Real Gas Effects Research Articles

Research on electron density measurements for high enthalpy flows

The high enthalpy shock tunnel, which can provide the high temperature gas conditions for hypersonic flight, is an effective ground facility for the research of reentry problems. It also has the ability of studying real gas effect. The hypersonic test flow condition, with the stagnation enthalpy of 16 MJ/kg and stagnation temperature of 7900 K, was achieved in the JF-10 high enthalpy shock tunnel. The electron density of the flow-field for the 10 degree wedge model was measured using the electrostatic probe, which can obtain sufficient spatial resolution without influencing the flow structure. Results showed that the electrostatic probe has high sensitivity and the spatial electron density can be preferable acquired. The constant bias method can get the dimensionless electron density coupling with the flow field parameters, but the new developed sweeping circuit can get the quantitative value on the basis of effectively reducing the induced noise in the circuit.

Real-Gas and Surface-Ablation Effects on Hypersonic Boundary-Layer Instability over a Blunt Cone

There has been little research into surface-ablation effects on hypersonic boundary-layer instability, and the current understanding of real-gas effects on hypersonic boundary-layer instability still contains uncertainties. The objective of the current work was to analyze the hypersonic boundary-layer transition process using linear-stability theory, in which surface ablation, as well as real-gas effects, is present, and the second mode is the dominant instability mode. A thermochemical nonequilibrium linear-stability-theory code with a gas-phase model that includes multiple carbon species, as well as a linearized surface graphite-pseudoablation model, is developed and validated. It is validated with previously published linear-stability analysis and direct-numerical-simulation results. A high-order method for discretizing the linear-stability equations is used, which can easily include high-order boundary conditions. The developed linear-stability code, with mean-flow solutions produced from a high-order shock-fitting direct-numerical-simulation method for hypersonic flows with thermochemical nonequilibrium and surface-chemistry boundary conditions for graphite pseudoablation, is used to study hypersonic boundary-layer instability for a 7 deg half-angle blunt cone at Mach 15.99 and the Reentry-F experiment at 100 kft. Multiple mean-flow simulations are obtained with the same geometry and freestream conditions to help separate real-gas, blowing, and carbon-species effects on hypersonic boundary-layer instability. For the case at Mach 15.99, an factor comparison shows that real-gas effects significantly destabilize the flow when compared to an ideal gas. Blowing is destabilizing for the real-gas simulation, and has a negligible effect for the ideal-gas simulation due to the different locations of instability onset. Notably, carbon species resulting from ablation are shown to slightly stabilize the flow for both cases. It is also found that ablating nose-cone effects may safely be excluded when determining the factor at transition for Reentry-F at 100 kft.

A 3D numerical study of LO2/GH2 supercritical combustion in the ONERA-Mascotte Test-rig configuration

Cryogenic propellants LOx/H2 are used at very high pressure in rocket engine combustion. The description of the combustion process in such application is very complex due essentially to the supercritical regime. Ideal gas law becomes invalid. In order to try to capture the average characteristics of this combustion process, numerical computations are performed using a model based on a one-phase multi-component approach. Such work requires fluid properties and a correct definition of the mixture behavior generally described by cubic equations of state with appropriated thermodynamic relations validated against the NIST data. In this study we consider an alternative way to get the effect of real gas by testing the volume-weighted-mixing-law with association of the component transport properties using directly the NIST library data fitting including the supercritical regime range. The numerical simulations are carried out using 3D RANS approach associated with two tested turbulence models, the standard k-Epsilon model and the realizable k-Epsilon one. The combustion model is also associated with two chemical reaction mechanisms. The first one is a one-step generic chemical reaction and the second one is a two-step chemical reaction. The obtained results like temperature profiles, recirculation zones, visible flame lengths and distributions of OH species are discussed.

実在気体効果を考慮した臨界ノズル流出係数特性に関する研究

実在気体効果を考慮した臨界ノズル流出係数特性に関する研究

Permeability of high-Kn real gas flow in shale and production prediction by pore-scale modeling

Although shale gas has been commercially exploited, the gas transport mechanism in shale is still unclear. Because nanoscale pores are dominant in shale, the Knudsen number of the flow is relatively high so that the conventional Darcy's law fails. What is more, the shale gas in situ is under high pressure and high temperature so that the real gas (or non-ideal gas) effect is significant. Aiming at these two challenges, we did a pore-scale modeling by using lattice Boltzmann method in this work. We developed a pore-field-iteration (PFI) method to bridge up the pore-scale modeling results with the field-scale concerns, such as inflow performance relationship and decline curve analysis. Our results show that the high Knudsen effect leads to a higher gas flow rate, while the real gas effect causes lower gas flow rate. The gas production may be overestimated at early stage due to the real gas effect, while underestimated at late stage because of the high Knudsen number effect. These results may be very helpful for better understanding of gas transport mechanism in shale and for possible process optimization of shale gas developments in future.

Advanced validation of CFD-FDTD combined method using highly applicable solver for reentry blackout prediction

An analysis model of plasma flow and electromagnetic waves around a reentry vehicle for radio frequency blackout prediction during aerodynamic heating was developed in this study. The model was validated based on experimental results from the radio attenuation measurement program. The plasma flow properties, such as electron number density, in the shock layer and wake region were obtained using a newly developed unstructured grid solver that incorporated real gas effect models and could treat thermochemically non-equilibrium flow. To predict the electromagnetic waves in plasma, a frequency-dependent finite-difference time-domain method was used. Moreover, the complicated behaviour of electromagnetic waves in the plasma layer during atmospheric reentry was clarified at several altitudes. The prediction performance of the combined model was evaluated with profiles and peak values of the electron number density in the plasma layer. In addition, to validate the models, the signal losses measured during communication with the reentry vehicle were directly compared with the predicted results. Based on the study, it was suggested that the present analysis model accurately predicts the radio frequency blackout and plasma attenuation of electromagnetic waves in plasma in communication.

A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effect–adsorption-mechanic coupling

Multiple transport mechanisms coexist in nanopores of shale gas reservoirs with complex pore size distribution and different gas-storage processes, including continuum flow, slip flow and transition flow of bulk gas and surface diffusion for adsorbed gas. The force between gas molecules and the volume of the gas molecules themselves cannot be negligible in shale gas reservoirs with high pressure and nanoscale pores, influences gas transport and must be taken into account as a real gas effect. During depressurization development of shale gas reservoirs, the adsorbed gas desorption and a decrease in an adsorption layer influence gas transport. Meanwhile, due to the stress dependence, decreases in intrinsic permeability, porosity and a pore diameter also influence gas transport. In this work, a unified model for gas transport in organic nanopores of shale gas reservoirs is presented, accounting for the effects of coupling the real gas effect, stress dependence and an adsorption layer on gas transport. This unified model is developed by coupling a bulk gas transport model and an adsorbed gas surface diffusion model. The bulk gas transport model is validated with published molecular simulation data, and the adsorbed gas surface diffusion model is validated with published experimental data. The results show that (1) in comparison with the previous models, the bulk gas transport model developed on the basis of a weighted superposition of slip flow and Knudsen diffusion can more reasonably describe bulk gas transport, (2) surface diffusion is an important transport mechanism, and its contribution cannot be negligible and even dominates in nanopores with less than 2nm in diameter, and (3) the effect of stress dependence on fluid flow in shale gas reservoirs is significantly different from that in conventional gas reservoirs, and is related to not only the shale matrix mechanical properties and the effective stress but also the gas transport mechanisms.

Supersonic plasmatron nozzle profiling with the real properties of high temperature working gas

The effects of real gases (excitation of vibrational degrees of freedom, dissociation and ionization) taken into account for supersonic nozzle profiling. The paper presents the method of the supersonic nozzle profiling for non-monotonic dependence of adiabatic index on temperature. The results of nozzle profile calculation for two sets of input parameters, based on independently determined specific heat for molecular nitrogen N2 and products of its thermal decomposition in the temperature range of 260–105 K and atmospheric pressure are presented. The experimental set-up based on proposed method of supersonic nozzle has been developed and manufactured. The gas velocity at different distances from the nozzle outlet has been measured. Results show the existence of the supersonic and transsonic flow regimes after the nozzle.

Design Space of Foil Bearings for Closed-Loop Supercritical CO2 Power Cycles Based on Three-Dimensional Thermohydrodynamic Analyses

The closed-loop Brayton cycle with supercritical CO2 (S-CO2) as an operating fluid is an attractive alternative to conventional power cycles due to very high power density. Foil gas bearings using CO2 are the most promising for small S-CO2 turbomachinery but there are many problems to address: large power loss due to high flow turbulence, lack of design/analysis tool due to nonideal gas behavior, and lack of load capacity when they are used for large systems. This paper presents high-level design/analysis tool involving three-dimensional (3D) thermohydrodynamic (THD) analyses of radial foil bearings considering real gas effect and flow turbulence inside the film. Simulations are performed for radial foil bearing with 34.9 mm in diameter and lubricated with CO2 and N2 under various ambient conditions up to above 40 bar gauge pressure. The simulation results using the turbulence model still underpredict the measured data in open literature. However, the error between the prediction and measurements decreases as either speed or ambient pressure increases. In addition, general behavior of substantial increase in power loss with ambient pressure agrees with the measured data. The simulation results indicate the importance of detailed THD analysis of the foil bearings for prediction of power loss under severe turbulent condition. A conceptual layout of rotor system for 10 MWe S-CO2 loop is also presented along with realistic rotor weight and bearing load. A hybrid foil bearing with diameter of 102 mm is suggested for gas generator rotor, and its power losses and minimum film thicknesses at various operating conditions are presented.

An Investigation of Real Gas Effects in Supercritical CO2 Centrifugal Compressors

This paper presents a comprehensive assessment of real gas effects on the performance and matching of centrifugal compressors operating in supercritical CO2. The analytical framework combines first principles based modeling with targeted numerical simulations to characterize the internal flow behavior of supercritical fluids with implications for radial turbomachinery design and analysis. Trends in gas dynamic behavior, not observed for ideal fluids, are investigated using influence coefficients for compressible channel flow derived for real gas. The variation in the properties of CO2 and the expansion through the vapor-pressure curve due to local flow acceleration are identified as possible mechanisms for performance and operability issues observed near the critical point. The performance of a centrifugal compressor stage is assessed at different thermodynamic conditions relative to the critical point using computational fluid dynamics (CFD) calculations. The results indicate a reduction of 9% in the choke margin of the stage compared to its performance at ideal gas conditions due to variations in real gas properties. Compressor stage matching is also impacted by real gas effects as the excursion in corrected mass flow per unit area from inlet to outlet increases by 5%. Investigation of the flow field near the impeller leading edge at high flow coefficients shows that local flow acceleration causes the thermodynamic conditions to reach the vapor-pressure curve. The significance of two-phase flow effects is determined through a nondimensional parameter that relates the time required for liquid droplet formation to the residence time of the flow under saturation conditions. Applying this criterion to the candidate compressor stage shows that condensation is not a concern at the investigated operating conditions. In the immediate vicinity of the critical point however, this effect is expected to become more prominent. While the focus of this analysis is on supercritical CO2 compressors for carbon capture and sequestration (CCS), the methodology is directly applicable to other nonconventional fluids and applications.

Blast wave from a high-pressure gas tank rupture in a fire: Stand-alone and under-vehicle hydrogen tanks

This study addresses one of knowledge gaps in hydrogen safety science and engineering, i.e. a predictive model for calculation of deterministic separation distances defined by the parameters of a blast wave generated by a high-pressure gas storage tank rupture in a fire. An overview of existing methods to calculate stored in a tank internal (mechanical) energy and a blast wave decay is presented. Predictions by the existing technique and an original model developed in this study, which accounts for the real gas effects and combustion of the flammable gas released into the air (chemical energy), are compared against experimental data on high-pressure hydrogen tank rupture in the bonfire test. The main reason for a poor predictive capability of the existing models is the absence of combustion contribution to the blast wave strength. The developed methodology is able to reproduce experimental data on a blast wave decay after rupture of a stand-alone hydrogen tank and a tank under a vehicle. In this study, the chemical energy is dynamically added to the mechanical energy and is accounted for in the energy-scaled non-dimensional distance. The fraction of the total chemical energy of combustion released to feed the blast wave is 5% and 9%, however it is 1.4 and 30 times larger than the mechanical energy in the stand-alone tank test and the under-vehicle tank test respectively. The model is applied as a safety engineering tool to four typical hydrogen storage applications, including on-board vehicle storage tanks and a stand-alone refuelling station storage tank. Harm criteria to people and damage criteria for buildings from a blast wave are selected by the authors from literature to demonstrate the calculation of deterministic separation distances. Safety strategies should exclude effects of fire on stationary storage vessels, and require thermal protection of on-board storage to prevent dangerous consequences of high-pressure tank rupture in a fire.

Real gas transport through nanopores of varying cross-section type and shape in shale gas reservoirs

A model for real gas transport in nanopores of shale gas reservoirs (SGRs) was proposed on the basis of the weighted superposition of slip flow and Knudsen diffusion, where the ratios of the intermolecular collisions and the molecule–nanopore wall collisions to the total collisions are the weighted factors of slip flow and Knudsen diffusion, respectively. The present model takes account of slip effect and real gas effect, additionally, the effects of cross-section type and its shape of nanopores on gas transport are also considered in this paper. The present model is successfully validated against existing molecular simulation data collected from different sources in literature. The results show: (1) the present model is reasonable to describe all of the gas transport mechanisms known, including continuum flow, slip flow and transition flow in nanopores of SGRs; (2) the cross-section type and shape of nanopores both affect gas transport capacity: at the same cross-sectional area, gas transport capacity of nanopores with a circular cross section is greater than that with a rectangular cross section, and gas transport capacity of nanopores with a rectangular cross section decreases with an increasing aspect ratio; compared to the cross-section type, the effect of the cross-section shape on gas transport capacity is stronger; (3) a real gas effect improves gas transport capacity, which becomes more obvious with an increasing pressure and a decreasing pore size; (4) and compared to nanopores with a circular cross section, the effect of real gas effect on gas transport capacity of nanopores with a rectangular cross section is stronger, and the effect increases with an increasing aspect ratio. The proposed model can provide some theoretical support in numerical simulation of reservoir behavior in SGRs.

Preliminary design criteria of Stirling engines taking into account real gas effects

This article deals with the main geometric parameters, operating variables and experimental results of engines with different size and characteristics, as well as simulation predictions at operating conditions for which the working fluid may evidence real gas effects. The concept of dimensionless quasi-static indicated work, introduced previously, is computed assuming both ideal and real gas models. Both values are compared with the Schmidt's model prediction, to evaluate separately how the mechanism simplification and the equation of state affect. The influence of physical gas properties are also analysed regarding the gas circuit performance and mechanical efficiency. Pending of experimental corroboration, some simulations show the possibility of obtaining interesting operating conditions under real gas effects.Semi-empirical equations and experimental correlations are proposed as preliminary design criteria. The ratio between the dimensionless values of the maximum indicated power (a sort of ‘indicated’ Beale number) and the quasi-static indicated work is analysed. The procedure to estimate the maximum indicated power is completed by analysing the characteristic Mach number (dimensionless rotation frequency). Analogous procedure is applied for the maximum brake power and corresponding engine speed. Use of dimensionless variables facilitates the generalization of analyses by means of dynamic similarity criteria.

An experimental and computational study of the flow pattern in a refrigerant ejector. Validation of turbulence models and real-gas effects

This investigation presents a study based on experimental and numerical flow pattern in a R134-a ejector. Furthermore, the entrainment ratio has also been analysed. The geometry of the ejector has a long tapered mixing chamber designed to improve pressure recovery. The numerical simulation is used to explain the flow features related with the static pressure profiles measurements, as well as a test case for the CFD validation. In this regard, an initial study has been undertaken in order to gain an insight into the CFD uncertainties in three relevant cases related to the ejector flow physics, namely turbulence modelling, real gas thermodynamics and shock-wave turbulent boundary layer interaction.The double-choked and mixed regime have been realized in this study. Both the standard k−ε and the SST k−ω turbulence models show good agreement between the experimental and computed pressure profiles. Regarding the entrainment ratio prediction, it was better for the latter in the double-choked regime. However, for the mixed regime, it was found that the numerical analysis could not yield a reliable entrainment ratio value using any of the turbulence models employed, although the pressure profile was accurately computed. An explanation for this contradiction has been found in this investigation. Furthermore, the numerical analysis has helped to explain the differences found between the measured pressure profiles and the one-dimensional theory prediction.

Numerical simulation of a twin screw expander for performance prediction

With the increasing use of twin screw expanders in waste heat recovery applications, the performance prediction of these machines plays an important role. This paper presents a mathematical model for calculating the performance of a twin screw expander. From the mass and energy conservation laws, differential equations are derived which are then solved together with the appropriate Equation of State in the instantaneous control volumes. Different flow processes that occur inside the screw expander such as filling (accompanied by a substantial pressure loss) and leakage flows through the clearances are accounted for in the model. The mathematical model employs all geometrical parameters such as chamber volume, suction and leakage areas. With R245fa as working fluid, the Aungier Redlich-Kwong Equation of State has been used in order to include real gas effects. To calculate the mass flow rates through the leakage paths formed inside the screw expander, flow coefficients are considered as constant and they are derived from 3D Computational Fluid Dynamic calculations at given working conditions and applied to all other working conditions. The outcome of the mathematical model is the P-V indicator diagram which is compared to CFD results of the same twin screw expander. Since CFD calculations require significant computational time, developed mathematical model can be used for the faster performance prediction.

Large-eddy simulation of a supercritical channel flow using a shock capturing numerical scheme

This paper investigates the simulation of supercritical fluids flowing inside small cooling channels. In the context of liquid rocket engines, a strong heat flux coming from the combustion chamber (locally ϕ≈80MW/m2 for the Ariane 5 main-engine) may lead to very steep density gradients close to the wall. These gradients have to be thermodynamically and numerically captured to really understand the mechanism of heat transfer from the wall to the fluid. A shock-capturing WENO numerical scheme, usually used with the ideal gas law, was extended to real gases and applied to the simulation of an academic channel flow configuration that uses hydrogen as fluid. Results showed very elongated ligaments in the streamwise direction with a deep penetration in the wall-normal direction. A linear analysis was performed to link the fluctuations of compressibility factor (Z′) to temperature fluctuations (T′) in the case of an adiabatic and isothermal wall. The usual Strong Reynolds Analogy (SRA) could not be confirmed with real gas effects. Z fluctuations was found lower than 1%, thus becoming harder to distinguish the physical fluctuations from the numerical error and a more refine simulation should be require to deliver a definitive conclusion.

On Shock Reflection–Diffraction in a van der Waals Gas

The problem of a weak shock, reflected and diffracted by a wedge, is studied for the two‐dimensional compressible Euler system. Some recent developments are overviewed and a perspective is presented within the context of a real gas, modeled by the van der Waals equation of state. The regular reflection configuration and the detachment criterion are studied in the light of real gas effects. Some basic features of the phenomenon and the nature of the self‐similar flow pattern are explored using asymptotic expansions. The analysis presented here predicts several inviscid flow properties of the real gases undergoing shock reflection–diffraction phenomenon.

Numerical Simulation of Sonic Boom from Hypersonic Meteoroids

Meteoroids entering the Earth atmosphere at high hypersonic velocities are sources of sonic booms that are recorded as infrasound signals at the ground level. The boom pressure field is simulated by solving Euler equations for a spherical meteoroid. The numerical challenge is to capture the acoustical regime of weak shock waves in the very far field at several hundreds or thousands times the meteoroid diameter. Computational fluid dynamics simulations are then matched to nonlinear geometrical acoustics for long-range atmospheric propagation down to the ground. The numerical process is validated through comparison with an analytical model, considering for perfect gases the meteoroid as a line source of strong shock in the near field, matched to a weak shock -wave in the far field. Compared with a perfect gas, real gas effects at thermochemical equilibrium induce a reduced amplitude at the source, along with a shorter signal duration at the ground level. Simulations are illustrated for the well-documented Carancas meteorite that impacted on Peru in 2007.

The Evaluation of the Equations of State Used for the Joule-Thomson Effect Analysis in the Dry Gas Seal

The Joule-Thomson (JT) effect will occur when the gas flows through the components of filters, valves, orifices and end faces in the system of the dry gas seal, which may cause the temperature of the seal gas to decrease, and even the emergence of liquid condensation. Generally, the Joule-Thomson effect is reflected by the Joule-Thomson coefficient. As to the hydrogen, nitrogen, carbon dioxide and air, which are often met in the dry gas seal, the corresponding Joule-Thomson (JT) coefficients were calculated by four classical equations of state (EOS) of VDW, RK, SRK and PR, which are compared with the experimental data in the literature. The results show that the JT coefficients calculated by RK equation are most close to the experimental data in the literature, whose relative error is lowest and less than 4%. When the JT effect of real gas in the dry gas seal is analyzed, the RK equation of state is recommend.

A one-dimensional model of a jet-ejector in critical double choking operation with R134a as a refrigerant including real gas effects

The geometrical simplicity of a jet-ejector is in stark contrast to the complexity of the flow phenomena occurring in ejector operation. The available flow models range from empirical models to models based on computational fluid dynamics, differing considerably in complexity and thus explanatory power. The one-dimensional flow models of semi-empirical nature are based on experiments at comparatively low motive pressures and thus on ideal gas equations. In contrast, a one-dimensional, experimentally validated model of a jet-ejector in critical double choking operation which includes real gas effects and relies on a single physically interpretable loss coefficient is introduced in the present paper. Real gas effects impact on the state quantities and the critical mass flow of the expansion in the supersonic nozzle in particular which should be considered in the determination of the entrainment ratio or the absolute motive and suction mass flows of the ejector and in ejector design.