid critical point. Computational results of SCO2 flow with the real gas properties predicted with the K-K EOS is compared with Span and Wagner (SW EOS) and ideal EOS.

Spontaneous flux concentrations from the negative effective magnetic pressure instability beneath a radiative stellar surface

Context. The formation of sunspots requires the concentration of magnetic flux near the surface. The negative effective magnetic pressure instability (NEMPI) might be a possible mechanism for accomplishing this, but it has mainly been studied in simple systems using an isothermal equation of state without a natural free surface. Aims. We study NEMPI in a stratified Cartesian mean-field model where turbulence effects are parameterized. We use an ideal equation of state and include radiation transport, which establishes selfconsistently a free surface. Methods. We use a Kramers-type opacity with adjustable exponents chosen such that the deeper layers are approximately isentropic. No convection is therefore possible in this model, allowing us to study NEMPI with radiation in isolation. We restrict ourselves to two-dimensional models. We use artificially enhanced mean-field coefficients to allow NEMPI to develop, thereby making it possible to study the reason why it is much harder to excite in the presence of radiation. Results. NEMPI yields moderately strong magnetic flux concentrations a certain distance beneath the surface where the optical depth is unity. The instability is oscillatory and in the form of upward traveling waves. This seems to be a new effect that has not been found in earlier models without radiative transport. The horizontal wavelength is about ten times smaller than what has previously been found in more idealized isothermal models. Conclusions. In our models, NEMPI saturates at field strengths too low to explain sunspots. Furthermore, the structures appear too narrow and too far beneath the surface to cause significant brightness variations at the radiative surface. We speculate that the failure to reproduce effects resembling sunspots may be related to the neglect of convection.

Adjoint Method for Shape Optimization in Real-Gas Flow Applications

An adjoint-based shape optimization approach for supersonic turbine cascades is proposed for application to organic Rankine cycle (ORC) turbines. The algorithm is based on an inviscid discrete adjoint method and encompasses a fast look-up table (LuT) approach to accurately deal with real-gas flows. The turbine geometry is defined by adopting state-of-the-art parameterization techniques (NURBS), enabling to handle both global and local control of the shape of interest. A preconditioned steepest descent method has been chosen as gradient-based optimization algorithm to efficiently search for the nearest minimum. The potential of the optimization approach is first verified by application on the redesign of an existing converging–diverging turbine nozzle operating in thermodynamic regions characterized by relevant real-gas effects. A significant efficiency improvement and a more uniform flow at the blade outlet section are achieved, with expected beneficial effects on the aerodynamics of the downstream rotor. The optimized configuration is also assessed by means of high-fidelity turbulent simulations, which point out the capability of the present inviscid approach in optimizing supersonic turbine cascades with very limited computational burdens. Finally, the newly developed real-gas adjoint method is compared against adjoints based on ideal equations of state on the same design problem. Results show that the performance gain obtained by a fully real-gas optimization strategy is by far higher than that achieved with simplified approaches in case of ORC turbines. This proves the relevance of including accurate thermodynamic models in all steps of ORC turbine design.

Equilibration in quark gluon plasma

The hydrodynamic expansion rate of quark gluon plasma (QGP) is evaluated and compared with the scattering rate of quarks and gluons within the system. Partonic scattering rates evaluated within the ambit of perturbative Quantum Choromodynamics (pQCD) are found to be smaller than the expansion rate evaluated with ideal equation of state (EoS) for the QGP. This indicate that during the space-time evolution the system remains out of equilibrium. Enhancement of pQCD cross sections and a more realistic EoS keep the partons closer to the equilibrium.

Thermal photon production in Au + Au collisions: Viscous corrections in two different hydrodynamic formalisms

We calculate the spectra of produced thermal photons in Au+Au collisions taking into account the nonequilibrium contribution to photon production due to finite shear viscosity. The evolution of the fireball is modeled by second-order as well as by divergence-type 2+1 dissipative hydrodynamics, both with an ideal equation of state and with one based on Lattice QCD that includes an analytical crossover. The spectrum calculated in the divergence-type theory is considerably enhanced with respect to the one calculated in the second-order theory, the difference being entirely due to differences in the viscous corrections to photon production. Our results show that the differences in hydrodynamic formalisms are an important source of uncertainty in the extraction of the value of η/s from measured photon spectra. The uncertainty in the value of η/s associated with different hydrodynamic models used to compute thermal photon spectra is larger than the one occurring in matching hadron elliptic flow to RHIC data.

Laboratory astrophysics and non-ideal equations of state: the next challenges for astrophysical MHD simulations

Laboratory astrophysics holds great promise not only as a highly effective validation tool for astrophysical magneto-hydrodynamics (MHD) codes but it also presents a unique challenge for these codes. The high-density plasmas found in these experiments are not well modeled by the ideal equations of state (EOS) found in most astrophysical simulation codes. To solve this problem, we replaced the ideal EOS scheme in an existing MHD code, AstroBEAR, with a non-ideal EOS method and validated our implementation with van der Waals shock tube tests. The improved code is also able to model flows that contain more than one material, as required in laboratory experiments. Simulations of jet experiments performed at the OMEGA Laser reproduce the morphology of the jet much better than when the code used a single material and an ideal EOS.

Structural models and surface equation of state for pulmonary surfactant monolayers

A simple surface equation of state is proposed to describe π- A isotherms of pulmonary surfactant monolayers. The monolayer is considered as undergoing three characteristic states during the compression: the disordered liquid-expanded (LE) state, the ordered liquid-condensed (LC) state and the collapse state. Structural models of pure protein (SP-B and SP-C) monolayer are proposed to interpret the behavior characteristics of monolayer in the states. The area, A LC, is defined as an instantaneous LC-state area when the monolayer is under the complete LC state. The area, A t , is defined as a transition area from the ordered LC state to the collapse state. And the collapse pressure, π max, is defined as the maximum surface pressure that the monolayer can bear before collapse. The ideal equation of state is revised by A LC, A t and π max, and a new equation of state is obtained, which is applicable for pure components of pulmonary surfactant. The theoretical π- A isotherms described by the equation of state are compared with the experimental ones for SP-B, SP-C, DPPC and DPPG, and good agreements are obtained. The equation of state is generalized to protein–lipid binary mixtures by introducing mixing rules. The predicted π- A isotherms agree with the experimental ones for various pulmonary surfactant components and the average deviation is about 9.2%.

Kinetics of coarsening of helium bubbles during implantation and post-implantation annealing

To understand the effects of He on irradiated metals requires modeling of helium-vacancy cluster evolution. A new method of solving the two-dimensional master equation (ME) describing He-vacancy cluster evolution has been applied to calculate helium bubble evolution in a stainless steel irradiated with alpha particles near room temperature and annealed in the temperature range of 600–900°C. For the first time, the evolution of the helium bubble size distribution function was precisely calculated in 2-D phase space and good agreement with experimental results was obtained. The results indicate that Brownian motion of bubbles via surface vacancy diffusion provides a reasonable explanation for bubble evolution during annealing, most bubbles are found to be near the equilibrium state during the evolution at temperatures of 700°C and higher, lack of vacancies at temperatures lower than 700°C prevents bubble growth, and use of a non-ideal He equation of state (EOS) increases the bubble density and size relative to the case when the ideal EOS is used.

The standard Gibbs energy of adsorption from the bulk at the surface of liquid mixtures: reinterpretation of Traube's ruleAnalysis of the ΔadsG0 contributions under the Extended Langmuir model

In this paper, it is shown that the symmetrically normalized activity coefficient of the solute in the bulk solution, γBb, makes a non-negligible contribution to the standard Gibbs energy of adsorption of solute from the bulk at the surface of binary liquid mixtures, Δ adsG0. With a view to defining this change with practical purposes, we selected the pure solute and a surface pressure π of 1 mN m -1 as standard states for the bulk and surface phases, respectively. Besides, we assumed availability of data in the highly dilute region, where the two-dimensional ideal equation of state holds. In this way, Δ adsG0 = -RT ln(π/γBbxB). When γBb is taken into account, Traube's rule (that ln(π/xB)xB→0 increases linearly with chain length in the water + 1-alkanol series) does not imply that ΔadsG0 increases linearly with chain length. On the contrary, together with the fact that in this series ln(γBb,∞) increases with chain length at the same rate as ln(π/xB)xB→0, Traube's rule implies that ΔadsG0 is constant in this series. This can be interpreted in molecular terms as indicating that in highly dilute solutions the hydrocarbon chain of alkanol molecules at the surface does not lie in or on the surface (as is implied by a linear increase in ΔadsG0 with chain length), but resides completely in the gas phase, as is now known to be true. The constancy of ΔadsG0 also explains why water + 1-alkanol systems share the same π versus γBbxB curve except at high surface concentrations, where the degree of discrepancy is in any case limited by the small differences in surface tension among the pure alkanols. We conclude by using the "Extended Langmuir" model of surface behaviour to split ΔadsG0 into five distinct physically meaningful contributions. © 2004 Elsevier B.V. All rights reserved.

An adaptive numerical scheme for high-speed reactive flow on overlapping grids

We describe a method for the numerical solution of high-speed reactive flow in complex geometries using overlapping grids and block-structured adaptive mesh refinement. We consider flows described by the reactive Euler equations with an ideal equation of state and various stiff reaction models. These equations are solved using a second-order accurate Godunov method for the convective fluxes and a Runge–Kutta time-stepping scheme for the source term modeling the chemical reactions. We describe an extension of the adaptive mesh refinement approach to curvilinear overlapping grids. Numerical results are presented showing the evolution to detonation in a quarter-plane provoked by a temperature gradient and the propagation of an overdriven detonation in an expanding channel. The first problem, which considers a one-step Arrhenius reaction model, is used primarily to validate the numerical method, while the second problem, which considers a three-step chain-branching reaction model, is used to illustrate mechanisms of detonation failure and rebirth for the channel geometry.

Computer simulation of a shock-absorbing pneumatic cylinder

A mathematical simulation model of a double-acting pneumatic cushioning cylinder, designed to absorb periodic shock loads, is presented, which is based on the following assumptions: ideal equation of state, isentropic flow through a port-bleed orifice, isentropic compression process, single degree of freedom piston-cylinder dynamics, and the energy-equivalent linear damping. Because of the non-linear differential equation and a requirement for simultaneous iterative solution, a computer simulation model is employed to predict pressure and motion time histories, and cylinder performance indices. Predictions for both untuned and tuned cylinder example cases are compared with measurements. Good correlations between simulation and experiment are evident even though empirical models for discharge coefficients and damping have been used. The computer simulation has been successful in evaluating a number of products, and thus can be used as a design tool. However, more experimental work must be done to improve its prediction capabilities.

Some aspects of blast from fuel-air explosives

Numerical solutions of the blast wave flow from a spherical explosive charge were obtained using the artificial viscosity technique as employed by Oppenheim. The flow is treated as adiabatic and inviscid and ideal equations of state are used for reactants, products and the surrounding air environment. Differences are noted in the peak pressure, static impulse and dynamic impulse resulting from three representative types of idealized initiation: (1) centrally initiated, self-similar Chapman-Jouguet detonation, (2) edge initiated spherical implosion and (3) constant volume energy release followed by sudden venting to the environment. These are compared to the ideal point blast with counterpressure of the same total energy release. In addition, numerical solutions are presented for centrally initiated, stoichiometric hydrogen-oxygen mixtures surrounded by air for detonation and for deflagration according to an empirically determined, non-steady flame velocity. The greater energy transfer to the environment in the case of detonation is demonstrated.

Supersonic Flow With Variable Specific Heat

Abstract Formulas are developed for stagnation conditions and one-dimensional flow through shock waves, including Rankine-Hugoniot values, taking into account the variation of the specific heat of air with temperature by means of the concept of mean specific heats. These formulas are reduced to correction factors that may be applied to the widely used constant specific-heat formulas up to a Mach number of 7. The corrections involved are appreciable in the case of the density change through a shock wave and for the total pressure ratio across a shock wave, as well as for stagnation pressures and temperatures. The limitations imposed by the deviation of a gas at high pressure from the ideal equation of state, relaxation time, and dissociation are discussed.