Real Gas Effects Research Articles

Variation in aerodynamic coefficients with altitude

Precise aerodynamics performance prediction plays key role for a flying vehicle to get its mission completed within desired accuracy. Aerodynamic coefficients for same Mach number can be different at different altitude due to difference in Reynolds number. Prediction of these aerodynamics coefficients can be made through experiments, analytical solution or Computational Fluid Dynamics (CFD). Advancements in computational power have generated the concept of using CFD as a virtual Wind Tunnel (WT), hence aerodynamic performance prediction in present study is based upon CFD (numerical test rig). Simulations at different altitudes for a range of Mach numbers with zero angle of attack are performed to predict axial force coefficient behavior with altitude (Reynolds number). Similar simulations for a fixed Mach number ‘3’ and a range of angle of attacks are also carried out to envisage the variation in normal force and pitching moment coefficients with altitude (Reynolds number). Results clearly depict that the axial force coefficient is a function of altitude (Reynolds number) and increase as altitude increases, especially for subsonic region. Variation in axial force coefficient with altitude (Reynolds number) slightly increases for larger values of angle of attacks. Normal force and pitching moment coefficients do not depend on altitude (Reynolds number) at smaller values of angle of attacks but show slight decrease as altitude increases. Present study suggests that variation of normal force and pitching moment coefficients with altitude can be neglected but the variation of axial force coefficient with altitude should be considered for vehicle fly in dense atmosphere. It is recommended to continue this study to more complex configurations for various Mach numbers with side slip and real gas effects.

Propagation characteristics of terahertz waves in temporally and spatially inhomogeneous plasma sheath

The plasma sheath is produced by high-temperature heating during the reentry of a hypersonic vehicle to the Earth atmosphere. Temperature around the vehicle rises rapidly because of severe friction with air. The vehicle temperature behind friction is high enough to excite various real gas effects including chemical reactions of air, which contains ablation particles of vehicle, free electrons, and ions. The plasma sheath greatly affects the transmission of electromagnetic waves and has very strong interference on the communication signals, which results in interrupt between the target and the ground station, namely, blackout. The electron density of plasma sheath surrounding the aircraft is inhomogeneous and varies with time. Temperature and pressure will also change at different altitudes. Therefore, it is meaningful to investigate the propagation characteristics of electromagnetic waves in temporally and spatially inhomogeneous plasma sheath. The temporally and spatially inhomogeneous plasma sheath model is introduced and the electron density data of the National Aeronautics and Space Administration (NASA) reentry vehicle is employed. The relationships among temperature, pressure, and collision frequency are obtained with the empirical formula of collision frequency. Then, the reflection coefficient and transmission coefficient of time-varying single layer plasma are calculated with the shift operator finite-difference time-domain (SO-FDTD) method. These results are compared to verify the correctness of the proposed method. Finally, the LTJEC-FDTD method is used to calculate the reflection coefficient, transmission coefficient and absorptivity at different relaxation time, temperature, and pressure in the terahertz (THz) band. The results show that the higher temperature and pressure will enable the electromagnetic wave to penetrate the plasma sheath at high relaxation time of electron density. If the incident wave frequency is lower than the cut-off frequency of plasma, the reflection of electromagnetic wave will be more obvious. However, when the incident wave frequency is in the THz band, the effects of temperature and pressure on the propagation of electromagnetic wave are obviously weakened. The absorption of electromagnetic wave by plasma will be more obvious when the relaxation time, temperature, and pressure decrease. If the relaxation time of electron density is shorter than or equal to the period of THz wave, more energy of electromagnetic wave will be absorbed by the plasma sheath. Contrarily, if the relaxation time of electron density is much longer than the period of THz wave, the absorption of electromagnetic energy will decrease. This study gives some insight into the temporally and spatially inhomogeneous plasma sheath, and provides a theoretical basis for solving the blackout problem.

Simulation of real gas effects in supersonic methane jets using a tabulated equation of state with a discontinuous Galerkin spectral element method

Abstract Modern direct gas injectors for natural-gas-powered internal combustion engines operate at ever-increasing pressures to maximize efficiency. At the operating point of current devices, real gas effects already become relevant, for example in the determination of mass flow rates. These effects have to be considered in the design process of such components. Motivated by this fact, we investigate the real gas effects of high-pressure supersonic methane jets. A discontinuous Galerkin spectral element method for computational fluid dynamics is used in combination with a tabulated equation of state for methane. We first evaluate self-similar profiles for subsonic jets to validate our simulation approach. Then we discuss our simulations of a supersonic jet, where we observe well-resolved shocks and transient structures. Additionally, real and ideal gas modeling are compared and we discuss the significant differences in general flow structure as well as density, pressure and mass flow that occur and make an ideal-gas description inappropriate for our simulation. The influence of pressure level and temperature on the behavior of the jet is discussed. We analyze the influence of the thermodynamic and viscous properties of the gas for the shock location and mass flow. The use of a tabulated equation of state makes jet simulations with occurring phase changes possible.

Rayleigh-Brillouin scattering in SF6 in the kinetic regime

Rayleigh-Brillouin spectral profiles are measured with a laser-based scatterometry setup for a 90° scattering angle at a high signal-to-noise ratio (r.m.s. noise below 0.15% w.r.t. peak intensity) in sulfur-hexafluoride gas for pressures in the range 0.2–5bar and for a wavelength of λ=403.0nm. The high quality data are compared to a number of light scattering models in order to address the effects of rotational and vibrational relaxation. While the vibrational relaxation rate is so slow that vibration degrees of freedom remain frozen, rotations relax on time scales comparable to those of the density fluctuations. Therefore, the heat capacity, the thermal conductivity and the bulk viscosity are all frequency-dependent transport coefficients. This is relevant for the Tenti model that depends on the values chosen for these transport coefficients. This is not the case for the other two models considered: a kinetic model based on rough-sphere interactions, and a model based on fluctuating hydrodynamics. The deviations with the experiment are similar between the three different models, except for the hydrodynamic model at pressures p≲2bar. As all models are in line with the ideal gas law, we hypothesize the presence of real gas effects in the measured spectra.

A simple extension of Roe's scheme for real gases

The purpose of this paper is to develop a highly accurate numerical algorithm to model real gas flows in local thermodynamic equilibrium (LTE). The Euler equations are solved using a finite volume method based on Roe's flux difference splitting scheme including real gas effects. A novel algorithm is proposed to calculate the Jacobian matrix which satisfies the flux difference splitting exactly in the average state for a general equation of state. This algorithm increases the robustness and accuracy of the method, especially around the contact discontinuities and shock waves where the gas properties jump appreciably. The results are compared with an exact solution of the Riemann problem for the shock tube which considers the real gas effects. In addition, the method is applied to a blunt cone to illustrate the capability of the proposed extension in solving two dimensional flows.

A fractal model for real gas transport in porous shale

A model for real gas flow in shale gas matrices is proposed and consists of two main steps: (a) developing a microscopic (single pore) model for a real gas flow by generalizing our previously reported Extended Navier‐Stokes Equations (ENSE) method and (b) by using fractal theory concepts, up‐scaling the single pore model to the macroscopic scale. A prominent feature of the up‐scaled model is a predictor for the apparent permeability (AP). Both models are successfully validated with experimental data. The impact of the deviation of the gas behavior from ideality (real gas effect) on the gas transport mechanisms is investigated. The effect of the structural parameters (porosity Ф, the maximum pore diameter Dmax, and the minimum pore diameter Dmin) of the shale matrix on the apparent permeability is studied and a sensitivity analysis is performed to evaluate the significance of the parameters for gas transport. We find that (1) the real gas transport models for a single pore and porous shale matrix are both reliable and reasonable; (2) the real gas effect affects the thermodynamic parameters of the free gas and the adsorption and transport capacity of the adsorbed gas; (3) the real gas effect decreases the effective permeability for convective flow and surface diffusion; i.e., the derivation degree of the effective permeability for bulk diffusion and Knudsen diffusion increases with increasing pressure but presents a bathtub shape when the pore diameter is smaller than 10 nm; and (4) the apparent permeability increases with Ф, Dmax, and Dmin. It is more sensitive to Dmax, followed by the porosity. Dmin has a minor impact. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1430–1440, 2017

Thermodynamic Simulation on the Performance of Twin Screw Expander Applied in Geothermal Power Generation

A three-dimensional (3D) geometry model of twin screw expander has been developed in this paper to measure and analyze geometric parameters such as groove volume, suction port area, and leakage area, which can be described as functions of rotation angle of male rotor. Taking the suction loss, leakage loss, and real gas effect into consideration, a thermodynamic model is developed using continuity and energy conservation equation. The developed model is verified by comparing predicted results of power output and internal efficiency with experimental data. Based on the model, the relationship between mass flow rate through inlet port and leakage path with rotation angle of male rotor as well as effects of the inlet parameter and operating parameter on the performance of the expander are analyzed.

Catalytic Effect of CeO2‐Stabilized ZrO2 Ceramics with Strong Shock‐Heated Mono‐ and Di‐Atomic Gases

The reducibility of synthesized ceria‐stabilized zirconia (CSZ) with strong shock‐heated test gases is investigated. Free piston‐driven shock tube operating at hypersonic speed at Mach number of 6–8 has been used to heat the ultrahigh pure test gases like Ar to ~12800 K, N2 to ~7960 K, and O2 to ~5500 K at a medium reflected shock pressure (5.0–7.4 MPa) for a short duration of 1–2 ms test time. Under this extreme thermodynamic condition, test gases undergo real gas effects. The structural and spectroscopic investigations of CSZ (Ce2Zr2O8) after interaction with shock‐heated argon gas show pyrochlore structure of Ce2Zr2O7−δ which is observed to be black in color. In presence of shock‐heated N2 gas, CSZ remains in fluorite structure by changing its color to pale green as nitrogen atoms fill oxygen vacancies. After O2 interaction with the shock wave, CSZ remains pale yellow but the X‐ray diffraction pattern shows the presence of monoclinic ZrO2 due to phase separation. During reduction process, Ce4+ has been reduced to Ce3+ which is an unusual effect. In this study, the catalytic and surface recombination effects of CSZ due to shock‐induced compression in millisecond timescale are presented.

Numerical investigation of the flow of supercritical carbon dioxide injected into the bottom hole during drilling with special emphasis on the real gas effects

Supercritical carbon dioxide jets formed in the bottom hole can assist the drilling process and a better understanding of the flow in the bottom hole is crucial for improving shale gas exploitation. A CFD model that includes the real gas effects of carbon dioxide was used to investigate the impinging flow field in the bottom hole. The simulations show that the model accurately predicts the carbon dioxide bottom hole flow in the liquid and supercritical regions which cover the typical operating ranges used in petroleum engineering. The results indicate that increasing the inlet temperature will increase the axial velocity but will slightly reduce both the mass flow rate and the impact of the carbon dioxide jet. An increase in the inlet pressure not only increase the mass flow rate and the dynamic pressure of the supercritical carbon dioxide jet but also increase both the pressure gradient and the temperature gradient along the impinging wall which are beneficial to the jet-assisted drilling process. Additionally, the Joule-Thompson throttling effects are much more prominent at higher inlet temperature and larger pressure drops. The findings reported in the paper will provide guidance for engineering applications.

Thermal analysis of near-isothermal compressed gas energy storage system

Due to the increasing generation capacity of intermittent renewable electricity sources and an electrical grid ill-equipped to handle the mismatch between electricity generation and use, the need for advanced energy storage technologies will continue to grow. Currently, pumped-storage hydroelectricity and compressed air energy storage are used for grid-scale energy storage, and batteries are used at smaller scales. However, prospects for expansion of these technologies suffer from geographic limitations (pumped-storage hydroelectricity and compressed air energy storage), low roundtrip efficiency (compressed air energy storage), and high cost (batteries). Furthermore, pumped-storage hydroelectricity and compressed air energy storage are challenging to scale-down, while batteries are challenging to scale-up. In 2015, a novel compressed gas energy storage prototype system was developed at Oak Ridge National Laboratory. In this paper, a near-isothermal modification to the system is proposed. In common with compressed air energy storage, the novel storage technology described in this paper is based on air compression/expansion. However, several novel features lead to near-isothermal processes, higher efficiency, greater system scalability, and the ability to site a system anywhere. The enabling features are utilization of hydraulic machines for expansion/compression, above-ground pressure vessels as the storage medium, spray cooling/heating, and waste-heat utilization. The base configuration of the novel storage system was introduced in a previous paper. This paper describes the results obtained from a transient, analytical, physics-based thermodynamic system model used for the system design and evaluation of three design configurations (including base configuration). The system model captures real gas effects and all loss mechanisms. The model demonstrates an energy storage roundtrip efficiency of 82% and energy density of 3.59MJ/m3. Experimental evaluation of system performance and detailed cost-analysis will be presented in future publications.

Shock-tunnel investigations on the evolution and morphology of shock-induced large separation bubbles

ABSTRACTShock-tunnel experiments are carried out to study the strong interaction between an impinging shock wave and boundary layer on a flat plate, accompanied bylargeseparation bubble with a length comparable to the distance of the location of shock impingement from the leading edge of the plate. For nominal freestream Mach numbers ranging from 6 to 8.5, moderate to high total enthalpies of 1.3MJ/kg to 6MJ/kg are simulated in the Indian Institute of Science's hypersonic shock tunnels HST-2 (a conventional Hypersonic Shock Tunnel) and Free Piston Shock Tunnel (FPST) with freestream Reynolds numbers ranging from 4 × 106/m to 0.3 × 106/m. The strong impinging shock is generated by a wedge (or shock generator) at an angle of 30.96° to the freestream. From the time-resolved Schlieren flow visualisations using a high-speed camera and surface pressure measurements on the flat plate using fast response sensors, a statistically steady flow field with a large separation bubble was established within the short test time of the shock tunnels (around 600µs in HST-2 and 300µs in FPST). The role of various parameters on the interaction – Mach number, location of shock impingement and flow total enthalpy – are investigated from the measured separation length and surface pressure distribution. For the nominal Mach number of 8.5, with shock impingement at 100mm from the leading edge, the separation length increased from 60mm to 70mm as the total enthalpy is increased from 1.6MJ/kg to 2.4MJ/kg; whereas it dropped drastically to 30-40mm at 6MJ/kg. This is due to the prominence of real gas effects at higher enthalpies.

The influence of real gas effects on the performance of supercritical CO2 dry gas seals

The current work investigates dry gas seals operation with supercritical CO2 (sCO2) at two operating conditions using CFD. One close and one far from the critical point. At the operating condition far from the critical point a maximum change of 1.7% in pressure, 0.4% in temperature and 1.1% in density are observed. Contrary, closer to the critical point a maximum change of 6.5% in pressure, 6.7% in temperature and 39.5% in density are observed. These changes also influence opening force and leakage rate. Far from the critical point the maximum changes are 0.7% and 3.1%, whereas close to the critical point maximum changes of 3.4% and 10.3% are observed. The centrifugal effect plays an important role when operating with dense gases.

Apparent gas permeability in an organic-rich shale reservoir

Accurate models of gas transport in shale gas reservoirs must consider complex gas transport mechanisms and phase behavior in nanopores, as well as different pore types. The gas transport mechanisms in shale gas reservoirs include viscous flow, Knudsen diffusion, surface diffusion, adsorption and desorption. In this study, a unified model of nanopore gas transport in shale gas reservoirs is presented. Gas storage patterns are different in organic pores and inorganic pores. Therefore, we develop two fully coupled apparent permeability models to describe gas transport in organic pores and inorganic pores separately. The apparent permeability model of organic pores considers the gas transport mechanisms of viscous flow, Knudsen diffusion, surface diffusion, adsorption and desorption. The apparent permeability model of inorganic pores considers the gas transport mechanisms of viscous flow and Knudsen diffusion. In both models, stress dependence, real gas effects and phase behavior are taken into account. Then, the influences of pore pressure, effective stress, real gas effects, pore radius, phase behaviors and transport properties on apparent gas permeabilities in organic pores and inorganic pores are analyzed based on the proposed models.

Delusive Influence of Nondimensional Numbers in Canonical Hypersonic Nonequilibrium Flows

AbstractA finite volume–based unstructured inviscid flow solver has been developed for the study of nonequilibrium effects in high enthalpy flows. Four different inviscid flux computation schemes are tested for literature reported test cases like unsteady wave motion in a shock tube and high enthalpy flow over cylinder/sphere. During the present assessment, encouraging agreement has been noticed in capturing all the essential flow features in the reacting media. Here, the Rusanov scheme is noticed to be computationally cheaper among all the schemes with noticeable diffusion around strong gradients. Shock tube test case revealed the existence of various shock Mach numbers for a given driving pressure ratio in the presence of reactions. Similarly, freestream Mach number is found to have limitations in representing the shock standoff distance in case of high enthalpy flow over cylinder and sphere. In line with this, real gas effects are prominently observed for the case of the cylinder in comparison with the...

Fore-body and base heat flux measurements on a typical crew module in short duration impulse facilities

Experiments are carried out to measure forebody and base heat flux on a typical Crew Module at Mach numbers 5.8 and 8 over the enthalpy range of 1.5–3.73MJ/kg. Towards this, two scaled down models namely 1:55 and 1:40 are tested in 0.15m pressure and in 1m combustion driven shock tunnels. Forebody and stagnation point heat flux are measured through E-type co-axial thermocouples whereas, platinum thin film gauges are used to measure base heat flux. Forebody heat flux for the range of α (0–20deg) shows that the stagnation point heat flux move towards the bottom surface and the top surface experiences low heat flux as the angle of attack increases. At the base, the level of heat flux is found to be low and the maximum value is 3% of the stagnation point heat flux. The minimum heat flux is observed to be at the center of the base and increases radially outwards. The measured stagnation point heat flux is found to be ∼50% higher than the Fay–Riddell correlation for dissociated air, using Newtonian velocity gradient. On the other hand, if the Fay–Riddell correlation is modified by incorporating experimentally generated velocity gradient, the difference reduces to 14.25%. Finally, once the real gas effect is added to the Fay–Riddell correlation along with experimentally generated velocity gradient, the difference further reduces to 9.4%. Thus, the correct choice of transport properties and velocity gradient plays a crucial role to accurately predict the stagnation point heat flux.

An analytical model for real gas flow in shale nanopores with non‐circular cross‐section

An analytical model for gas transport in shale media is proposed on the basis of the linear superposition of convective flow and Knudsen diffusion, which is free of tangential momentum accommodation coefficient. The present model takes into the effect of pore shape and real gas, and is successfully validated against experimental data and Lattice–Boltzmann simulation results. Gas flow in noncircular nanopores can be accounted by a dimensionless geometry correction factor. In continuum‐flow regime, pore shape has a relatively minor impact on gas transport capacity; the effect of pore shape on gas transport capacity enhances significantly with increasing rarefaction. Additionally, gas transport capacity is strongly dependent of average pore size and streamline tortuosity. We also show that the present model without using weighted factor can describe the variable contribution of convective flow and Knudsen diffusion to the total flow. As pressure and pore radius decrease, the number of molecule‐wall collisions gradually predominates over the number of intermolecule collisions, and thus Knudsen diffusion contributes more to the total flow. The parameters in the present model can be determined from independent laboratory experiments. We have the confidence that the present model can provide some theoretical support in numerical simulation of shale gas production. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2893–2901, 2016

Effect of pressure on hydrogen/oxygen coupled flame–wall interaction

The design and optimization of liquid-fuel rocket engines is a major scientific and technological challenge. One particularly critical issue is the heating of solid parts that are subjected to extremely high heat fluxes when exposed to the flame. This in turn changes the injector lip temperature, leading to possibly different flame behaviors and a fully coupled system. As the chamber pressure is usually much larger than the critical pressure of the mixture, supercritical flow behaviors add even more complexity to the thermal problem. When simulating such phenomena, these thermodynamic conditions raise both modeling and numerical specific issues. In this paper, both subcritical and supercritical hydrogen/oxygen one-dimensional, laminar flames interacting with solid walls are studied by use of conjugate heat transfer simulations, allowing to evaluate the wall heat flux and temperature, their impact on the flame as well as their sensitivity to high pressure and real gas thermodynamics up to 100 bar where real gas effects are important. At low pressure, results are found in good agreement with previous studies in terms of wall heat flux and quenching distance, and the wall stays close to isothermal. On the contrary, due to important changes of the fluid transport properties and the flame characteristics, the wall experiences significant heating at high pressure condition and the flame behavior is modified.

Expansion of a wedge of non-ideal gas into vacuum

We study the problem of expansion of a wedge of non-ideal gas into vacuum in a two-dimensional bounded domain. The non-ideal gas is characterized by a van der Waals type equation of state. The problem is modeled by standard Euler equations of compressible flow, which are simplified by a transformation to similarity variables and then to hodograph transformation to arrive at a second order quasilinear partial differential equation in phase space; this, using Riemann variants, can be expressed as a non-homogeneous linearly degenerate system provided that the flow is supersonic. For the solution of the governing system, we study the interaction of two-dimensional planar rarefaction waves, which is a two-dimensional Riemann problem with piecewise constant data in the self-similar plane. The real gas effects, which significantly influence the flow regions and boundaries and which do not show-up in the ideal gas model, are elucidated; this aspect of the problem has not been considered until now.

Aerodynamic performance analysis of a winged re-entry vehicle from hypersonic down to subsonic speed

The paper deals with the aerodynamic performance analysis at a phase-A design level of a reusable and unmanned flying laboratory designed to perform a high lift return from low Earth orbit. The flying test bed aims to provide experimental data in the framework of re-entry technologies. The vehicle concept is a wing body with rather sharp leading edges and slender aerodynamic configuration. Several design approaches, ranging from engineering-based to computational fluid dynamics analyses, have been addressed in this work. In particular, vehicle aerodynamic performances for a wide range of freestream flow conditions, from subsonic to hypersonic regime, including reacting and non-reacting flow and different angles of attack have been provided and compared. Highlights on aerodynamic control surfaces' effects, vehicle longitudinal and lateral–directional static stability are provided as well. Computational fluid dynamics results confirm that high temperature real gas effects seem to be fundamental for the assessment of the concept aerodynamics, especially concerning pitching moments evaluation.

Numerical study of a one-stage VM cryocooler operating below 10K

A numerical method for simulating cryocooler below 10K, especially for VM cryocooler, is carried out based on the finite volume method. Compressibility, real gas effect, temperature dependence of properties and porous heat transfer are considered simultaneously in this model. The under-relaxation method is used to increase the stability of simulation. By comparison of the simulation results and experimental results, the simulated and tested no-load temperatures and cooling powers agree with each other very well. By using a computer program written, the lowest temperature, the pressure in three cavities, the real gas effect and the losses of cold displacer are comprehensively analyzed. Furthermore, the phase angle, the cold regenerator and the hot end temperature are optimized.