Isentropic Models Research Articles

Equations of State, Thermodynamics, and Miscibility Curves for Jovian Planet and Giant Exoplanet Evolutionary Models

The equation of state of hydrogen–helium (H–He) mixtures plays a vital role in the evolution and structure of gas giant planets and exoplanets. Recent equations of state that account for H–He interactions, coupled with H–He immiscibility curves, can now produce more physical evolutionary models, such as accounting for helium rain with greater fidelity than in the past. In this work, we present a set of tools for planetary evolution that provides a Python interface for existing tables of useful thermodynamic quantities, state-of-the-art H–He equations of state, and pressure-dependent H–He immiscibility curves. In particular, for a collection of independent variable choices, we provide scripts to calculate the variety of thermodynamic derivatives used to model convection and energy transport. These include the chemical potential derived from the internal energy, which is a modeling necessity in the presence of composition gradients when entropy is the other primary variable. Finally, an entropy-based convection formalism is presented and fully described that highlights the physical differences between adiabatic and isentropic interior models. This centralized resource is meant to facilitate both giant planet structural and evolutionary modeling and the entry of new research groups into the field of giant planet modeling. All tables of thermodynamic quantities and derivatives are available at https://github.com/Rob685/hhe_eos_misc, along with a unified Python interface. Tutorials demonstrating the interface are also available in the repository.

Fundamental influence of irreversible stress–strain properties in solids on the validity of the ramp loading method

The widely used quasi-isentropic ramp loading technique relies heavily on back-calculation methods that convert the measured free-surface velocity profiles to the stress–density states inside the compressed sample. Existing back-calculation methods are based on one-dimensional isentropic hydrodynamic equations, which assume a well-defined functional relationship P(ρ) between the longitudinal stress and density throughout the entire flow field. However, this kind of idealized stress–density relation does not hold in general, because of the complexities introduced by structural phase transitions and/or elastic–plastic response. How and to what extent these standard back-calculation methods may be affected by such inherent complexities is still an unsettled question. Here, we present a close examination using large-scale molecular dynamics (MD) simulations that include the detailed physics of the irreversibly compressed solid samples. We back-calculate the stress–density relation from the MD-simulated rear surface velocity profiles and compare it directly against the stress–density trajectories measured from the MD simulation itself. Deviations exist in the cases studied here, and these turn out to be related to the irreversibility between compression and release. Rarefaction and compression waves are observed to propagate with different sound velocities in some parts of the flow field, violating the basic assumption of isentropic hydrodynamic models and thus leading to systematic back-calculation errors. In particular, the step-like feature of the P(ρ) curve corresponding to phase transition may be completely missed owing to these errors. This kind of mismatch between inherent properties of matter and the basic assumptions of isentropic hydrodynamics has a fundamental influence on how the ramp loading method can be applied.

Comparison of models for the warm-hot circumgalactic medium around Milky Way-like galaxies

ABSTRACT A systematic comparison of the models of the circumgalactic medium (CGM) and their observables is crucial to understanding the predictive power of the models and constraining physical processes that affect the thermodynamics of CGM. This paper compares four analytic CGM models: precipitation, isentropic, cooling flow, and baryon pasting models for the hot, volume-filling CGM phase, all assuming hydrostatic or quasi-hydrostatic equilibrium. We show that for fiducial parameters of the CGM of a Milky Way (MW)-like galaxy ($M_{\rm vir} \sim 10^{12}~{\rm M}_{\odot }$ at $z\sim 0$), the thermodynamic profiles – entropy, density, temperature, and pressure – show most significant differences between different models at small ($r\lesssim 30$ kpc) and large scales ($r\gtrsim 100$ kpc) while converging at intermediate scales. The slope of the entropy profile, which is one of the most important differentiators between models, is $\approx 0.8$ for the precipitation and cooling flow models, while it is $\approx 0.6$ and 0 for the baryon pasting and isentropic models, respectively. We make predictions for various observational quantities for an MW mass halo for the different models, including the projected Sunyaev–Zeldovich effect, soft X-ray emission (0.5–2 keV), dispersion measure, and column densities of oxygen ions (O vi, O vii, and O viii) observable in absorption. We provide Python packages to compute the thermodynamic and observable quantities for the different CGM models.

Generalised Isentropic Relations in Thermodynamics

Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents γPv, γTv and γPT are introduced to replace the ideal gas isentropic exponent γ to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed.

Total pressure in thermionic orificed hollow cathodes: Controlling mechanisms and their relative importance

A statistical analysis is conducted to identify which physically relevant non-dimensional parameters influence the total (neutral, ion, and electron) static pressure inside thermionic orificed hollow cathodes. It is critical to uncover and order the importance of the physical mechanisms that affect the pressure inside hollow cathodes because it influences the plasma attachment length, the electron temperature, and the sheath potential. These plasma parameters, in turn, affect the emitter lifetime. A principal component analysis of total pressure data obtained from the literature reveals that four non-dimensional variables can account for most of the variation in the total-to-magnetic pressure ratio over five orders of magnitude. The relevant variables are identified with a backward stepwise selection process and an exhaustive grid search and include, by order of importance: the gasdynamic-to-magnetic pressure ratio, the ratio of the mass flow rate to the discharge current, the orifice-to-insert diameter ratio, and the orifice Reynolds number. It is also shown, using various models and regression analyses, that empirical, Poiseuille, or isentropic flow models should not be used for predictive cathode design work. The data-driven study suggests that, while viscous effects may be important, the variation in those effects between cathodes is negligible compared to the effects of the modification of the gas constant due to the plasma, the transitional flow, the flux of heavy species on the orifice plate, and the Lorentz force.

Comparative Valuation of Global Solar Radiation on Horizontal and Tilt Surfaces in Owerri, Nigeria

Comparative valuation of global solar radiation on horizontal and tilt surfaces with the use of Angstrom-Page and four isotropic models for Owerri has been carried out in this paper. Angstrom linear regression model is developed from thirty years (1992-2022) of sunshine hour and average monthly global solar radiation sourced from NIMET and NASA, respectively. The Angstrom regression coefficients 𝑎 and 𝑏determined for Owerri is 0.210 and 0.696, respectively. The developed model is used to estimate average monthly global solar radiation on horizontal surface and consequently, the amount of incident solar radiation received on tilt surface by the isotropic models. The MBE, RMSE and MPE values are estimated to be 0.0083, 0.0029 and -0.0041%, respectively, for the developed Angstrom-Page model. A strong coefficient of determination of 76.6% was obtained and Analysis of Variance (ANOVA) significant of 100% was observed, which shows the goodness of fitness of the model. Among the isentropic models studied, one of the models poorly estimated solar radiation on horizontal and tilt surfaces for the study location

Magma Pressure-Temperature-Time Paths During Mafic Explosive Eruptions

We have constrained syneruptive pressure-temperature-time (P-T-t) paths of mafic magmas using a combination of short-timescale cooling and decompression chronometers. Recent work has shown that the thermal histories of crystals in the last few seconds to hours of eruption can be constrained using concentration gradients of MgO inside olivine-hosted melt inclusions, produced in response to syneruptive cooling and crystallization of olivine on the inclusion walls. We have applied this technique to the study of melt inclusions erupted by arc and ocean island volcanoes, including the 1974 subplinian eruption of Fuego volcano; the 1977 fire-fountain eruption of Seguam volcano; and three eruptions of Kilauea volcano (episode 1 of the 1959 Kilauea Iki fire-fountain eruption, the 1500 CE vigorous fire-fountain eruption, and the 1650 CE subplinian eruption). Of the eruptions studied so far, melt inclusions from the 1959 Kilauea Iki eruption record the highest syneruptive cooling rates (3–11°C/s) and the shortest cooling durations (4–19 s), while inclusions from the 1974 Fuego eruption record the slowest cooling rates (0.1–1.7°C/s) and longest cooling durations (21–368 s). The high cooling rates inferred for the Kilauea Iki and Seguam fire fountain eruptions are consistent with air quenching over tens of seconds during and after fragmentation and eruption. Melt inclusions sampled from the interiors of small (∼6 cm diameter) volcanic bombs at Fuego are found to have cooled more slowly on average than inclusions sampled from ash (with particle diameters < 2 mm) during the same eruption, as expected based on conductive cooling models. We find evidence for a systematic relationship between cooling rates and decompression rates of magmas, in which rapidly ascending gas-bearing magmas experience slower cooling during ascent and eruption than slowly ascending magmas. Our magma P-T-t constraints for the Kilauea Iki eruption are in broad agreement with isentropic models that show that the dominant driver of cooling in the conduit is adiabatic expansion of a vapor phase; however, at Fuego and Seguam, our results suggest a significant role for latent heat production and/or open-system degassing (both of which violate assumptions required for isentropic ascent). We thereby caution against the application of isentropic conduit models to magmas containing relatively high initial water concentrations (e.g., arc magmas containing ∼4 wt% water). We note that several processes that have been inferred to occur in volcanic conduits such as magma stalling, magma mingling, open- and closed-system degassing, vapor fluxing, and vapor accumulation (in foam layers or as slugs of gas) are associated with different implied vapor volume fractions during syneruptive ascent. Given the sensitivity of magma P-T-t paths to vapor volume fraction, the syneruptive thermometer presented here may be a means of identifying these processes during the seconds to hours preceding the eruption of mafic magmas.

Applicable and Comparative Research of Compressor Mass Flow Rate and Isentropic Efficiency Empirical Models to Marine Large-Scale Compressor

A compressor is an indispensable component of marine large two-stroke diesel engines. For this type of engine, the compressor mass flow rate and isentropic efficiency empirical models are preferred for both the working cycle dynamic simulation research and the design and testing of control and diagnostics algorithms due to their compact and simple structures, and satisfactory prediction accuracy. Due to absence of comprehensive applicable and comparative research on compressor mass flow rate and isentropic efficiency empirical models for large-scale marine compressors in the literature, two marine compressors with different size, flow rate range, and speed range were selected as research objects in this paper, and a relevant study was conducted to compare and analyze the prediction ability of several classical models, and some recently proposed compressor mass flow rate and isentropic efficiency empirical models. The range of this comparative study includes the prediction accuracy in the design operating area and the extrapolation ability in off-design operating areas. Based on the obtained research results, several guidelines are summarized, which can be followed when developing compressor mathematical models, especially for marine applications. In addition, several research interests are discussed and presented, which can be further studied in the future.

Non-isentropic study of a closed-circuit oscillating-water-column wave energy converter

The thermodynamics of the air inside a conventional Oscillating Water Column (OWC) is commonly modelled using the isentropic relationship between pressure and density. The innovative Tupperwave device is based on the OWC concept but uses non-return valves and two extra reservoirs to rectify the flow into a smooth unidirectional air flow harnessed by a unidirectional turbine. The air, flowing in closed-circuit, experiences a temperature increase due to viscous losses across the valves and turbine along the repetitive cycles of the device's operation. In order to study this temperature increase which represents a potential issue for the device operation, a non-isentropic wave-to-wire model of the Tupperwave device is developed taking into account the irreversible thermodynamic processes. The model is based on the First Law of Thermodynamics, and accounts for viscous losses at the valves and turbine as well as solar radiation and heat transfer across the device walls and inner free-surface. The results reveal that the temperature increase in the device remains harmless for its operation. The difference between the power performance of the Tupperwave device based on the non-isentropic and isentropic models is found to be relatively small. Its performance are also compared to the corresponding conventional OWC device.

Radial piston expander as a throttling valve in a heat pump: Focus on the 2-phase expansion

Two-phase expansion devices are a practicable solution for improving the energy efficiency of heat pumps. The study of the fluid behavior in such machines has not yet been investigated in detail. In the present study, a radial piston expander was used in a heat pump operating with R134a in place of the throttling valve. Special attention was paid to investigate both numerically and experimentally the behavior of the fluid inside a cylinder within a full cycle of the engine, at different inlet thermodynamic conditions and rotational speeds. The measured indicated cycles were compared with those predicted by a quasi-steady model and a rather large difference between them was noticed. Therefore, a non-isentropic model to predict the in-cylinder pressure trend during the expansion phase at closed valves, developed on the basis of a model proposed for water at atmospheric conditions, was applied. The results achieved with the improved non isentropic model showed a significantly higher accuracy in predicting the experimental results along the expansion phase at closed valves, thus filling the gap registered with the full isentropic models, which lack in this part of the cycle.

Study of thermoviscous dissipation on axisymmetric wave propagating in a shear pipeline flow confined by rigid wall. Part II. Numerical study

Axisymmetric acoustic wave propagating in a shear pipeline flow confined by a rigid wall is studied in the two-part paper. The effects of viscous friction and thermal conduction on the acoustic wave propagating in the liquid and perfect gas are respectively analyzed under different configurations of acoustic frequency and shear mean flow. In Part 2 of this paper, comprehensive analysis of the effects of shear mean flow and acoustic frequency on the features (relative phase velocity and attenuation coefficient) of the acoustic wave are numerically addressed in cases of water and perfect gas respectively. Comparisons between the non-isentropic and isentropic models are provided in details. Meanwhile, discussions of the thermoviscous effects on the acoustic wave between water and perfect gas are given.

Non-axisymmetric magnetic modes of neutron stars with purely poloidal magnetic fields

We calculate non-axisymmetric oscillations of neutron stars magnetized by purely poloidal magnetic fields. We use polytropes of index $n=1$ and 1.5 as a background model, where we ignore the equilibrium deformation due to the magnetic field. Since separation of variables is not possible for the oscillation of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. Solving the oscillation equations as the boundary and eigenvalue problem, we find two kinds of discrete magnetic modes, that is, stable (oscillatory) magnetic modes and unstable (monotonically growing) magnetic modes. For isentropic models, the frequency or the growth rate of the magnetic modes is exactly proportional to $B_{\rm S}$, the strength of the field at the surface. The oscillation frequency and the growth rate are affected by the buoyant force in the interior, and the stable stratification tends to stabilize the unstable magnetic modes.

Two-dimensional MHD model of the Jovian magnetodisk

A self-consistent stationary axially symmetric MHD model of the Jovian magnetodisk is constructed. This model is a generalization of the models of plane current sheets that have been proposed earlier in order to describe the structure of the current sheet in the magnetotail of the Earth [1, 2]. The model takes centrifugal force, which is induced by the corotation electric field, and the azimuthal magnetic field into account. The configurations of the magnetic field lines for the isothermic (plasma temperature assumed to be constant) and the isentropic (plasma entropy assumed to be constant) models of the magnetodisk are determined. The dependence of the thickness of the magnetodisk on the distance to Jupiter is obtained. The thickness of the magnetodisk and the magnetic field distribution in the isothermic and isentropic models are similar. The inclusion of a low background plasma pressure results in a considerable reduction in the thickness of the magnetodisk. This effect may be attributed to the fact that centrifugal force prevails over the pressure gradient at large distances from the planet. The mechanism of unipolar induction and the related large-scale current system are analyzed. The direct and return Birkeland currents are determined in the approximation of a weak azimuthal magnetic field. The modeling results agree with theoretical estimates from other studies and experimental data.

Pipe Networks: Coupling Constants in a Junction for the Isentropic Euler Equations

Abstract The modelling of junctions in pipe networks with subsonic flows is discussed, where pipes are described by one-dimensional, single-phase isentropic flow models. We first study the Riemann problem in a pipe to understand what information is needed to couple two pipes in a flat junction. Using this insight, we generalise the Riemann problem to an arbitrary number of pipes meeting together at a junction. Three coupling strategies found in the literature are presented, where only one leads to physically sound solutions for all the selected test cases. The theoretical derivation is performed in previously published literature. The junction is considered to be a point with no volume. The three coupling strategies are, first, to impose all the pipe sections to be at the same pressure at the junction. The second is to impose equal momentum fluxes at the inlet of all the pipes coupled to the junction. The third is to impose all the pipe sections to reach the junction at a unique stagnation enthalpy, that is, equal for all of them. Only the latter satisfies the second law of thermodynamics, expressed through an entropy condition, in all the test cases run in the study. For the two former coupling strategies, test cases where the entropy condition is violated could be found and are presented. The different coupling strategies are implemented in a numerical model. The one-dimensional models for the pipe sections are solved using a Roe scheme. We illustrate with numerical cases that we can find initial conditions for which the entropy condition is violated for the two first coupling strategies, while the third verifies it in all the cases.

Thermodynamic Analysis of Thermal Responses in Horizontal Wellbores

Wellbore models are required for integrated reservoir management studies as well as optimization of production operations. Distributed temperature sensing (DTS) is a smart well technology deployed for permanent downhole monitoring. It measures temperature via fiber optic sensors installed along horizontal wellbores. Correct interpretation of DTS surveys has thus become of utmost importance and analytical models for analysis of temperature distribution behavior are critical. In this study, we first show how thermodynamic analysis can describe in detail the physical changes in terms of pressure and temperature behavior from the simplest cases of “leaky tank” to the horizontal wellbore itself. Subsequently, rigorous single-phase thermodynamic models for energy, entropy, and enthalpy changes in horizontal wellbores are derived starting from 1D conservative mass, momentum, and energy balance equations and a generalized thermal models, along with their steady-state temperature profile subsets, are presented. Steady-state applications are presented and discussed. The analysis presents the factors controlling horizontal wellbore steady-state temperature responses and demonstrates that wellbore thermal responses are neither isentropic nor isenthalpic and that the isentropic expansion-driven models and Joule–Thompson-coefficient (JTC) driven may be used interchangeably to analysis horizontal wellbore thermal responses.

On linearized coupling conditions for a class of isentropic multiphase drift-flux models at pipe-to-pipe intersections

In this paper a general drift-flux model describing a subsonic and isentropic multi-phase fluid in connected pipes is considered. Each phase is assumed to be isentropic with its own sonic speed. The components are gamma-law gases with γ>1. For such, a computational challenge at a junction is the computation of rarefaction waves which do not have a readily available analytical form. Firstly, the well-posedness of the Riemann problem at the junction is discussed. It is suggested that rarefaction waves should be linearized in order to obtain a more efficient numerical method for coupling such multi-component flow. Some computational results on the dynamics of the multi-phase gas in the pipes demonstrate the qualitative behavior of this approach.

Vanishing Capillarity Limit of the Compressible Fluid Models of Korteweg Type to the Navier--Stokes Equations

In this paper, we consider the three-dimensional isentropic compressible fluid models of Korteweg type, called the compressible Navier--Stokes--Korteweg system. We mainly present the vanishing capillarity limit of the smooth solution to the initial value problem. Precisely, we first establish the uniform estimates of the global smooth solution with respect to the capillary coefficient $\kappa$. Then by the Lions--Aubin lemma, we show that the unique smooth solution of the three-dimensional Navier--Stokes--Korteweg system converges globally in time to the smooth solution of the three-dimensional Navier--Stokes system as $\kappa$ tends to zero. Also, we give the convergence rate estimates for any given positive time.

A strong solution for a class of compressible full non-Newtonian models

The aim of this paper is to discuss the existence and uniqueness of a local solution for a class of isentropic compressible full non-Newtonian models in one-dimensional bounded intervals. The first important point in this paper is that we allow the initial vacuum; another one is that the viscosity term and the Newtonian potential term are fully nonlinear.

Contribution to the Modeling and Understanding of Cold Pulsating Flow Influence in the Efficiency of Small Radial Turbines for Turbochargers

In the present paper, an unsteady approach to determine the performance of a small radial inflow turbine working under cold pulsating flow is presented. It has been concluded that a reasonably good characterization of turbine behavior working with pulsating flow can be obtained using, in a quasi-steady way, models of the turbine isentropic efficiency and turbocharger mechanical efficiency. Both models have been fitted using data obtained from a steady flow characterization procedure. Turbocharger-measured parameters from the cold pulsating flow campaign have been compared with the ones obtained from one-dimensional gas dynamics computational modeling. The modeling approach is based on quasi-steady isentropic and mechanical efficiency models. Reasonably good accuracy in compressor and turbine variables prediction has been obtained for most of the operative conditions. Influence of amplitude and frequency of the pulsating flow over the instantaneous and average turbine efficiency has been studied to put some light on the analysis of the involved physical phenomena. The main conclusion is that the biggest effect of unsteady flow on turbine efficiency is through the influence on blade jet to speed ratio. It has been also concluded that, for the same average blade jet to speed ratio, pulses’ amplitude does not influence turbine efficiency when it is closed, but does at other variable geometry turbine (VGT) positions. The effect of pulses’ frequency is less evident and only influences VGT performance at the highest VGT openings.

Spin change of a proto-neutron star by the emission of neutrinos

We investigate the structure of proto-neutron stars (PNSs) with trapped neutrinos by using a quark-meson coupling model. We adopt a phenomenological lepton density which is diffuse near the surface. We calculate the populations of baryons and leptons, the equations of state, and the mass-radius relation for isentropic PNS models. In addition, the moment of inertia is calculated for both PNS and cold-neutron-star (CNS) models as a means to study the change of the spin period due to the neutrino emission from a PNS. Neutrino emission from a hyperonic neutron star is shown to increase the spin by about 10$%$ of the initial spin, while the spin of a nucleonic neutron star with a central density above ${\ensuremath{\rho}}_{C}\ensuremath{\approx}5{\ensuremath{\rho}}_{0}$ is decreased by a few $%$ by the emission of neutrinos. Therefore, the spin change owing to the leakage of neutrinos from a PNS is a small ($&lt;$10$%$) correction compared to other processes related to the spin change.