Gas Equation Of State Research Articles

A Three-Dimensional Model of a Spherically Symmetric, Compressible Micropolar Fluid Flow with a Real Gas Equation of State

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of R3 bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail.

Estimation of gas diffusion coefficient for gas/oil-saturated porous media systems by use of early-time pressure-decay data: An experimental/numerical approach

This paper presented a novel numerical method for estimating the gas diffusion coefficient based on the early-time pressure-decay data. Experimentally, “flooding–soaking” procedures were developed to perform the gas diffusion in an oil-saturated tight core under different gas phase volume conditions. After flooding, the capillary bundle model was used to calculate the oil–gas contact area. The early-time pressure-decay data of the gas phase were monitored and recorded during the soaking process. Theoretically, a non-equilibrium inner boundary condition coupled with the characteristics of experimental early-time pressure had been incorporated to develop a diffusion model for a gas/oil-saturated tight core system. Based on gas-phase mass balance equations and gas equation of state, the diffusion coefficients were optimized once the discrepancy between experimental data and numerical solutions was minimized. According to the estimated results in this study, the CH4 diffusion coefficients were 3.74 × 10−11 and 3.86 × 10−11 m2/s in tight core saturated with crude oil, respectively. Moreover, the oil–gas contact area significantly impacts the diffusion flux in oil-saturated porous media. Specifically, an additional 10% contact area results in a 75% increase in CH4 diffusion mass. In addition, with the application of our proposed model to CH4/bitumen and CO2/bitumen systems, the diffusion coefficients were in close agreement with the results reported in previous literature, indicating that the proposed model was applicable to both gas/liquid and gas/liquid-saturated porous media systems.

Self-similar flow behind a shock wave in a gas under the effect of viscosity, heat conduction, and variable ambient density

Self-similar solutions have been investigated to describe the propagation of planar shock waves in a non-ideal gas generated by a piston under viscous stress and heat flux. The equation of state for non-ideal gas incorporates the correction in pressure and volume of the gas. The piston position and ambient density vary exponentially with time. Newton’s law of viscosity is used for the viscous stress and Fourier’s law of heat conduction is taken for heat flux. The viscosity coefficient is taken as constant whereas the thermal conductivity coefficient varies with temperature and density following the power law. The shock jump conditions have been derived for the viscous non-ideal gas using integral form of conservation laws. The shock Reynolds number Re s has been introduced to study the effect of viscosity on shock propagation in non-ideal gas. It is found that similarity solution exists only in an ideal gas under the condition that the ambient density exponent is equal to twice the shock position exponent. This study shows that shock Reynolds number Re s and heat conduction parameter Γ c can be used to control the variation of the flow variables and piston position significantly. The shock strength decreases with increase in the value of shock Reynolds number Re s but is independent of the heat conduction parameter Γ c . The pressure, density, and adiabatic compressibility have significant deviations from high to low viscous flow of ideal gas but the velocity and heat flux undergo negligible change. The results do not support the claim of negligible effect of viscosity in earlier studies and establish the impact of viscosity and heat flux on shock propagation in an ideal gas.

Generally applicable physics-based equation of state for liquids

Physics-based first-principles pressure-volume-temperature equations of state (EOS) exist for solids and gases but not for liquids due to the long-standing fundamental problems involved in liquid theory. Current EOS models that are applicable to liquids and supercritical fluids at liquid-like density under conditions relevant to planetary interiors and industrial processes are complex empirical models with many physically meaningless adjustable parameters. Here, we develop a generally applicable physics-based (GAP) EOS for liquids including supercritical fluids at liquid-like density. The GAP equation is explicit in the internal energy, and hence links the most fundamental macroscopic static property of fluids, the pressure-volume-temperature EOS, to their key microscopic property: the molecular hopping frequency or liquid relaxation time, from which the internal energy can be obtained. We test our GAP equation against available experimental data in several different ways and find good agreement. Our GAP equation, unavoidably and similarly to solid EOS, contains a semi-empirical term giving the energy of the static sample as a function of volume only (EST(V)). Our testing includes studies along isochores, in order to examine the validity of the GAP equation independently of the validity of any function we may choose to utilize forEST(V). The only other adjustable parameter in the equation is the Grüneisen parameter for the fluid. We observe that the GAP equation is similar to the Mie-Grüneisen solid EOS in a wide range of the liquid phase diagram. This similarity is ultimately related to the condensed state of these two phases. On the other hand, the differences between the GAP equation and EOS for gases are fundamental. Finally, we identify the key gaps in the experimental data that need to be filled in to proceed further with the liquid EOS.

Bose–Einstein condensation of photons in a vertical-cavity surface-emitting laser

Many bosons can occupy a single quantum state without a limit. It is described by the quantum-mechanical Bose–Einstein statistic, which allows Bose–Einstein condensation at low temperatures and high particle densities. Photons, historically the first considered bosonic gas, were late to show this phenomenon, observed in rhodamine-filled microcavities and doped fibre cavities. These findings have raised the question of whether condensation is also common in other laser systems with potential technological applications. Here we show the Bose–Einstein condensation of photons in a broad-area vertical-cavity surface-emitting laser with a slight cavity-gain spectral detuning. We observed a Bose–Einstein condensate in the fundamental transversal optical mode at a critical phase-space density. The experimental results follow the equation of state for a two-dimensional gas of bosons in thermal equilibrium, although the extracted spectral temperatures were lower than the device’s. This is interpreted as originating from the driven-dissipative nature of the photon gas. In contrast, non-equilibrium lasing action is observed in the higher-order modes in more negatively detuned device. Our work opens the way for the potential exploration of superfluid physics of interacting photons mediated by semiconductor optical nonlinearities. It also shows great promise for enabling single-mode high-power emission from a large-aperture device.

Real Gas Corrections Based on the Interaction of One-Dimensional Unsteady Waves in a Shock Tube

There are multiple unsteady wave system interactions such as shock waves, expansion waves, and reflection, transmission, and intersection of the contact surface inside a shock tube. Studying the law of unsteady wave system interaction has important guiding significance for the design of gas wave equipment. This paper proposes a solution method for the interaction law of unsteady wave systems based on real gas equation of state (EoS) and applies it to shock tubes. The results show that the temperature maximum error between the code based on ideal gas EoS and simulation results is 3.64%, and the error of wave velocity results is between 2.99% and 18.27%. While the error of temperature results between code based on real gas EoS and simulation is not exceed 3%. More importantly, the wave velocity calculated by the code based on real gas EoS is pretty consistent with the simulation results. The code based on the real gas model can help to solve the problem of offset design point. Research has also shown that as pressure and temperature gradually increase, the deviation between ideal and real gases increases, which also proves that the influence of real gas effects is becoming increasingly significant.

A transient gas pipeline network simulation model for decoupling the hydraulic-thermal process and the component tracking process

The metering mode is gradually changing from volumetric metering to energy metering under the open-access operation of gas pipelines. The gas component tracking by operating simulation is an effective method to realize the energy metering of gas networks. In this paper, coupling and decoupling transient component tracking models of gas networks are proposed. The pipeline governing equations, compressor equations, valve equations, and node relationship equations are considered in the proposed models. The implicit central difference method and the damped Newtonian method are adopted to solve the models. The coupling model considers the component tracking part and hydraulic-thermal simulation as a whole, while the decoupling model splits the whole process into the gas component tracking part, the parameters calculation part, and the hydraulic-thermal simulation part. In the component tracking part, the spatiotemporal variation of the gas mass fraction and density can be obtained through the input velocity of each node. Then, the parameters in the gas state equation can be solved, the hydraulic-thermal simulation can be performed, and the new velocity of each node can be calculated. The iteration for each time step ends if the deviation of flow velocity in the component tracking process and the hydraulic-thermal process satisfies the requirements. Two cases are studied to verify the effectiveness of the proposed models, and the boundary condition adaptability of the transient simulation models is analyzed. The proposed models can efficiently simulate the spatiotemporal variation of the operating variables and gas components, providing a reference in the operation of natural gas pipeline networks.

Analysis of the flow and thermal-fluid–solid coupling of crude oil in circular pipe caused by variable pressure gradient

Abstract Globally, enhanced oil recovery (EOR) has become a pressing issue as the demand for crude oil continues to increase. This study investigates the flow and thermal-fluid–solid coupling of crude oil in a rod pump during hot water recovery and obtains the maximum recovery of crude oil in a vertical pipeline through numerical analysis. The pressure gradient in the pump barrel was first developed and deduced based on the ideal gas state equation and Bernoulli’s equation. According to the rheological experiment results, it was proven that the light crude oil conforms to the Newtonian constitutive equation. Subsequently, the momentum equation of crude oil flowing in the pipeline and fluid–solid coupling heat transfer equations were established and solved using the finite difference method. The effects of the thermal recovery temperature T w , wall thickness c, and stroke time n of the rod pump on flow Q are discussed. In particular, the flow Q within 1 min first increases and then slows down with the increase in stroke time n and reaches its maximum value at n = 7 r/min. Furthermore, flow Q decreases with an increase in c but increases as T w increases; c = 1.2 cm, T w = 363 K is the best oil recovery scheme.

A Reduced Kinetics Model for the Oxidation of Transcritical/Supercritical Gasoline Surrogate/Ethanol Mixtures Using Real Gas State Equations

ABSTRACT Efforts to combat the harmful effects of vehicle emissions on our environment and health include exhaust emissions and fuel efficiency regulations. One promising solution is direct fuel injection in supercritical conditions, where the fuel mixture is above critical temperature and pressure. This study presents a reduced kinetics mechanism (129 species and 1015 reactions) utilizing real gas equations to simulate the combustion of supercritical/transcritical gasoline surrogate/ethanol blends. It was developed by combining two reduced models – a Toluene reference fuel (TRF) with a Diisobutylene (DIB) and an ethanol model – and validated through simulations of ignition delay time (IDT). The Arrhenius parameters of key reactions for each fuel component were modified to improve accuracy. An adjusted Redlich-Kwong cubic state equation was employed to segregate each surrogate mixture tested as supercritical, transcritical, or subcritical. The new mechanism was then validated against experimental results using high-pressure conditions and the cubic Peng-Robinson and Redlich-Kwong equation of state parameters. Critical properties of each species were obtained through Joback’s Group Method and the Ambrose-Walton vapor pressure equation. The TRF/DIB/E mechanism results were consistent with shock tube experimental data at high pressure, indicating a potential for modeling combustion in ultra-high pressure direct injection engines.

Gas state equation and flow mechanism of gas–liquid two-phase flow in airlift pump system

Airlift pumps (ALPs) have a simple structure and significant application potential. However, previous studies on ALPs have generally assumed that the gas density remains constant. In this paper, the gas state equation (GSE) for ALP is established based on the van der Waals formula, which explicitly considers the density of gas. An electrical resistance tomography system is used to collect the gas void fractions at different heights under different gas flow rates, and an empirical formula for the gas void fraction is established. To verify the effectiveness of the proposed model, high-precision pressure sensors and a high-speed camera are used alongside an electrical resistance tomography system to determine the realistic ALP flow parameters. The results of 409 sets of experiments show that: (1) the gas in ALP cannot be regarded as ideal gas, because the ideal GSE cannot distinguish between different gas flow rates; (2) the state change of gas in ALP is a quasi-equilibrium process, whereby the GSE of ALP can be obtained from the pressures under several locations; (3) the axial pressures predicted by the proposed GSE for ALP are in good agreement with experimental data; and (4) a single parameter of the GSE uniquely determines the state process. The proposed model and the experimental data provide a new methodology and comprehensive references for studying the working mechanism and efficiency of ALPs.

A self-similar model of galaxy formation and dark halo relaxation

We develop a spherical self-similar model for the formation of a galaxy through gas collapsing in an isolated self-gravitating dark matter halo. As is well known, the self-similarity assumption makes the problem eminently tractable by reducing it to a system of ordinary differential equations. We improve upon the existing literature on self-similar collapse in two ways. First, we include the effects of radiative cooling and the formation of a pseudo-disk at the center of collapse, in a parametrised manner. More importantly, we solve for the evolution of gas and dark matter simultaneously and self-consistently using a novel iterative approach. As a result, our model produces shell trajectories of both gas and dark matter that qualitatively agree with the results of full hydrodynamical simulations of self-gravitating systems. We discuss the impact of various ingredients such as the accretion rate, gas equation of state, disk radius and cooling rate amplitude on the evolution of the gas shells, although we leave the inclusion of stellar and black hole activity to future work. The self-consistent evolution of gas and dark matter allows us to study the response (or `quasi-adiabatic relaxation') of the dark matter trajectories to the presence of collapsing gas, an effect that has gained increasing importance recently in the context of precision estimates of small-scale statistics like the matter power spectrum. Our default configuration produces a relaxation relation in qualitative agreement with that seen in cosmological hydrodynamical simulations, and further allows us to easily study the impact of the model ingredients mentioned above. As an initial application, we vary one ingredient at a time and find that the accretion rate and gas equation of state have the largest impact on the relaxation relation, while the cooling amplitude plays only a minor role. Our model thus provides a convenient framework to rapidly explore the coupled nonlinear impact of multiple astrophysical processes on the mass and velocity profiles of dark matter in galactic halos, and consequently on observables such as rotation curves and gravitational lensing signals.

Optimization of the Internal Ballistic Performance of Supercritical Nitrogen Ejection

This paper investigates a scheme of introducing TNT into a high-pressure chamber containing supercritical nitrogen as the working substance to enhance the utilization of the working substance and the mass of the ejection missile. Based on the S-R-K real gas state equation and the quasi-static pressure and temperature prediction model of TNT, the internal ballistic equations for supercritical nitrogen are established for a missile of 30000 kg, so as to demonstrate the scheme for ejecting a large mass missile and analyze its optimization. Meanwhile, the influence of the high-pressure chamber volume and TNT initiating time on internal ballistic performances is studied, respectively. Simulation results indicate that when the capacity of the high-pressure chamber decreases and the initiating time is delayed, the peak acceleration of the missile and its ejection velocity could be steadily lowered, but the utilization of nitrogen working substance increases. Moreover, the duration of high temperatures in the low-pressure chamber increases as the delay of the initiating time grows. These conclusions could be utilized as a reference for optimizing the design of ejectors.

Experimental and simulation study on the expansion mechanism of polyurethane grout

Understanding the expansion mechanism of polyurethane polymer grout can supply guidance for accurate grouting. However, most of the polymer grout expansion calculations were defined simplistically by the polymer density-expansion pressure empirical relationship expression, which failed to meet the time history of the expansion pressure during the polymer reaction process. The objective of this paper was to investigate the expansion mechanism of polyurethane foam in various constraint conditions during the whole polymer reaction process. A model describing the expansion mechanism of polyurethane foam was established based on the energy conservation principle, the chemical reaction kinetic equation solved by the Runge-Kutta method, and the ideal gas state equation. The model was proved applicable compared to the experiments under fixed volume and fixed confining pressure boundaries. In addition, the effects of grouting quantity, confining pressure, initial temperature, and physical foaming agent content on the grout expansion pressure, density, and components conversions were discussed. The results showed that the expansion pressure of polymer grout gradually increased with time under the fixed volume conditions, and the grout expansion pressure increased as the density increased. The final grout expansion pressure will increase with the increase of initial temperature or the content of physical blowing agent. Under the fixed confining pressure condition, the polymer grout density gradually decreased with time, the grout density increased as the confining pressure increased while the conversions of the two components alcohol and isocyanate increased. The final density decreases with the increase of initial temperature or the content of physical blowing agent.

Dynamic Measurement and Prediction of Sulfur Hexafluoride Gas Weight Based on Non-Ideal Gas State Equation and Improved Random Forest

Real-time knowledge of sulfur hexafluoride (SF6) gas weight can effectively manage and maintain the power equipment using SF6. Firstly, the gas pressure and temperature sensors are utilized to measure SF6 gas pressure and temperature dynamically. Secondly, the measured gas pressure and temperature values are converted to the SF6 gas weight using equations for calculating non-ideal gas states. Finally, the dynamic prediction model of the SF6 gas weight is developed by combining the improved chimp optimization algorithm and random forest algorithm. The dynamic prediction model is trained using measured pressure and temperature data as inputs and the calculated SF6 gas weight as outputs. The trained prediction model enables the dynamic prediction of SF6 gas weight. The experimental results show that the mean absolute error, root mean square error, and mean absolute percentage error of the proposed prediction model reaches 51.54 kg, 103.59 kg, and 11.62%.

GROUP OF SYMMETRIES FOR THE DYNAMICS SYSTEM OF EQUATIONS OF RAREFIED TWO-PHASE MEDIUM

The symmetries of the system of equations of a two-phase medium are found, where the first phase is gas and the second one is solid particles. The second phase is considered rarefied, it is expressed in the absence of pressure in the equations of motion of the second phase. The medium is assumed to be nonisothermal. Using the methods of group analysis, the Lie algebras of symmetries of the model under study are found in the one-dimensional and three-dimensional cases. The paper describes in detail the process of searching for symmetries in the case of equations of state for a perfect gas. Some partially invariant solutions are found for the one-domensional system.

Virial equation of state for a granular system.

The equation of state for an ideal gas is simple, which is . In the case of imperfect gases where mutual interactions among the constituents are important, pressure P can be expressed as the series expansion of density n with appropriate coefficients, known as virial coefficients . In this paper, we have obtained the first four virial coefficients for a model interaction potential using multidimensional Monte-Carlo integration and importance sampling methods. Next, we perform molecular dynamics simulations with the same for a many-particle system to obtain P as a function of T and n. We compare our numerical data with the virial equation of state.

Adaptive thermodynamic consistency control via interface thickness in pseudopotential lattice Boltzmann method across wide temperature ranges

Multiphase flow phenomena are ubiquitous in real-life applications, and the pseudopotential-based lattice Boltzmann multiphase simulation method has gained extensive usage in fields such as fuel cells, energy storage materials, and boiling heat transfer. Over the past two decades, significant improvements have been made to the pseudopotential model. These advancements have greatly enhanced its accuracy in simulating various processes. In this paper, we employ a numerical stability-based unit conversion scheme to ensure an accurate representation of real-world material properties. Additionally, we introduce a more precise non-ideal two-parameter gas state equation Modified Peng-Robinson (MPR) that closely aligns with experimental data, surpassing the commonly used single-parameter Peng-Robinson state equations. Furthermore, we compare the accuracy of the two-state equations for polar and non-polar substances, finding improved accuracy for non-polar substances and a higher degree of fidelity for polar substances when using the MPR equation. We analyze the constant correction coefficients chosen for thermodynamic consistency regulation from the perspectives of vapor-liquid interface thickness and numerical stability, both when held constant and when employing a dynamic correction approach that balances vapor-liquid interface width, numerical stability, and thermodynamic consistency. Finally, we validate to ensure its practical applicability.

A parameter determination method of powder burn model based on Levenberg-Marquardt optimization

ABSTRACT The powder burn model is a mathematical model used to characterize the combustion behavior of energetic materials. In this paper, a parameter determination method for the powder burn model is proposed based on the Levenberg-Marquardt (L-M) optimization algorithm, establishing connections between internal ballistics parameters and powder burn model parameters. Taking a 4/1 single-base propellant as an example, the detailed fitting process is presented, and error analysis is conducted. The fittings of the gas state equation and reaction rate equation of powder burn model converge at the 15th and 22nd iterations, respectively. Both fittings displayed a high level of accuracy, with an R-squared value of 0.999. The comparison with the results of the closed bomb experiments demonstrates excellent agreement between pressure-time curves calculated by the powder burn model and the internal ballistics model, confirming their suitability for describing the combustion behavior of propellants. This method provides a foundation for numerically simulating the internal ballistics combustion behavior of energetic materials.

Internal Pressure-Temperature Coupling Analysis Method for Thermal Decomposition of GFRP Composites Based on the Overlapping Elements Method.

A method of internal pressure-temperature coupling analysis for the thermal decomposition of GFRP composites under high-temperature conditions was established, which incorporates coupled calculations of heat transfer equations, the Arrhenius equation, Darcy's law, and the ideal gas state equation. Using the overlapping mesh method, the coupling calculation of temperature and internal pressure is realized based on the UMATHT and USDFLD user subroutines developed. Specifically, two user subroutines, UMATHT-1 and UMATHT-2, are used to define the heat transfer equation and gas diffusion equation separately. Numerical simulations are conducted to simulate the polymers' thermal decomposition in high-temperature environments. For glass fiber/vinyl ester composites and glass fiber/phenolic composites, the predicted temperature and pressure values are in good agreement with experimental measurements, and porosity and permeability are then analyzed. Due to the accumulation of thermal decomposition gases, inter-pressure within the material surged and reached a peak value. After that, it began to decrease, but the factors affecting the pressure decrease vary at different positions. Specifically, the pressure closest to the heating surface is influenced by the combined effects of decomposition rate, permeability, and porosity, while the pressure far away from the heating surface is only affected by the initial permeability. The pressure in the intermediate region may be influenced by both increased porosity and initial permeability.

Molecular CO2 Storage: State of a Single-Molecule Gas.

CO2 evolution is one of the urgent global issues; meanwhile, understanding of sorptive/dynamic behavior is crucial to create next-generation encapsulant materials with stable sorbent processes. Herein, we showcase molecular CO2 storage constructed by a [60]fullerenol nanopocket. The CO2 density reaches 2.401 g/cm3 within the nanopore, showing strong intramolecular interactions, which induce nanoconfinement effects such as forbidden translation, restricted rotation, and perturbed vibration of CO2. We also disclosed an equation of state for a molecular CO2 gas, revealing a very low pressure of 3.14 rPa (1 rPa = 10-27 Pa) generated by the rotation/vibration at 300 K. Curiously enough, the CO2 capture enabled to modulate an external property of the encapulant material itself, i.e., association of the [60]fullerenol via intercage hydrogen-bonding.