Real 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.

Rgfrosh: A Python package for calculating shock conditions using real gas equations of state

rgfrosh: A Python package for calculating shock conditions using real gas equations of state

Monitoring overloaded trucks with infrared thermal imaging of tire sidewall

Overloaded trucks have long posed a threat to the road safety. To assess truck payload more effectively, this study focus on tire temperature data obtained through infrared thermal imaging. It is feasible to analyse the payload by monitoring one single representative tire. Tire sidewall surface is the best area for data extraction. Truck overload caused significant increase of gas temperature in tires, as well as external temperature. The internal temperature can be calculated with real gas equation of state. By studying the relationship between internal gas temperature of tire and payload, it is demonstrated that monitoring the temperature of tire sidewall surface is an innovative, remote, and real-time method to assess the payload situation of moving trucks.

Theoretical Expression and Screening of Real Gas Effect of Spiral Groove Dry Gas Seal

The emergence of dry gas seals has revolutionized the form of fluid sealing. The traditional research and analysis of dry gas seals is carried out by considering the lubricating medium gas as an ideal gas, but at this stage, the sealing application environment is complicated, so it is necessary to consider the real gas effect of the lubricating medium gas to expand and break through the design system of dry gas seals. We choose seven common lubricating media in dry gas seal applications and screen the optimal density expression of the real gas using different real gas equations of state. Then, we study the extent to which the compression factors of different lubricating gases deviate from the ideal gas and analyze the errors of different real gas equations of state. These results can provide an optimal expression to clarify the mechanism by which the real gas effect affects the dry gas seal performance, which helps to grasp the nature of dry gas seals, predict the dry gas seal behavior, and guide the dry gas seal application.

Огляд і бібліометричне дослідження надкритичних енергетичних циклів CO2. Поточний стан досліджень і розробок

Recent decades have been characterized by growing interest in research into improving the efficiency of these cycles. The purpose of this work is a bibliometric analysis based on Scopus data (2001-2024) and an overview of the main trends associated with supercritical cycles operating in the region of the carbon dioxide critical point. The objective is to provide a comprehensive overview of research productivity, impact, and trends in supercritical carbon dioxide cycling research over the past two decades, providing useful information for strategic research planning. The methods used were from the Scopus database due to its extensive collection of documents. The review of work lasted from 2001 to 2024, covering a significant time in this area. The literature search was conducted for the following specific keywords: “Supercritical”, “Cycle”, “Carbon dioxide”, “Equation of State”, “Energy Cycle”. The results show growing research interest in this area, which is mainly led by the United States, China, the United Kingdom, Canada, Italy, and Germany. Covering a variety of industries such as engineering, energy, and the environment, this research delves into technical areas such as supercritical carbon dioxide cycles and the real gas equation of state, which allow modeling of the flow of a working fluid in a compression loop. Conclusions. The bibliometric analysis presented in this work offers information on the evolution of research on supercritical carbon dioxide cycles and the equations of state of real gas in the metastable region of carbon dioxide from both academic and industrial viewpoints. By exploring the industry context and the relationships between the findings and the scope of key journals, this analysis illuminates the significance of the findings and their practical implications. New topics identified through keyword analysis can stimulate research planning in the scientific sector. Thus, this comprehensive bibliometric study serves as an independent reference for technology forecasting and monitoring.

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 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.

Effects of microscopic pore-throat structure on gas–liquid relative permeability: Porous media construction and pore-scale simulation

The porous media structure of the oil/gas reservoir changes greatly after long-term development, which subsequently influences the macroscopic relative permeability. To clarify the effects of microscopic pore-throat structure on macroscopic relative permeability, we first proposed a method to generate two-dimensional porous media images with adjustable structure parameters. The method is based on Delaunay triangulation and is similar to the pore-network generation process, which can provide binary images for direct numerical simulation of flow through porous media. Then, we established the single component multiphase Shan–Chen lattice Boltzmann method coupling the real gas equation of state. Finally, we discussed the effect of pore radius, coordination number, pore-throat ratio, pore shape, and wettability on the gas–liquid relative permeability curve using the lattice Boltzmann simulation. This study provides an effective method to generate porous media and explain the mechanism of relative permeability change at the pore scale.

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.

Method for considering real gas equations of state in through-flow programs

Numerical methods are significant in the turbomachine design process and off-design analysis. One of these methods is the through-flow method in the meridional plane, which is utilized in an early design phase. It provides a robust and quick numerical turbomachinery analysis by only giving a few characteristic geometric parameters.This work shows an extension of the through-flow method by considering real gas equations of state (EOSs) in throughflow programs. This is implemented in an in-house through-flow program called tFlow. This enables the method to support a more reliable calculation regarding, for instance, carbon dioxide (CO2) in a high-pressure region, where the gas does not behave like an ideal gas. The incorporation of real gas EOSs is validated with two-dimensional (2D) calculations of nozzle flows and with quasi-three-dimensional (3D) calculations of supercritical CO2 (sCO2) centrifugal compressors. A straightforward method for modifying the Riemann inlet boundary conditions for real gases is presented enabling a quick extension of through-flow codes to real gases and providing a stable solution process. Look-up tables (LUTs) are used instead of common high-degree polynomials to solve the real gas thermodynamic properties and reduce the computation time by a factor of about 20. Additionally, the calculation results verify the application of the Jameson–Schmidt–Turkel (JST) scheme in terms of real gas EOSs. Finally, the predictions are compared against 1D solutions for 2D cases and against the experimental data of the sCO2-HeRo compressor for 3D cases.

Calculating the acoustic and internal gravity wave dispersion relations in Venus's supercritical lower atmosphere

There is a growing interest in quantifying Venusian seismic events through their infrasonic signatures detected by balloon-borne sensors at ∼ 55 km altitude. The extreme pressure and temperature at Venus’s surface correspond to supercritical conditions in the planet’s deep atmosphere. Therefore, an appropriate real-gas equation of state (EoS) must be used to study the acoustic properties and thermodynamics in the Venusian lower atmosphere. In previous work, the Peng-Robinson (P-R) EoS was used to obtain the acoustic sound speed and attenuation coefficient in the lower atmosphere of Venus. Here, the P-R EoS is coupled with the fluid dynamics equations in order to derive the acoustic and internal gravity wave (IGW) dispersion equations. Results show that in Venus’s deep atmosphere, the acoustic cut-off frequency corresponds to a period of ∼480 s (0.0020 Hz), and the buoyancy frequency corresponds to a period of ∼600 s (0.0016 Hz). By comparison, the values in Earth’s lower atmosphere are ∼310 and ∼340 s, respectively. These differences in acoustic and IGW propagation characteristics will be useful in later efforts to discriminate between the various waves detected by high-altitude sensors.

A compressible flow solver for turbomachinery of the real gases with strongly variable properties

Accurate prediction of real gas flows with strongly variable properties is an essential prerequisite for turbomachinery performance analysis. This paper presents a density-based solver for real gas flows in turbomachinery. The solver employs a third-order discretization scheme to improve computational accuracy. Real gas equations of state and look-up table are utilized in the solver to account for the strong nonlinear variations of thermophysical properties. The preconditioning method is adopted for simulations, including low-Mach flow regions, to address convergence difficulties. The implicit Time Consistent Preconditioned Gauss-Seidel Scheme (TCPGS) is employed for the time-stepping. The solver is validated by transonic compressor cascade wind tunnel experiments. Numerical test cases are adopted to evaluate the solver performance, including NASA Rotor 67, NASA Rotor 37, real gas flows in the Laval nozzle, and compressor seal. It has been proved that the numerical test results are consistent with published technical data. The advantages of this solver include numerical stability, computational efficiency, and physical accuracy, which indicate its applicability in the turbomachinery design process for real gases.

Off-design performance assessment of an axial turbine for a 100 MWe concentrated solar power plant operating with CO2 mixtures

This paper presents an investigation of the aerodynamic performance of a 130 MW axial turbine operating with a CO2/SO2 mixture using a mean-line off-design performance model; where the validity of this model has been confirmed through verification against results from the literature and computational fluid dynamic (CFD) simulations. This analysis also includes assessing the impact of varying the number of stages on the part-load operation. Additionally, the application of similitude theory to non-dimensionalise performance characteristics is validated by assessing the performance of the same turbine with different working fluids, mixture compositions, and rotational speeds. The mean-line performance model applied throughout this study is based on the Aungier loss model, whilst a multi-stage, Reynolds averaged CFD model is employed to assess the 3D flow behaviour using the k−ωSST turbulence model. Significant deviations in total-to-total efficiency were observed between the mean-line and CFD results during part-load operation, especially at lower mass flow rates. These deviations can reach up to 18% when the blade Mach number exceeds the design point by 12%. This is attributed to flow separation, which is evident from the CFD simulations, and the mean-line loss model fails to predict. From a purely aerodynamic standpoint, the turbine can operate at part-load conditions up to 88.5% of the design flow coefficient based on the CFD results and achieve an efficiency of 80.2%. It was also found that increasing the number of stages from 4 to 14 can improve the off-design total-to-total efficiency by approximately 7.7% at 93% of the design flow coefficient. This demonstrates that increasing the number of stages enhances turbine performance at both design and part-load operations. Finally, the similitude scaling laws formulated using real-gas equation of state were found to remain valid for all the mixtures, molar compositions, and operating conditions considered.

Numerical simulation study on the leakage and diffusion characteristics of high-pressure hydrogen gas in different spatial scenes

This paper presents a computational fluid dynamics (CFD) model for simulating high-pressure hydrogen leakage and diffusion. The model incorporates heat exchange during hydrogen leakage diffusion and the real gas equation of state in high-pressure conditions. The CFD model can provide superior predictions of pressure, temperature, hydrogen density, and mass flow rate within the hydrogen storage cylinder changes during high-pressure hydrogen leakage compared to existing models. Moreover, the model validated by experimental data enables simulation of the spatiotemporal evolution law of hydrogen concentration and the change of the combustible region in space following a high-pressure hydrogen storage cylinder leak in various spatial scenarios. It can also determine the safe distance after the hydrogen leakage and simulate the impact of the hydrogen leakage on the surrounding environment in terms of temperature, pressure and other physical factors. Furthermore, the model is applicable for simulating the leakage and diffusion behavior of high-pressure hydrogen in various leakage conditions. This capability helps researchers understand the characteristics of high-pressure hydrogen leakage and diffusion, and further study the phenomenological evolution law of hydrogen safety accidents, so as to formulate emergency response strategies.

Multidimensional numerical simulation of thermodynamic and oscillating gas flow processes of a Gifford-McMahon cryocooler

Abstract The Gifford-McMahon cryocoolers are considered to be prominent candidates for the cooling of high-temperature superconducting magnets, liquefaction of permanent gases, helium recondensation in magnetic resonance imaging machines, cooling of superconducting quantum interference device, etc. In this paper, multi-dimensional numerical simulation is performed to visualize the oscillating heat and fluid flow processes that happen in a mechanically driven GM cryocooler. Influence of the ideal gas equation and real gas equation of states on the cooling behaviour is explained. The minimum achievable refrigeration temperature of a uniform mesh regenerator is compared with a multi-mesh regenerator. It is noticed that a multi-mesh regenerator produces a lower refrigeration temperature as compared to a uniform mesh regenerator. In addition to this, a one-dimensional simulation is conducted and results are compared with multi-dimensional numerical simulation. The no-load temperature value calculated by the one-dimensional model and multi-dimensional model with ideal gas is lower than that of real gas equations. Additionally, the refrigerating capacity calculated by the one-dimensional model and multi-dimensional model with the ideal gas equation is higher than those of the real gas equation of state.

Modeling of the Gas Dynamic Processes with Different Equations of State

The work is devoted to the study of the features of gas-dynamic processes at the high pressures. The flows of air, hydrogen and water vapor are considered. The results obtained using the ideal gas equation and two real gas equations - van der Waals and Soave-Redlich-Kwong are analyzed. The comparison has been done on the numerical simulation results for the safety valve operation problem. The problem was solved in a three-dimensional non-stationary formulation using the finite volume method. Numerical solution method was built on the basis of the Godunov’s method. The results of a comparison of isotherms for each media are presented. Those are obtained using the considered equations of state in the regions when the gases thermodynamic parameters are changed. The influence of the gas model on the processes in the safety valve has been studied in detailsfor hydrogen. A detailed comparison of the local distributions of pressure, temperature, density, and flow velocity has been made. The complex impact of the flow parameters was studied using the integral characteristics - the gas-dynamic force acting on the disk and the gas flow rate. It has been found the gas-dynamic forces obtained within the framework of ideal gas model and the Soave-Redlich-Kwong gas are close to each other in magnitude and exceed the force for the van-der-Waals gas. However, the flow rate of ideal gas significantly exceeded that for both real gases. It is due to a twofold increase in density, which is not compensated by a decrease in the flow velocity. Thus, to obtain accurate data on the dynamic and velocity effects of gas flows on technical devices at high pressures it is necessary to use the real gas equations of state.

Kinetic-energy- and pressure-equilibrium-preserving schemes for real-gas turbulence in the transcritical regime

Numerical simulations of compressible turbulent flows governed by real-gas equations of state, such as high-pressure transcritical flows, are strongly susceptible to instabilities. In addition to the inherent multi-scale nature of the flow, the presence of a pseudo-interface can generate spurious pressure oscillations when conventional schemes are utilized. This study proposes a general framework to derive and analyze discretization methods that are able to preserve kinetic energy by convection, and simultaneously maintain pressure equilibrium in discontinuity-free compressible real-gas flows. The formal analysis reveals that the discrete pressure-equilibrium condition can be fulfilled at most to second-order accuracy, as it requires the spatial differential operator to satisfy a discrete chain rule when total or internal energy are directly discretized. A novel class of schemes based on the solution of a pressure equation is thus proposed, which preserves mass, momentum, kinetic energy and pressure equilibrium, but not total energy. Extensive numerical tests of increasing complexity confirm the theoretical predictions, and show that the proposed scheme is capable of providing non-dissipative, stable and oscillation-free simulations, unlike existing methods tailored for the transcritical regime.

Numerical investigation of the flame suppression mechanism of porous muzzle brake

An excellent flame suppression effect can be achieved using a novel porous brake. To understand the flame-suppression mechanism of a porous brake, combustion using a muzzle brake is investigated. A set of internal ballistic equations is employed to provide accurate velocity and pressure for a projectile moving to the muzzle. The multispecies transport Navier–Stokes equations, which incorporate complex chemical reactions, are solved by coupling a real gas equation of state, the Soave–Redlich–Kwong model, and a detailed chemical reaction kinetic model. The development of muzzle flow with a chemical reaction is simulated, and the interaction between chemical reactions with the muzzle flow field is numerically calculated to explain the muzzle combustion mechanism with a porous brake. The underlying mechanism is analyzed in detail. The results demonstrate that, first, the gas is fully expanded in the brake, leading to a reduction in pressure and temperature at the muzzle, thereby reducing the initial flame. In addition, the shock wave weakens due to the expansion and separation process, leading to a reduction in the mixture of gas and air, ultimately resulting in a reduction in the intermediate and secondary flames.

Numerical prediction of impulse and overpressure for a green high energy metal organic framework (HE-MOF) using computational fluid dynamics

Computational fluid dynamics (CFD) technology was employed to investigate the detonation characteristics of a green high-energy metal–organic framework (HE-MOF) material. Experimental work on this relatively new class of materials is limited. Therefore, high-fidelity large-eddy Simulation (LES) is performed to investigate the impact of the explosive on the shockwave propagation and the latter interaction with obstacles. First, we validate the numerical framework against the laboratory measurements carried out for trinitrotoluene (TNT). Among the HE-MOF materials, [Cu(Htztr)2(H2O)2]n is selected due to its appropriate explosive specifications owing to its special chemical structure. The real gas equation of state of Beker–Kistiakowsky–Wilson (BKW) is employed to account for large density change of air during the explosion. For LES, an extended solver is developed within the open-source OpenFOAM package. Supersonic flow visualization clearly shows positive reflected and incident pressure. Comparisons between the TNT and HE-MOF demonstrate higher blast wave intensity and larger affected area for HE-MOF at identical times. The results of the current study suggest that the HE-MOF produces an impulse 2.5 and 2.28 times greater than TNT in the non-obstructed and obstructed sides of the explosion, respectively.

The influence of cryogenic temperature on the shock structure of impinging under-expanded flow over a convex surface

This study comprehensively investigates the effect of cryogenic nozzle inlet temperature on the flow structure and interactions of an under-expanded supersonic jet with a spherical solid surface. A combined experimental and numerical approach was employed to achieve this goal, utilizing high-speed Z-type schlieren visualization and Reynolds-averaged Navier–Stokes simulations with a Redlich–Kwong real gas equation of state. This study is significant as it addresses a relatively unexplored area of research on the flow structure of the cryogenic under-expanded supersonic jet. The study examines the shock pattern and interaction region through varying static inlet temperature (Tin = 178–290 K) and nozzle pressure ratio (NPR 5–14). Additionally, parameters including nozzle exit-to-throat area ratio (A/A* = 1.277), the distance between the sphere and the nozzle (1.5 cm), and the diameter of the sphere (d = 1.5 cm) were considered fixed. The results show that the supersonic jet exhibits a change in shock patterns in the first shock cell concerning the location and width of the Mach disk, accompanied by a shift in the location of the last shock crossing point and the shock plate. The simulation provides a more detailed insight into the flow, indicating a temperature drop to 105 K in the case of the cryogenic nozzle inlet. At such a low temperature, the compressibility factor exhibits a 5% reduction from unity, while in the case of the ambient nozzle inlet, the minimum temperature at the nozzle exit reached 170 K, leading to only a 1% drop in the compressibility factor, which is negligible. It triggers different flow structures concerning the nozzle inlet temperature. These findings can contribute to the complex flow structures of supersonic jets seen in different industrial and scientific fields.