Ideal Gas Law Research Articles

Evaluation of reduced-order models for the rapid aerodynamic analysis of supersonic and hypersonic bodies

Abstract This paper presents a comprehensive evaluation of reduced-order models (ROMs) for the determination of pressure coefficient distributions on supersonic and hypersonic bodies. The study investigates the limitations, aerodynamic precision and computational performance associated with various methodologies, ranging from simplistic Newtonian theory-based approaches to more advanced first and second-order shock-expansion theories. Validation is performed by comparing computed results with experimental and computational data for pressure distributions, drag and lift coefficients and centres of pressure for fundamental geometries and authentic vehicle design over a wide range of freestream conditions. The study also includes a comprehensive computational complexity analysis, demonstrating the superiority of finite-element ROM approaches over traditional finite-volume computational fluid dynamics (CFD) simulations. The primary objective of this paper is to scrutinise the extension of these methodological classes to the low supersonic regime. Hence, thermo-chemical reactions within the flow are disregarded, and the ideal gas law is adopted. A value of $\gamma = 1.4$ is chosen for consistency and comparability across the analyses. The proposed ROMs show remarkable potential for reducing high-speed simulation execution times by four orders of magnitude, maintaining accuracy within 20 per cent and as low as 1 per cent. The study unveils three key findings: first, the accuracy degradation of Newtonian-based theories for inclined elements, particularly around 45 degrees, and their reduced dependency on Mach number at large inclination. Secondly, the study presents novel insights into the impact of shock-wave-Mach-wave interactions on pressure distribution calculations, emphasising the Mach number as a crucial metric governing recompression effects. Lastly, the study demonstrates the exceptional accuracy of DeJarnette’s method, providing ${C_P}$ results within 2 per cent for a wide range of conditions, offering an attractive alternative to the Taylor-Maccoll equation.

Investigation of heat absorption or release in an ideal gases system

Abstract In this paper, the heat transfer mechanisms (absorption or release of heat) in an ideal gas system are investigated. The thermodynamic process is described using a pressure-volume diagram, and the relationship between pressure and volume is expressed as a quadratic equation with one variable. The methods employed include graphical analysis and computational techniques. The graphical method involves incorporating adiabatic lines as auxiliary references, while the computational method utilizes both the ideal gas law and the first law of thermodynamics for evaluation. 

Transient Thermal Analysis of a Kiln Using Different Numerical Approaches by Means of CFD

A transient study for the prediction of the temperature of hot gases inside a kiln loaded with bricks, using Computational Fluid Dynamics (CFD), is presented in this work. The prediction of transient thermal performance is obtained through four different approaches: the Properties Fitted to Temperature Polynomials (PFTP) model, the density changes according to the Boussinesq Approximation (BA) model with a Constant Thermal Expansion Coefficient (CTEC), the BA model with a Variable Thermal Expansion Coefficient (VTEC) and the density changes according to the Ideal Gas Law (IGL) model. Furthermore, the effects of a layer of ceramic fiber as insulation are investigated. The numerical results of the transient temperature of the hot gases inside the kiln were validated with experimental data. The mean relative error of the transient temperature was 5.0%, 32.6%, 26.4% and 4.4% for the PFTP model, BA model with a CTEC, BA model with a VTEC and IGL model, respectively. It was concluded that IGL model is the best approach to predict the transient temperature of the kiln. Finally, an increase in the temperature of the hot gases of 12.7% was obtained by applying the IGL model and using a layer of 0.07 m of ceramic fiber as insulation. The results of this work could be helpful to improve the design and performance of kilns in further works.

SU2-COOL: Open-source framework for non-ideal compressible fluid dynamics

We present a fully open-source framework for the numerical simulation of Non-Ideal Compressible Fluid Dynamics (NICFD). The open-source Computational Fluid Dynamics suite SU2 is coupled to the open-source thermophysical library CoolProp, which includes state-of-the-art thermodynamic models of numerous pure fluids and mixtures relevant to applications. Accurate thermodynamic models are needed due to non-ideal operating conditions in which the fluid thermodynamics cannot be described by the simple ideal-gas law (Pv=RT). The coupling interface implements new C++ classes, which allow the automatic exchange of information between SU2 and CoolProp, and it is made directly available as an additional module integrated into the open-source SU2 suite. To assess the performance of the NICFD simulation framework, we present three test cases: a nozzle flow exhibiting non-ideal thermodynamics effects, a nozzle flow with non-monotone Mach number variation, a representative non-ideal gasdynamics effect, and a non-classical rarefaction oblique shock over a wedge. Results are verified against available experiment data and solutions obtained with different implementations of non-ideal thermodynamics in SU2. Performance of the new framework is assessed on user-friendliness, scalability, solution accuracy, and computational efficiency.

Compressibility effects in microchannel flows between two-parallel plates at low reynolds and mach numbers: Numerical analysis

Under certain circumstances, flow in microchannels can exhibit compressibility effects even at Reynolds numbers (Re) around (below 2,300) and low Mach numbers (below 0.3). This is particularly true for gases, especially when the flow undergoes significant pressure changes or acceleration within the microchannel. This study investigates the compressibility effects encountered in two-parallel plates microchannels at these low Reynolds and Mach numbers, due to the high-pressure drop associated with the small scale of the microchannels. This uncommon flow is characterized by an exceptionally small channel diameter-to-length aspect ratio (∼10–3), resulting in a friction coefficient that deviates from the typical value for laminar flow between parallel plates (f = 96/Re). Both steady and transient effects on the flow field are examined under low Re subsonic flow, assuming continuum behavior. The ideal gas equation is used to model gas density, while the isothermal Tait-Murnaghan equation models liquid density. For gases, compressibility effects are observed primarily when the inlet pressure ratio exceeds 0.1. The results show that these effects are less pronounced for liquids, even at elevated inlet pressure ratios. Additionally, a flow delay across the channel exhibits a first-order transient response. For liquid flow, this effect depends on the channel resistance, the total fluid volume within the channel, and the liquid's bulk properties, rather than the inlet pressure ratio.

Modelling of enhanced gas extraction in low permeability coal seam by controllable shock wave fracturing

The controlled shock wave (CSW) fracturing is an effective method for enhancing permeability of coal seam to promote gas extraction. Based on Fick’s law, Darcy’s law, the ideal gas law and the Langmuir equation, a damage-seepage-deformation coupling mathematical model of CSW fracturing in coal seam combined with the maximum tensile stress and the Mohr-Coulomb criterion is established. This model is implemented into COMSOL Multiphysics to simulate the coal seam CSW fracturing and subsequent gas extraction. When the shock wave and isotropic in-situ stress are applied on the borehole wall, the coal damage zone is an annular shape, and the permeability in the damage zone increases sharply. The CSW can effectively increase the efficiency of gas extraction and reduce the gas pressure and gas content in coal seam. With the increase of CSW action times, the damage in coal mass reaches a threshold and tends to be stable after several shocks. The damage area and the gas extraction efficiency are positively correlated with the shock intensity. Under the anisotropic ground stress, the larger diversity of the stress in different directions is, the more obvious damage extension in the fractured coal along the maximum stress direction is. Ground stress can inhibit the extension of cracks in the CSW fractured coal seam. This inhibition effect becomes more obvious with the increase of in-situ stress. Parameters are substantiated of controlled shock wave impact on the coal seam, which ensures increased methane extraction from low-permeability reservoirs, are substantiated.

Influence of the equation of state for moderate to high pressure gaseous systems

For transportation and defense systems, equations of state describe the thermodynamical behavior of gases, as a function of pressure, density, and temperature and are often used to close systems of equation (such as Navier–Stokes for fluid mechanics). For low pressure system (under a few dozen MPa), the ideal gas equation can be used, whereas for high pressure system (above 1000 MPa), dedicated equations of state are used (Jones-Wilkins-Lee: JWL or Becker-Kistiakowsky-Wilson: BKW). For intermediate pressure systems, such as interior ballistics or pyromechanisms, where the pressure is around a few hundreds MPa and many phenomena interact closely and simultaneously (multiphysics system: combustion, fluid dynamics, thermics, fluid-structure interaction, thermodynamics…), the ideal gas equation is not valid anymore and nor are the JWL or BKW equations. A dedicated equation of state is then necessary for intermediate level of pressures, and its choice is not obvious. This paper presents a comparison of equations of state for this range of pressure (Noble-Abel, Van der Waals, virial), details the calculations of the involved coefficients and their effects on uncertainties, and studies the influence of the equation of state on the predictions of pressure, density, pressure coefficient, and heat transfer, with both analytical and numerical approach. The results highlight the importance of the choice of the equation of state, especially for a multiphysics system, as the equation of state influences not only thermodynamical properties (pressure, density, temperature) but also thermical properties of a system, such as heat transfer.

Analysis of the behavior of a gas-generating system under runaway conditions in a closed vessel

In the event of a runaway reaction, emergency relief systems (ERS) act as the last line of defense against the vessel explosion. To date, ERS design for scenarios involving the runaway of chemical mixtures that generate gaseous reaction products remains very challenging as it requires the prediction of the gas generation rate under runaway conditions at large scale. Current methodologies for the assessment of the gas generation rate are based on pseudo-adiabatic calorimetric experiments at laboratory scale in which the temperature and pressure profiles resulting from the runaway are used to assess the gas generation rate using the ideal gas law. The gas generation rate needs to be further corrected for the thermal inertia (φ-factor), of the calorimetric cell used (φ>1) to predict large scale behavior (φ≈1). The work described in this paper focuses on evaluating the capability of this approach to accurately assess the gas generation rate. It uses a dynamic simulator tool based on rigorous thermodynamics to calculate the temperature, pressure, and the composition of each component in a closed vessel containing a gas generating reactive mixture (decomposition of 20 % w/w di-tert butyl peroxide in toluene) under runaway conditions over a range of initial vessel fill levels. The results were analyzed to develop a better understanding of the phenomena that govern the thermal behavior of the mixture, the overall pressurization of the vessel, rate of generation of the gaseous products and its distribution in the liquid and vapor phase of the vessel as the runaway reaction occurs. The simulated pressure, temperature and phase composition data rigorously calculated by the simulator were used to assess and highlight the limitations of using the temperature and pressure in a closed vessel and the ideal gas law to evaluate the gas generation rate. The simulations were also used to evaluate the validity of φ-factor correction methods currently available in the literature.

Numerical Simulation of Weak Shock Wave Reflection in Water Media

Abstract Shock wave reflection (SWR) is an interesting physical phenomenon that plays an important role in the ocean engineering. The existing research mainly focused on the gas SWR. Compared with the gas SWR, the water SWR has distinctive features. This article uses numerical methods to study the reflection mode and regularity inside a gas-filled and water-filled wedge. Specifically, we use the fifth-order weighted essentially nonoscillatory method in space and the third-order Runge–Kutta (RK) method in time to solve the compressible Euler equations. The ideal gas equation of state and water equation of state are also considered in the simulations. We developed a numerical solver using the Fortran language based on these equations and numerical methods. The reliability and accuracy of the developed program were validated by the existing theoretical solution and experiment data. Results show that the reflections are different in gas and water media. Regular reflection (RR) and Mach reflection are observed in a gas-filled wedge. However, only the RR is observed in a water-filled wedge for the weak water shock. Besides, it is found that the reflected shock (RS) wave in water is straighter than that in gas medium. Under the same pressure condition, the curvature of the RS wave is larger in a gas medium. The difference in SWR mode can be attributed to the difference in compressibility between the gas and water. It is found that there is a significant increase in temperature behind the incidence shock in the gas due to its high compressibility, which causes the change of local wave speed especially near the reflected wave. However, the temperature and wave speed are approximately constant during the SWR process in water. These distinctions can well explain the difference in SWR modes between gas and water.

High-precision temperature control of helium Joule–Thomson cryocooler: Long-term temperature stability

To meet the refrigeration requirements of scientific instruments for mK-level temperature stability over a long-time range in the liquid helium temperature, the temperature characteristics and high-precision control strategies of the helium Joule-Thomson cryocooler (JTC) have been experimentally investigated for the first time. Based on the Ideal Gas Law, the influencing mechanism of pre-cooling temperature, gas reservoir volume, and liquid phase volume fraction on refrigeration temperature were qualitatively analyzed and experimentally verified. An active control studies of pre-cooling temperature, low-pressure and heat load were carried out to verify the feasibility of active temperature control of helium JTC. Finally, a long-term temperature stability of ±1 mK/h was successfully achieved when a multi-stage active control strategy was adopted, which is the optimal long-term temperature stability of helium JTC that have been reported to date.

High-efficiency parametric iterative schemes for solving nonlinear equations with and without memory

Many practical problems, such as the Malthusian population growth model, eigenvalue computations for matrices, and solving the Van der Waals' ideal gas equation, inherently involve nonlinearities. This paper initially introduces a two-parameter iterative scheme with a convergence order of two. Building on this, a three-parameter scheme with a convergence order of four is proposed. Then we extend these schemes into higher-order schemes with memory using Newton's interpolation, achieving an upper bound for the efficiency index of 7.8874813≈1.99057. Finally, we validate the new schemes by solving various numerical and practical examples, demonstrating their superior efficiency in terms of computational cost, CPU time, and accuracy compared to existing methods.

Xenon fluid state model and evaluation of working medium in satellite electric propulsion system

Xenon, the working medium of satellite electric propulsion system, is easy to enter the supercritical state, and does not follow the ideal gas equation of state in filling and in-orbit application. The error of fluid state and parameter evaluation of xenon is large. In view of this difficulty, the working fluid state test system and test method of xenon were established. The saturation vapor pressure, gas phase PVT and supercritical PVT characteristics of xenon were tested. A new saturation vapor pressure equation of xenon was established. The relative deviation between the saturated vapor pressure test results and the NIST equation is less than 0.2 %. The Helmholtz equation established on the basis of xenon experimental data has a high accuracy, and the deviation from the experimental data is less than 0.5 % within 273 K–358 K. In 358 K–373 K, the deviation from the test data is better than 0.05 %, and the second dimension coefficient is used to prove the accuracy and reliability of the model, which provides a state model for satellite xenon filling and in-orbit application.

Vapor-Buoyancy Feedback in an Idealized GCM

Abstract Humid air is lighter than dry air at a given temperature and pressure, as the molecular weight of water vapor is less than that of dry air. This effect is known as vapor buoyancy (VB). Although this effect is a well-understood consequence of the ideal gas law, its influence on climate has been under-studied. This study investigates VB’s influence on atmospheric temperature, radiation, and clouds. In mechanism-denial experiments, we remove VB from the dynamics and parameterizations of an idealized general circulation model (GCM). These experiments show that VB warms the tropical free troposphere by approximately 1 K in an Earth-like climate, and the magnitude of this effect increases with warming. This additional atmospheric warming causes greater outgoing longwave radiation (OLR) to be emitted as the climate warms. This constitutes a negative climate feedback which attains a magnitude of 0.1 to 0.2 W/m2/K in the tropics. The simulations further show that, despite warming the atmosphere, VB does not introduce a countervailing positive water vapor feedback. Finally, we find that VB makes the net cloud feedback in the model more negative than it otherwise would be, reinforcing the clear-sky feedback.

Analysis of the Effect of Sampling Probe Geometry on Measurement Accuracy in Supersonic Gas Flow

The accuracy of sampling of gas components has a significant impact on the measurement of various performance parameters in the combustion chamber of an aero-engine. In order to investigate the effect of the probe geometry of a six-point gas sampling probe on sampling accuracy in supersonic gas flow, a three-dimensional probe gas flow characteristic solution model is established through numerical simulation methods of components of transport and fluid–solid coupling. Probes with three angles of 28°, 30°, and 32° and an optimized conical probe are constructed. The sampling accuracy of the probes with different geometries is compared and evaluated by the deviation of the component volume fraction before and after sampling and the resulting combustion efficiency error. This paper presents a set of calculation methods for solving the relative deviation of volume fraction by an iterative method based on the ideal gas law and the Redlich–Kwong equation (R-K equation). The method is designed to solve the exact component volume fraction problem in the simulation calculation. The study results demonstrate that the 28° and optimized conical probes improve sampling accuracy more effectively than the original 30° structure. The deviation of the volume fractions of the two structures is less than 1.7%, and the combustion efficiency error is less than 0.09%. The developed iterative calculation method can significantly reduce the theoretical calculation error to less than 0.06%. The experimental data of the test bench are in good agreement with the simulation results, thereby demonstrating the reliability and accuracy of the sampling probe following structural optimization.

Development of portable gas sensing system for measuring gas emission concentration and diffusivity using commercial manometric sensors in gas exposed polymers: Application to pure gases, H2, He, N2, O2 and Ar

Low-cost gas sensing system to measure the emission concentration and diffusion coefficient of the gas emitted from specimens, which were exposed by gas under high pressure, was developed using the commercial manometric sensors. The gas emitted from two polymer specimens [low density polyethylene (LDPE) and nitrile butadiene rubber (NBR)] during desorption produced a measurable increase in pressure; this pressure was recorded by a portable data logger in the specimen container chamber. Thus, the molar concentration and diffusivity of the released gas were calculated via the ideal gas equation and diffusion analysis program. As results, gas sensor immediately responded without any chemical interaction and emitted gas weight per specimen weight up to 1400×10−6 with a controllable sensitivity/resolution. The performance test confirmed that our developed sensing technique had good reliability, adjustable measurable range and independence to fluctuations in temperature and pressure. Consequently, the developed simple sensing system was successfully used for the simultaneous real-time detection and transport characterizations for pure gases (H2, He, N2, O2 and Ar).

Study Reviews Reservoir Engineering Aspects of Geologic Hydrogen Storage

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 23943, “Reservoir Engineering Aspects of Geologic Hydrogen Storage,” by Johannes F. Bauer, Mohd M. Amro, SPE, and Taofik Nassan, SPE, Technical University Bergakademie Freiberg, et al. The paper has not been peer reviewed. Copyright 2024 International Petroleum Technology Conference. Reproduced by permission. _ Safe and effective large-scale storage of hydrogen (H2) is one of the greatest challenges of the global energy transition and can be realized only through storage in geological formations. The aim of the study detailed in the complete paper is to address and discuss the reservoir engineering aspects of geological H2 storage (GHS). The study is based on two sources: first, a comprehensive literature review and, second, experimental and numerical work performed by the authors’ institute. H2 Pressure/Volume/Temperature (PVT)/Phase Behavior The definition of the PVT/phase behavior of reservoir fluids is crucial in GHS because thermodynamic properties significantly affect safety and effectiveness. The properties of H2 are widely known and modeled, but its reaction with other gases, such as in-situ gases like natural gas in depleted gas reservoirs (DGR), currently is under investigation. Although the ideal gas law can account for H2 behavior at low pressure, accurate depiction of its thermodynamic properties requires more-sophisticated equations of state (EOS), especially when it is mixed with other gases such as methane. Most commercial reservoir simulators use EOS packages that can model the complex properties of these mixtures, mostly within required reliability. In most instances, calibration is still required if experimental PVT data are available. Reservoir Engineering of GHS. GHS projects must meet three crucial technical benchmarks for underground storage: capacity (storage volume), injectivity/productivity (rate of injection/withdrawal in relation to wellhead pressure), and containment integrity (prevention of leakage). Economic sustainability requires that projects must adhere to these standards, which may vary according to the selected geological formations. Although various subsurface structures can store H2, only specific formations such as salt caverns (SCs), saline aquifers (SAs), and depleted gas/oil reservoirs (DGRs and DORs), fulfill the requirements. While the complete paper discusses all three of these formation types in detail, this synopsis will concentrate on SCs. GHS in SCs. SC storage typically involves up to three wells for one cavern with a volume of up to 500,000 std m3, providing a delivery rate of 8,500–17,000 std m3/day. Working gas accounts for up to 65% of the total gas, while water should be kept to a minimum. SCs usually allow between six and 12 operating cycles per year, each lasting approximately 10 days for withdrawal periods. SCs offer high H2 purity and sealed storage. The storage capacity of caverns in Germany is determined by their volume and pressure limitations while avoiding any negative geomechanical effects. These caverns can range in depth from 500 to 2000 m, with heights of up to 400 m. Approximately 30 to 50% of the total stored volume is used as cushion gas to maintain production pressure. Estimating the capacity of these caverns relies on their geometry and thermodynamics, resulting in relatively lower uncertainties when compared with storages in porous media.

Convexity of shock polars

Abstract We show that the shock polars of compressible full potential flow are strictly convex if the enthalpy per mass is a convex function of volume per mass, in particular when the sound speed is a non-decreasing function of density. Counterexamples are given for some cases that violate the condition on enthalpy. For the full Euler equations with convex equation of state satisfying the ideal gas law, polars are strictly convex if heat capacity is constant, but counterexamples are given in variable cases, showing no useful generalizations are possible.

Identification of Students' Misconceptions to the Kinetic Gas Theory in Physics

This study aims to identify students' misconceptions on the material of Kinetic Gas Theory in physics learning. This study uses a qualitative approach and the type of research used is descriptive research. The subjects of this research were 20 students of class XI. The data was collected by means of a diagnostic test technique equipped with CRI (Certainty of Response Index) and free-guided interviews. The results of data analysis show that the average Lucky Guess level is 13%, concept understanding is 39%, not understanding concept is 20%, and average percentage of misconceptions are 28%. Based on the identification results, the highest misconceptions in students appear in the indicator of the question of calculating the ideal gas equation by 55%. The results of the analysis and interviews that have been carried out, misconceptions occur due to the students themselves because they do not understand the concept as a whole and the lack of interest of students to repeat the lesson.

Assessment of Multi-Physical Fields Reconstruction Approaches in Three-Dimensional Supersonic Flow with Shocks

The paper evaluates the application of several multi-physical fields reconstruction approaches based on the Tomographic Particle Image Velocimetry (PIV) in three-dimensional supersonic flows with shock waves, including the pressure, temperature, and density. The MacCormack method and the Flux Vector Splitting method with outstanding performance in two-dimensional supersonic flow are extended into three-dimensional forms. The conventional Poisson method is also considered because of its widespread application and high accuracy in subsonic and transonic flow. All of these approaches are established by the conservative Navier-Stokes equations and solved by the time-marching iteration process, combined with the perfect gas law and adiabatic flow assumption. The performances are evaluated by numerical velocimetry data. To simulate the typical three-dimensional features, the cases of uniform freestream at Mach 0.78 and 3 past a cone with a 20° half-angle are selected to obtain a sufficient spanwise velocity component. The results confirm the feasibility of the PIV-based reconstruction methods in the conical flow field. The conventional Poisson method performs well only in the subsonic case while the Flux Vector Splitting method has a better performance in supersonic flow, including higher accuracy, stability, and efficiency, with a low-level root-mean-square error of 0.449% and local maximum relative error of 1%.

Blood viscometer using capillary blood flow under disposable compliance pump

Blood viscosity is considered a promising indicator of cardiovascular disease and helps predict disease risks. However, conventional methods require two highly precise pumps to maintain consistent flow rates in co-flowing streams. In this study, a low-cost and disposable compliance pump was fabricated by inserting three components (a syringe needle, a blood-loaded syringe, and an air compliance unit [ACU]) into a three-way valve. Since the pump induces transient blood flow, accurately obtaining the transient flow rate is necessary. A correction factor was employed to improve the blood velocity obtained by microparticle image velocimetry. Air pressure inside the ACU was estimated using the ideal gas law. A discrete fluid circuit model was constructed to estimate the flow rate and pressure in a microfluidic channel. Four types of fluid physical properties (fluid resistance, fluid viscosity, time constant, and compliance coefficient) were obtained by analysing flow rate and pressure. The proposed method was employed to detect several types of suspended blood (variations in haematocrit, thermal-shocked RBCs, and RBC aggregation-enhanced blood). From the quantitative comparison, the proposed method provides better results than the previous method. Therefore, the proposed method is a promising tool for detecting biophysical variations in suspended blood.