Adiabatic Index Research Articles

A static spherically symmetric perfect fluid solution to model the interior of stars

An exact solution for modeling the interior of stars with perfect fluid is presented, the geometry of their interior is described by a static and spherically symmetric regular space-time. The hydrostatic functions are physically acceptable for the compactness rate u = GM/c2R ∈ (0, 0.3183497], the speed of sound is a monotonically decreasing function, positive and lower than the speed of light, which implies that the condition of causality is not violated, meanwhile the stability of the solution is guaranteed due to the adiabatic index γ > 3.08387 and it is a monotonically increasing function. The analysis of the solution is presented graphically for specific values of the compactness on the interval u ∈ [0.2509338, 0.3183497] with the minimum value of this interval associated to the neutron star PSR J0348+0432, for observational data which generates the maximum compactness when the radius is minimal R = 12.062 km and the mass is maximum M = 2.05 M¯, generating a value of the central density ρc = 7.520589 × 1017 kg/m3

Blood Plasma Calorimetric Profiles of Women with Preeclampsia: Effect of Oxidative Stress.

Preeclampsia is a pregnancy-related disease with poor placentation and presents itself through hypertension and proteinuria. The disease is also associated with the oxidative modification of proteins in maternal blood plasma. In this work, we combine differential scanning calorimetry (DSC), capillary electrophoresis, and atomic force microscopy (AFM) to evaluate the changes in the plasma denaturation profiles of patients with preeclampsia (PE) as compared with those of pregnant controls. Our results demonstrate that the last trimester of pregnancy substantially affects the main calorimetric characteristics of blood plasma from pregnant controls relative to nonpregnant women. These variations correlate well with the changes in protein levels determined by electrophoresis. DSC analysis revealed significant deviations in the plasma heat capacity profiles of preeclamptic patients from those of pregnant controls. These alterations are expressed mainly in a substantial reduction in albumin-assigned transitions and an upward shift in its denaturation temperature, lower calorimetric enthalpy changes, and a reduced ratio of heat capacity in the albumin/globulin-assigned thermal transitions, which are more pronounced in severe PE cases. The in vitro oxidation model shows that the alteration of PE thermograms is partly related to protein oxidation. AFM data detected numerous aggregate formations in the plasma of PE samples and fewer small ones in the pregnant controls, which are not found in healthy nonpregnant samples. These findings could serve as a basis for further investigations to reveal the possible relationship between albumin thermal stabilization, the increased inflammatory state and oxidative stress, and protein misfolding in preeclampsia.

The Rüchardt experiment revisited: using simple theory, accurate measurement and python based data analysis

This project uses the Rüchardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom f of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder–piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a year 2 undergraduate student and we detail our implementation of this team-based learning project. We present, for the Rüchardt experiment, simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and the experimental data. We find f(He) = 3.48 ± 0.14, f(N2) = 4.92 ± 0.24, f(Air) = 4.96 ± 0.25, f(CO2) = 6.46 ± 0.39 at room temperature and atmospheric pressure. The results for CO2 requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.

De Sitter potential in six dimensional Einstein–Gauss–Bonnet isotropic fluids

We present a physically reasonable stellar model in 6-dimensional Einstein–Gauss–Bonnet gravity by prescribing the de Sitter temporal metric potential. The model displays the necessary qualitative features of a compact star model with variable density profile. For a specified parameter space, the model is shown to be well-behaved in the sense that the energy density and pressure are both positive and smooth decreasing functions, with the pressure vanishing on a suitable hyper-surface, thus establishing a finite boundary for the isotropic distribution. Additionally, the model is causal, the energy conditions and adiabatic stability index are all satisfied. The exact solution does not contain the Einstein gravity model by switching off the higher curvature coupling. The model in the standard theory is constructed from the field equations, and its own associated parameter space is determined. The Einstein model displays some undesirable traits, which are eliminated when the higher curvature terms are active.

Numerical study of heat transfer of hydrogen combustion in noble gases atmosphere in compression ignition engine

The high energy content of hydrogen and zero carbon emission from hydrogen combustion is very important for compression ignition engine development. Hydrogen requires a very high auto-ignition temperature, which encourages replacing nitrogen with noble gases with higher specific heat ratio during compression process. In noble gases-hydrogen combustion, higher combustion temperature potentially leading to a higher heat loss. This paper aims to investigate the effect of hydrogen combustion in various noble gases on heat distribution and heat transfer on the cylinder wall. Converge CFD software was used to simulate a Yanmar NF19SK direct injection compression ignition engine. The local heat flux was measured at different locations of cylinder wall and piston head. The heat transfer of hydrogen combustion in various noble gases at different intake temperatures was studied using the numerical approach. As a result, hydrogen combustion in light noble gases such as helium produces faster combustion progress and higher heat temperature. The hydrogen combustion that experienced detonation, which happened in neon at 340 K and argon at 380 K, recorded a very high local heat flux at the cylinder head and piston due to the rapid combustion, which should be avoided in the engine operation. At a higher intake temperature, the rate of heat transfer on the cylinder wall is increased. In conclusion, helium was found as the best working gas for controlling combustion and heat transfer. Overall, the heat transfer data gained in this paper can be used to construct the future engine hydrogen in noble gases.

Conjugate heat transfer and flow around tandem tubes: Effect of thermophysical parameters and tube arrangement

Thermodynamic calculation and geometry parameters are key issues in thermo-equipment design. The flow and conjugate heat transfer around the tandem tubes are numerically investigated, in which the examined parameters include thermal conductivity ratio (kr), volumetric heat capacity ratio (φr), and Biot number (Bi) which are varied from 200 to 800, 1000 to 3000, and 0.1 to 1.0, respectively. Further, the effect of the space ratio (L/D = 1.0–10.0) between the tandem tubes on the flow pattern and heat transfer is also studied to obtain a proper tube arrangement. In particular, a difference method for lattice Boltzmann algorithm is validated and then adopted on the curve fluid-solid interface to calculate the conjugate heat transfer. Results demonstrate that the thermal conductivity ratio significantly affects the heat transfer performance of the tube while the volumetric heat capacity ratio only affects the rate of heating process. The growth in thermal conductivity ratio leads to a more uniform temperature distribution and higher thermal performance, and this effect becomes weaker as the kr grows. Meanwhile, the increase of Bi strengthens the convective heat transfer inside the tube, further changing the dominant way of heat transfer. Finally, the flow varies considerably with the space ratio, classifying into four typical regimes. It is found that the Nu is sensitive to the flow regime and the case with L/D = 4.0 provides the best thermal performance of tandem tubes. These results can provide more realistic predictions and indications in thermo-equipment design.

Effect of rotation and internal heat generation on Darcy–Brinkman convection in Oldroyd‐B liquid

AbstractConvection in an Oldroyd‐B liquid saturated highly permeable porous medium is studied via both linear and nonlinear theories. Estimating a convection threshold is the objective of linear‐stability analysis whereas convection amplitudes and heat transfer are elucidated by performing nonlinear‐stability analysis. The eigenvalue problem is solved by the Galerkin method of weighted residuals. The oscillatory mode becomes dominant over the stationary mode. This is because of the race among diffusivity, viscoelasticity, internal‐heat generation, and rotation. The increasing permeability, internal heat generation coefficient, and stress‐relaxation parameter are liable to subcritical motions while the rotation, viscosities ratio, heat capacities ratio, and strain retardation parameter are responsible for the system attaining a supercritical state. The Runge–Kutta–Gill method presents the mechanism to evaluate the amount of heat transfer. The increasing Rayleigh number, internal Rayleigh number, Darcy number, Deborah number, Prandtl number, and the heat capacities ratio enhance the heat transfer. This offers a convenient mechanism for regulating convection. The results obtained in the present paper are expected to play a decisive role in some of the real‐life applications such as oil‐reservoir modeling, crude oil extraction, crystal growth, medicine industries, geothermal‐energy utilization, and so on.

New anisotropic star solutions in mimetic gravity

We extract new classes of anisotropic solutions in the framework of mimetic gravity, by applying the Tolman–Finch–Skea metric and a specific anisotropy not directly depending on it, and by matching smoothly the interior anisotropic solution to the Schwarzschild exterior one. Then, in order to provide a transparent picture we use the data from the 4U 1608-52 pulsar. We study the profile of the energy density, as well as the radial and tangential pressures, and we show that they are all positive and decrease toward the center of the star. Furthermore, we investigate the anisotropy parameter and the anisotropic force that are both increasing functions of the radius, which implies that the latter is repulsive. Additionally, by examining the radial and tangential equation-of-state parameters, we show that they are monotonically increasing, not corresponding to exotic matter. Concerning the metric potentials, we find that they have no singularity, either at the center of the star or at the boundary. Furthermore, we verify that all energy conditions are satisfied, we show that the radial and tangential sound speed squares are positive and sub-luminal, and we find that the surface redshift satisfies the theoretical requirement. Finally, in order to investigate the stability we apply the Tolman–Oppenheimer–Volkoff equation, we perform the adiabatic index analysis, and we examine the static case, showing that in all cases the star is stable.

Design of a carbon capture system for oxy-fuel combustion in compression ignition engines with exhaust water recirculation

The oxy-fuel combustion engine concept with onboard oxygen generation and carbon capture (CC) is studied using as a starting point a baseline oxy-fuel combustion layout coupled to a mixed ionic-electronic conducting membranes for producing oxygen (O2) from the air. A CC system is designed accounting for the flash-out temperatures and the operating pressure of the last CO2 purification step. The proposed engine concept is optimized through the product of useful effective efficiency and engine brake power,which is maximized actuating on the start of injection (SOI) for every assessed gas path layouts. The additional cooling power required by the carbon capture system (CC) is also contemplated . Initially, two approaches are compared when the CC is coupled to the O2 generation unit, including or not an intake cooler. The use of intake cooler yields better engine performance than removing it but increases the cooling power requirements significantly. The extreme results from using or not the intake cooler, indicates that a proper solution could combine both cases, approaching for a different cooling concept. A mixer model is developed to recirculate part of the water condensed in the CC towards the cylinder inlet to lower the intake gas temperature and increase the oxidizer heat capacity ratio. From this layout, an optimum setup for SOI and recirculated water mass flow is found considering the trade-off between additional cooling power and engine performance. Indeed, this case reduces the total ICE additional cooling power required by the exclusive use of an intake cooler by about 27% and improves the engine performance by about 20% in comparison to the lack of intake cooling of the charge flow.

Investigation of non-ideal gas flows around a circular cylinder

The aerodynamic performance of a cylinder Pitot probe for velocity measurements in compressible non-ideal gas flows, such as those encountered in Organic Rankine Cycle (ORC) turbines, is investigated by means of Computational Fluid Dynamics. Numerical simulations are performed at subsonic and transonic conditions, and freestream Reynolds numbers are in the cylinder critical regime. The working fluid is the organic vapor Novec™ 649. Air flow simulations at similar inlet conditions are reported for comparison. Steady and unsteady RANS solutions are computed with the Spalart–Allmaras turbulence model. The results are assessed against experimental measurements collected in a wind tunnel. URANS is in good agreement with experimental data for all considered conditions, and delivers reasonably accurate estimations of the cylinder back pressure. Using a dense gas leads to a lower minimum pressure coefficient compared to air, alongside a reduced maximum Mach number due to the non-ideal speed of sound behaviour. In the experimentally studied range of compressibility factors and Mach numbers, discrepancies observed with respect to air flow are mostly an effect of the different isentropic exponents. In the transonic regime, shock waves causing boundary layer separation are weakened in the dense gas, but back pressure is also decreased, contributing to rising form drag.

Analytical study of ionizing blast waves in atomic hydrogen

The ionization effect on both the evolution and internal structure of a blast wave (BW) is determined in laboratory conditions. In a first step, the Rankine–Hugoniot equations describing the structure of the shock front together with the Saha equation modeling ionization are solved analytically in a consistent way for the conditions of a cold initial atomic hydrogen gas. In a second step, a simplified approach is used by introducing an effective adiabatic index γ * that takes into account ionization arising at the shock front. Finally, γ * is used as input data in the self-similar model derived formerly by Barenblatt to describe the structure and the dynamics of the ionizing BW. For the typical laboratory conditions of blast wave experiments, ionization achieves a hydrogen gas compression up to about 11 times at the shock front of the blast wave where a thin and dense shell forms. For such a compression, the value of the effective adiabatic index is γ * ≃ 1.2 leading to a self-similar evolution of the BW where its radius R(t) varies according to R ( t ) ∝ t α * with α * ≃ 0.33. This value of α * is lower than the adiabatic expansion stage α = 2 / 5, where the total energy of the BW is conserved. Thus, ionization is found to act as a cooling effect at the shock front where a fraction of kinetic energy is absorbed to ionize the gas.

Effects of Reynolds number on thermal wake in conjugate heat transfer between a sphere and its surrounding fluid

Unsteady conjugate heat transfer between an aluminum sphere and its surrounding water was investigated. The mass, momentum and energy equations were solved, and for Reynolds number greater than 400, the large eddy simulation with the Smagorinsky–Lilly model was used. 3D transient simulations were carried out for the sphere Reynolds numbers ranging from 1 to 10,000 (6.99 ≤Pe ≤ 69,900). This study particularly focuses on the effect of Reynolds numbers on the thermal wake phenomenon. The simulation results showed that under the condition of the conductivity ratio of 337.33 and the heat capacity ratio of 0.567, thermal wake exists when 1≤ Re <8000 (6.99 ≤ Pe < 55,920). The Reynolds number of 8000 (Pe = 55,920) was determined as the turning point that thermal wake disappears. Two modes of reverse heat transfer, laminar and vortical were identified. For laminar thermal wake, the thermal inversion point starts from the rear stagnation, while for vortical thermal wake, it occurs near the separation point.

The emergence of delta shock in the limit process for two‐dimensional steady nonisentropic relativistic Euler flow onto a straight wedge

AbstractIn this paper, we mainly study the limit of solutions to the two‐dimensional steady nonisentropic relativistic Euler flow onto a straight wedge. It turns out that the sequence of shock solutions tends to a delta wave adhering to the wedge surface when the velocity of the incident flow goes to the speed of light and the adiabatic index tends to 1 in turn. Meanwhile, it also verifies that the pressure coefficient in the limit case is consistent with the Newtonian sin‐squared law when the speed of light tends to infinity. To this end, we also derive the generalized Bernoulli equation, Taub adiabat (or the generalized Hugoniot adiabat) and a shock polar, and so forth. Furthermore, we give the construction of the delta wave by the definition of weak solution.

Stability of electrically charged stars, regular black holes, quasiblack holes, and quasinonblack holes

The stability of a class of electrically charged fluid spheres under radial perturbations is studied in this work. Among these spheres there are regular stars, overcharged tension stars, regular black holes, quasiblack holes, and quasinonblack holes, all of which have a Reissner-Nordstr\"om exterior. We formulate the dynamical perturbed equations by following the Chandrasekhar approach and investigate the stability against radial perturbations through numerical methods. It is found that (i) under certain conditions that depend on the adiabatic index of the radial perturbation, there are stable charged stars and stable tension stars; (ii) also depending on the adiabatic index there are stable regular black holes; (iii) quasiblack hole configurations formed by, e.g., charging regular pressure stars or by discharging regular tension stars, can be stable against radial perturbations for reasonable values of the adiabatic index; and (iv) quasinonblack holes are unstable against radial perturbations.

An analytical study on transient thermal behavior of a packed-bed molten salt thermocline thermal storage

A volume averaged set of the governing equations for local thermal non-equilibrium fluid saturated porous media was applied to study transient thermal behavior of convection and conduction within a packed-bed thermocline thermal storage tank. General analytical expressions, which agree well with numerical results, were derived for the prediction of transient temperature fields of molten salt and granulated material. Three important dimensionless parameters, namely, the solid fluid heat capacity ratio, interstitial Stanton number and Peclet number based on the effective thermal diffusivity, are identified to investigate their effects on the thermal response of the packed-bed thermocline thermal storage tank. An explicit analytical expression for the effective discharging efficiency has been derived as a function of the three important dimensionless parameters. The expression may serve as a powerful tool to design a packed-bed thermocline thermal storage tank according to required operational conditions.

Thermal analysis of the hybrid HVAC unit using interpolant function

This study aims to cover the thermodynamic aspect of a geothermal site using the Hermite interpolant. The energy distribution, determination of the system exergy and the energy ratio are some of the factors investigated thoroughly. The steady flow energy equation was used to determine the design parameters related to the hybrid heating, ventilation, and air condition (HVAC) system. For the underground heat exchanger, it was assumed that the heat capacity ratio, R, was small in magnitude. The energy ratio estimated in the corridor of the lecture hall increased by 17% as compared to the hall area. The exergy destruction of the system was estimated to be 25%, whereas the maximum exergy gain computed at the secondary side of the geothermal unit, followed by the second fan coil, the first fan coil, and the radiator. The calculated heating rate was found to be 25.273% lower than the required sensible heat gain. The installed unit could attain the maximum energy ratio of 4.031 if the convective losses across the building material are minimised.

The propagation of strong cylindrical shock wave in a rotating axisymmetric non‐ideal gas with radiation heat flux

In this manuscript, we studied a quasi‐linear hyperbolic system of partial differential equations which describes the one‐dimensional adiabatic unsteady flow behind a strong cylindrical shock wave propagating in a rotating non‐ideal gas, which has a varying azimuthal fluid velocity together with a varying axial fluid velocity, with radiation heat flux, and similarity solutions are obtained by using the Lie group‐theoretic method. The basic idea of this method is that it changes the system of PDEs representing the one‐dimensional flow through the similarity variable to the system of ODEs. The flow profiles are drawn behind the shock followed by a brief discussion on the behavior of the solutions via graphs. The effects of variation in non‐ideal parameter, adiabatic index of the gas, Alfven–Mach number and ambient azimuthal velocity exponent on the flow variables are described. All numerical calculations have been performed using the “Mathematica” software.

Stellar Model for Charged and Isotropic Rotating Neutron Stars in $$f(\mathcal {R},\mathcal {T})$$ Gravity

The modified theories of gravity have received a lot of attention in the last decade. These theories aim to describe the accelerated cosmic expansion by altering the theory of gravity, instead of introducing dark energy. The major goal of this research is to examine the spacetime surrounding charged compact star configurations in the context of $$f(\mathcal {R},\mathcal {T})$$ gravity and develop a workable model employing the Buchdahl metric potential (Phys. Rev. D 116, 1027 (1959)). We consider a simplified separable linear form for arbitrary function $$f(\mathcal {R},\mathcal {T})$$ given by, $$f(\mathcal {R},\mathcal {T})=\mathcal {R}+2\zeta \mathcal {T}$$ with the matter Lagrangian $$\mathcal {L}_\mathcal {M}=\rho$$ to depict the full solution of the modified field equations for the considered matter distribution. We assess various key characteristics, including effective energy density, effective pressure, sound velocities, relativistic adiabatic index, all energy conditions, and surface redshift, to determine the model’s physical viability and stability. For this investigation, we consider a rotating neutron star with isotropic configurations, namely Hercules X-1, as testing candidate. We also examine the effect of coupling constant $$\zeta$$ on the physical attributes of our model. The investigation illustrates that all our derived results lie within the physically accepted regime, demonstrating the model’s feasibility in $$f(\mathcal {R},\mathcal {T})$$ gravity.

Traversable Wormhole Solutions Admitting Noether Symmetry in f(R,T2) Theory

This paper uses the Noether symmetry approach to examine the viable and stable traversable wormhole solutions in the framework of the f(R,T2) theory, where R is the Ricci scalar and T2=TμνTμν is the self-contraction of the stress–energy tensor. For this purpose, we consider a specific model of this modified theory to obtain the exact solutions of the Noether equations. Further, we formulate the generators of the Noether symmetry and first integrals of motion. We analyze the presence of viable and stable traversable wormhole solutions corresponding to different redshift functions. In order to determine whether this theory provides physically viable and stable wormhole geometry or not, we check the graphical behavior of the null energy constraint, causality condition and adiabatic index for an effective stress–energy tensor. It is found that viable and stable traversable wormhole solutions exist in this modified theory.

Open-Source Energy, Entropy, and Exergy 0D Heat Release Model for Internal Combustion Engines

Internal combustion engines face increased market, societal, and governmental pressures to improve performance, requiring researchers to utilize modeling tools capable of a thorough analysis of engine performance. Heat release is a critical aspect of internal combustion engine diagnostic analysis, but is prone to variability in modeling validity, particularly as engine operation is pushed further from conventional combustion regimes. To that end, this effort presents a comprehensive open-source, zero-dimensional equilibrium heat release model. This heat release analysis is based on a combined mass, energy, entropy, and exergy formulation that improves upon well-established efforts constructed around the ratio of specific heats. Furthermore, it incorporates combustion using an established chemical kinetics mechanism to endeavor to predict the global chemical species in the cylinder. Future efforts can augment and improve the chemical kinetics reactions for specific combustion conditions based on the radical pyrolysis of the fuel. In addition, the incorporation of theoretical calculations of energy and exergy based on the change in chemical species allows for cross-checking of combustion model validity.