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Thermophysical Properties of Fluids. I. Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen
Abstract
The thermophysical properties of argon, ethylene, parahydrogen, nitrogen, nitrogen trifluoride and oxygen are presented. Properties are given in tables and a standard set of equations is described. The tables list pressure, density, temperature, internal energy, enthalpy, entropy, heat capacity at constant volume, heat capacity at constant pressure, and sound velocity. Also included are viscosity, thermal conductivity, and dielectric constant, for some of the fluids. The equation and related properties of this report represent a compilation from the cooperative efforts of two research groups: the NBS Thermophysical Properties Division and the Center for Applied Thermodynamics Studies of the University of Idaho.
... The previous reference equation of state for hydrogen, used as a reference in former versions of NIST's standard properties package REFPROP, was the one proposed in 1982 by Younglove [27]. This equation was based on experimental data for the thermodynamic properties of pure parahydrogen and was modified to predict the thermodynamic properties of normal hydrogen by replacing the ideal-gas heat capacity equation and fixed-point properties of the parahydrogen model with values for normal hydrogen. ...
... All the EoS existing to date for hydrogen have been studied in terms of their uncertainty in the work of Sakoda et al. [31]. Briefly, with respect to density, the EoS of Leachman et al. [24] for parahydrogen agrees within 0.2% with that of Younglove [27] at temperatures below 100 K and pressures up to 45 MPa. Above that, the differences between the two EoS grow quickly by up to 0.9%, with a better agreement with the experimental data of the EoS of Leachman et al. ...
... Above that, the differences between the two EoS grow quickly by up to 0.9%, with a better agreement with the experimental data of the EoS of Leachman et al. For temperatures above 473 K, the EoS of Younglove [27], Klimeck [28], and Leachman et al. [24] are also in agreement within 0.2% at pressures up to 120 MPa. However, the limited data available do not allow us to know more. ...
The accurate knowledge of thermophysical and thermodynamic properties of pure hydrogen and hydrogen mixtures plays an important role in the design and operation of many processes involved in hydrogen production, transport, storage, and use. These data are needed for the development of theoretical models necessary for the introduction of hydrogen as a promising energy carrier in the near future. A literature survey on both the available experimental data and the theoretical models associated with the thermodynamic properties of hydrogen mixtures, within the operational ranges of industrial interest for composition, temperature, and pressure, is presented in this work. Considering the available experimental data and the requirements for the design and operation of hydrogen systems, the most relevant gaps in temperature, pressure and composition are identified.
... The previous reference equation of state for hydrogen, used as a reference in previous versions of NIST's standard properties package REFPROP, was the one proposed in 1982 by Younglove [14]. This equation was based on experimental data for the thermodynamic properties of pure parahydrogen and was modified to predict the thermodynamic properties of normal hydrogen by replacing the ideal-gas heat capacity equation and fixed-point properties of the parahydrogen model with values for normal hydrogen. ...
... More than half of the VLE data (2260 of 4245, Figures 1, 2, 3, and 6), and most of the density data (4080 of 5083, Figures 9,10,11,and 14) and the speed of sound data, as well as other caloric properties (774 of 798, Figures 15,16,17,and 18), correspond to the binary systems of hydrogen with methane, nitrogen, carbon dioxide and carbon monoxide. The binary system hydrogen with methane is the only one with a binary specific departure function included in the GERG-2008 model [17], and new equations of state for the four binary systems of hydrogen with methane, nitrogen, carbon dioxide and carbon monoxide were proposed recently by Beckmuller et al. [21]. ...
... The range of validity for the new hydrogen EoS[16], developed for this purpose, is (14 to 700) K pressure up to 300 MPa. The new equation of state is explicit in the Helmholtz free energy, with 14 terms At the time of the development of the GERG 2004 there was already a pressure explicit equation for hydrogen[14], based on the modified BWR equation of state with 32 terms. The complex structure of this equation and its poor performance in the liquid phase and the supercritical region were the reasons for the necessity to develop a new equation of state for hydrogen. ...
The accurate knowledge of the thermophysical and thermodynamic properties of pure hydrogen and hydrogen mixtures plays an important role in the design and operation of many processes involved in hydrogen production, transport, storage and use. These data are needed for the development of theoretical models necessary for the introduction of hydrogen as a promising energy carrier in the near future. A literature survey on both the available experimental data and the theoretical models associated with the thermodynamic properties of hydrogen mixtures, within the operational ranges of industrial interest for composition, temperature and pressure, is presented in this work. Considering the available experimental data and the requirements for the design and operation of hydrogen systems, the more relevant gaps in temperature, pressure and composition are identified.
... As a tool, this calculation method is conceptually valid over wide temperature ranges, and it offers some advantages over currently available methods [45][46][47]. The calculated results of speed of sound for He, NF 3 , BCl 3 , CO 2 , Cl 2 , and Xe are compared with experimental and theoretical data [32,34,38,41], and results for Ar, O 2 , F 2 , H 2 , and air are compared with theoretical data [33,35,37,40,44,48]. The calculated results of speed of sound of GaCH 3 3 are compared with experimental data [41]. ...
... The calculated results of speed of sound of GaCH 3 3 are compared with experimental data [41]. The calculated results of the heat capacities at constant pressure for Ar, O 2 , He, Xe, NF 3 , BCl 3 , CO 2 , Cl 2 , F 2 , H 2 and air are compared with theoretical data [33,35,37,40,44,48]. The calculated results of heat capacities at constant volume for Ar, O 2 , He, Xe, F 2 , H 2 , and air are compared with theoretical data [33,[35][36][37]40,48,49]. ...
... The calculated results of the heat capacities at constant pressure for Ar, O 2 , He, Xe, NF 3 , BCl 3 , CO 2 , Cl 2 , F 2 , H 2 and air are compared with theoretical data [33,35,37,40,44,48]. The calculated results of heat capacities at constant volume for Ar, O 2 , He, Xe, F 2 , H 2 , and air are compared with theoretical data [33,[35][36][37]40,48,49]. The results of calculation of speed of sound and specific heat capacities for He are in good agreement in the wide range of parameters. ...
In this paper, by use of the second virial coefficient (12-6) in the Lennard–Jones potential, an analytical procedure to evaluate the specific heat capacity and speed of sound of gases is presented. The obtained formulas yield accurate and fast evaluation of both quantities. By using obtained analytical expressions, the heat capacity and speed of sound of the gases Ar, He, Xe, H2, O2, F2, Cl2, NF3, BCl3, Ga(CH3)3, CO2, and air were calculated in the temperature range from 100 to 2000 K and over the pressure range from 0.1 atm to approximately 15 atm. The computational results are in good agreement with the data available in the literature.
... The virial EOS provides a simple and reliable way to calculate the thermodynamic properties of real gases [14,15]. It expresses the Table 1 The LIR reduced parameters (A and B), the reduced second and third virial coefficients (B 2 and B 3 ), the coefficient of determination (R 2 ) and the pressure range of the data (Δp) at the given temperature for argon [18][19][20][21] where B j (T) is the jth virial coefficient. The truncated virial EOS can be written as Also, Eq. (1) may be written as ...
... Equations (16) and (17) suggest that the intercept and slope parameters (A and B) of the LIR and the virial coefficients (B 2 and B 3 ) likely have similar thermal behaviors. For this [18][19][20] reason, in the next section the thermal behavior of (B 2 and B 3 ) will be examined. ...
... where ε, λ and σ are the parameters of SW. Based on SW, B 2 is obtained as follows [16] where β = 1/k B T. Expansion of e (βε) − 1 is By replacing Eq. (20) in Eq. (19), we get the following result for Ne [22] By neglecting upper-order terms (first-order approximation), we can write the first-order thermal dependency of B 2 as By considering Eq. (16), A is written as follows Equation (23) Since b is proportional to σ 3 , proportionality results (A 1 ∝ εσ 6 and A 2 ∝ σ 6 ) are consistent with Eqs. (5) and ...
Linear isotherm regularity works very well for fluids at high densities, and it has been shown that it is compatible with the EOSs based on statistical–mechanical theory. On the other hand, at low densities, the first few terms of virial EOS have the most contribution to express the deviations from ideal behavior. For finding similarities between dense and dilute states, experimental p–v–T data of 14 fluids (He, Ne, Ar, Kr, H2, O2, N2, CO, NH3, CH3OH, CH4, C2H4, C2H6 and C3H8) are examined. Comparing the thermal dependencies of the attraction and repulsion terms (A and B) of the LIR with the second and third virial coefficients (B2 and B3) in liquid and supercritical regions (0.7 < Tr < 3.0) shows a remarkable similarity. Square-well potential is applied to examination and comparison of theoretical results with experimental results. It is shown that in liquid and supercritical regions, (1) the short-range potential governs among particles in dense fluids, and the long-range interactions become important in the less dense fluid, (2) similar to Boyle temperature, TB, in dilute state, there is a temperature as T′B (in dense fluids) that the attractive forces and the repulsive forces acting on the dense-fluid particles balance out; thus, probably there is a maximum σ (molecular diameter) at nearly 2Tc (T′B), and (3) in the liquid and supercritical regions (0.7 < Tr < 3.0), in the first-order approximation, there are no significant interactions higher than triple interactions in dense-fluid particles.
... В настоящей работе на основе экспериментальных данных РVTизмерений широкого класса жидкостей [25][26][27][28][29][30][31][32][33], используя величины критических показателей [10], определены величины амплитуд Г 0 , D 0 уравнений (1) и (2). Их значения представлены в таблице 1. ...
... Поэтому таких экспериментальных исследований полевых зависимостей ∆ρ(∆Р) вблизи критической температуры вещества значительно меньше, чем температурных исследований уравнения кривой сосуществования жидкость-газ ∆ρ(t). Анализ существующих экспериментальных данных РVTизмерений [25][26][27][28][29][30][31][32][33] в близкой окрестности КТ показывает, что при использовании в этих исследованиях различных значений критических показателей δ = 4.2÷5 для различных жидкостей реальная ошибка определения амплитуды D 0 (Z k ) составляет величину порядка (5 ÷ 10)%. Такой же реальной ошибкой характеризуется и величина амплитуды Г 0 (Z k ) сжимаемости вещества (1) при использовании различных значений критического показателя (γ = 1.1 ÷ 1.3). ...
Based on the literature data of PVT measurements, the amplitudes of the equations of the critical isotherm D0(Zk), the critical isochore Г0(Zk), the phase boundaries В0(Zk) are expressed in terms of the critical factor of compressibility of the substance Zk=PkVk/RTk in the entire fluctuation region near the critical point. By doing so, a phenomenological method has been used for calculating the values of the critical exponents of the fluctuation theory of phase transitions based on the introduction of small parameters into the equations of the fluctuation theory. It has been shown that, within the limits of the PVT measurement errors, these dependences D0(Zk) and В0(Zk) on the compressibility factor are linear, and Г0 practically does not depend on the compressibility factor Zk. The relationship of these amplitudes with the amplitudes a and k of the linear model of the system of parametric scale equations of state of substance near the critical point has been established. It has been shown that the dependences k(Zk) and а(Zk) are also linear in the entire fluctuation region near the critical point. The obtained dependences k(Zk) and а(Zk) agree with the known relationship between the amplitudes of the critical isotherm D0(Zk), critical isochore Г0(Zk), phase boundaries В0(Zk) Aerospace Institute of the National Academy of Sciences of Ukrainewithin the framework of the system of parametric scaling equations. The relations а(Zk), k(Zk) make it possible, on the basis of a linear model of the system of parametric scale equations of state of substance, to determine such important characteristics of the critical fluid as the temperature and field dependences of the correlation length Rc(T,m) and the fluctuation part of the thermodynamic potential Ф(T,m) in the entire fluctuation region near the critical point. Then, based on the form of the fluctuation part of the thermodynamic potential Ф(T,m)~Rc(T,m)-3, the results obtained allow one to calculate the field and temperature dependences of the thermodynamic quantities for a wide class of molecular liquids in the close vicinity of the critical point (DP<10-3, Dr<10-2, t<10-4), where precision experiments are significantly complicated, and its can also be used when choosing the conditions for the most effective practical application of the unique properties of the critical fluid in the newest technologies.
... The BKH experiments are conducted at the European Research and Technology test facility P8 for cryogenic rocket engines at DLR Lampoldshausen. Additional information on BKH can be found in [13]. ...
... In this new model, cryogenic oxygen is treated as an Eulerian continuum. Real gas properties are computed from the high ¦delity modi¦ed BenedictWebbRubin (MBWR) equation of state (EoS) of Younglove [13] and stored in a library during a preprocessing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc., are all computed consistently from the real-gas EoS. ...
An experimental combustor, designated BKH, is operated at DLR Lampoldshausen to investigate high-frequency combustion instability phenomena. The combustor operates with liquid oxygen (LOx) and gaseous or liquid hydrogen propellants at supercritical conditions analogous to real rocket engines. An externally imposed acoustic disturbance interacts with a series of 5 coaxial injection elements in the center of the chamber. A combination of experimental analysis and numerical modeling is used to provide further insight and understanding of the BKH experiments. Optical data from the BKH experiments are analyzed to extract the response of the §ame at the excitation frequency. A new method for reconstructing the acoustic ¦eld inside the chamber from dynamic pressure sensor data is used to describe the evolution of the acoustic mode and the local disturbance in the §ame zone. An Unsteady Reynolds-Averaged Navier�Stokes (URANS) model of a single BKH injection element subjected to representative transverse acoustic velocity excitation has been computed using a specialized release of the DLR TAU code. The single-element model reproduces the retraction of the dense LOx core during transverse velocity excitation as observed experimentally. The model also provides further insight into the §attening and §apping of the §ame. The §apping is identi¦ed as the oxygen core being transported by the transverse acoustic velocity.
... The BKH experiments are conducted at the European Research and Technology test facility P8 for cryogenic rocket engines at DLR Lampoldshausen. Additional information on BKH can be found in [13]. ...
... In this new model, cryogenic oxygen is treated as an Eulerian continuum. Real gas properties are computed from the high ¦delity modi¦ed BenedictWebbRubin (MBWR) equation of state (EoS) of Younglove [13] and stored in a library during a preprocessing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc., are all computed consistently from the real-gas EoS. ...
An experimental combustor, designated BKH, is operated at DLR Lampoldshausen to investigate high-frequency combustion instability phenomena. The combustor operates with liquid oxygen (LOx) and gaseous or liquid hydrogen propellants at supercritical conditions analogous to real rocket engines. An externally imposed acoustic disturbance interacts with a series of 5 coaxial injection elements in the center of the chamber. A combination of experimental analysis and numerical modeling is used to provide further insight and understanding of the BKH experiments. Optical data from the BKH experiments are analyzed to extract the response of the flame at the excitation frequency. A new method for reconstructing the acoustic field inside the chamber from dynamic pressure sensor data is used to describe the evolution of the acoustic mode and the local disturbance in the flame zone. An Unsteady Reynolds-Averaged Navier–Stokes (URANS) model of a single BKH injection element subjected to representative transverse acoustic velocity excitation has been computed using a specialized release of the DLR TAU code. The single-element model reproduces the retraction of the dense LOx core during transverse velocity excitation as observed experimentally. The model also provides further insight into the flattening and flapping of the flame. The flapping is identified as the oxygen core being transported by the transverse acoustic velocity.
... The properties of pure gases (e.g. [34][35][36][37][38][39]) as shown [25][26][27][28][29][30][31][32][33] in figure 3 are used in some gas quality measuring devices that are presented in subsequent chapters. Unique responses at different temperatures and pressures of the device should be obtained for any specific composition within the operating range. ...
... Several thermophysical properties of some components of natural gas are plotted as function of temperature to illustrate applicability of measurement principles (e.g.[34][35][36][37][38][39]), Ar and He are shown for thermal conductivity as typical carrier gases in GC analysis, higher temperatures are typical for thermal conductivity detectors. ...
Diversification of gas supply via the liberalization of the gas trade, the discovery of new fossil gas sources, and the increasing use of renewable gases, are favoring pronounced and more frequent fluctuations in gas quality. The knowledge of gas quality is crucial for custody transfer, and safe, efficient and low-emission operation of gas-driven processes. The onsite measurement of gas quality by the operators of gas production facilities, gas grids, gas storage and gas utilization facilities is an emerging requirement. This paper describes several different approaches for determining gas quality by direct, indirect and inferential methods based on the physicochemical properties of gas. Special emphasis is devoted to a discussion on the miniaturization of gas quality sensors and the incorporation of hydrogen detection and measurement into these sensors, due to potential hydrogen admixture to natural gas. In addition, an overview and analysis of the regulatory and normative requirements for gas quality measurements are presented. Furthermore, an overview of gas quality measurement devices and sensors, recent developments as well as challenges and benefits associated with gas quality measurement instrumentation, are provided.
... For the present investigations the MBWR EOS is chosen because of its accuracy compared to the experimental database of 1 NIST, see [4] and [3]. Detailed information about the equation of state can be found in [6]. ...
... The mass §ow rate and the inlet conditions of the hydrogen §ow and the hot-gas-side wall temperature are selected accord- [5,14]: ' m = 92.8 g/s, T in = 75 K, p in = 130 bar, and T w,hg = 800 K. Hydrogen thermodynamic behavior is described by means of the modi¦ed BenedictWebb Rubin equation of state [15] for both solvers. The 3D CFD solution has been veri¦ed by a grid convergence analysis that has been presented in [16]. ...
A trade-off analysis is performed on a cooling channel system representative of liquid rocket engine cooling systems. This analysis requires multiple cooling channel flow calculations which are performed by means of a proper numerical approach, referred to as quasi-two-dimensional (2D) model. This model, which is suited to high-aspect-ratio cooling channels (HARCC), permits to have a fast prediction of both the coolant §ow evolution and the temperature distribution along the whole cooling channel structure. Before using the quasi-2D model for the trade-off analysis, its validation by comparison with computational fluid dynamics (CFD) results is presented and discussed. The results show that the pump power required to overcome losses in the cooling circuit can be minimized selecting a channel shaped with a suitably high aspect ratio.
... These real-gas effects are included in the DLR TAU code real gas release to model the transcritical injection and combustion of cryogenic propellants. This real gas implementation has two [63] and stored in a library during a pre-processing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc. are all computed consistently from the real gas EOS. ...
The quantitative comparison of experimental data and results from CFD simulations is still an ongoing challenge in the investigation of high pressure combustion in rocket combustion chambers. This is due to the extreme environment which develops in liquid propellant rocket engines, which represent a challenge for experimental data collection. OH* radiation emitted from the flame has often been designated as an indicator of the combustion zone, because of its relative ease of detection with appropriate cameras. A method was developed to compare OH* radiation originating from cryogenic oxygen-hydrogen flames in an experimental combustor with the CFD simulation results. Pseudo-OH* images were obtained from CFD results of two combustors. The method consists in obtaining the path of a ray of light by a reverse ray tracing algorithm and sampling the thermodynamic properties along the path of the ray, simulating the emission and absorption spectra in the wavelength range of interest, in this case of OH* emission during combustion. The spectral radiance is then determined by solving the differential radiative transfer equation. Finally, the total radiance is calculated integrating the spectral radiance. The results obtained applying this method are then compared with former results of two test cases, a laminar and a turbulent flame, and with the related experimental data. An improvement of the comparison with the experimental data was achieved in terms of the prediction of self-absorption, which was underestimated in previous works by a factor of 15, and in terms of radiance near the injection plane, where difference is estimated to be about 40% when including refraction. The method allows for more direct comparison between 3D CFD results and 2D experimental images collected by the optical setup and probes.
... The compressibility factor Z is dependent on temperature T and pressure p. Younglove [72] and Lemmon et al. [48] developed relationships between density and pressure of hydrogen which are valid over a range of temperature and pressure. Later these relationships were revised by Leachman et al. [46] and Lemmon et al. [47] to expand the ranges of validity for temperature and pressure. ...
To reduce loss of hydrogen in storage vessels with high energy-to-weight-ratio, new materials, especially polymers, have to be developed as barrier materials. Very established methods for characterization of barrier materials with permeation measurements are the time-lag and flow rate method along with the differential pressure method, which resembles the nature of hydrogen vessel systems very well. Long measurement durations are necessary to gain suitable measurement data for these evaluation methods, and often restrictive conditions have to be fullfilled. For these reasons, common models for hydrogen permeation through single-layer and multi-layer membranes, as well as models for hydrogen gas properties were collected and reviewed. Using current computer power together with these models can reduce measurement time for characterization of the barrier properties of materials, while additional information about the quality of the measurement results is obtained.
... Thermal conductivity, k, is also a function of temperature but not pressure. Tabulated values for nitrogen at 300 and 600 K nearly double from approximately 26 mW/mK to 45 mW/mK, respectively [38][39][40][41]. Theory suggests that this variation scales as T 0.5 , but observations have found the variation to scale faster, around T 0.75 at these considered temperatures [42,43]. ...
Optical diagnostics of gas-phase pressure are relatively unusual. In this work, we demonstrate a novel, rapid, and robust method to use laser-induced grating scattering (LIGS) to derive this property in real time. Previous pressure measurements with LIGS have employed a signal fitting method, but this is relatively time-consuming and requires specialist understanding. In this paper, we directly measure a decay lifetime from a LIGS signal and then employ a calibration surface constructed using a physics-based model to convert this value to pressure. This method was applied to an optically accessible single-cylinder internal combustion engine, yielding an accuracy of better than 10% at all tested conditions above atmospheric pressure. This new approach complements the existing strength of LIGS in precisely and accurately deriving temperature with a simple analysis method, by adding pressure information with a similarly simple method.
... The Modified Benedict-Webb-Rubin (MBWR) and Benedict-Webb-Rubin-Starling (BWRS) are two modifications of BWR (Reid et al., 1987). MBWR originally is proposed by Jacobsen and Stewart for nitrogen (Jacobsen & Stewart, 1973) and employed by Younglove (Younglove, 1982) for hydrogen. Although using the BWR series encounters some difficulties in the computation process, it is preferred in some cases because of its high precision (Thomas, Dutta, Ghosh, & Chowdhury, 2012). ...
Abstract: Liquid hydrogen will likely play a significant role in the future of energy as its
applications are growing fast. Due to the low efficiency of the existing liquefaction plants,
many studies are dedicated to the liquefaction processes. The accuracy of the simulations
crucially depends on the fluid package and prediction of thermodynamic properties. Four
common equations of state implemented in Aspen HYSYS used for hydrogen liquefaction,
including PR, MBWR, SRK, and BWRS, are investigated to find their accuracy for estimating
volumetric and calorimetric properties, that are essential for precise simulation of hydrogen
liquefaction processes. Results show that MBWR is the best choice for hydrogen liquefaction
processes, which are simulated by Aspen HYSYS. MBWR predicts the thermodynamic
properties of hydrogen and parahydrogen very well, in the whole range of temperature and
pressure typically met in the liquefaction processes. The MBWR performs well in predicting
enthalpy of ortho-para conversion too. Although PR performs better than SRK and BWRS,
none of them yields reliable data in low temperatures, so they could not be applied for
liquefaction processes. However, they may lead to desirable results for processes that
experience higher temperatures range. An innovative, simplified hydrogen liquefaction cycle is
developed to be able to capture the mere effect of EOS on essential performance parameters of
the liquefaction cycles such as SEC and COP. Applying PR and MBWR to the developed cycle
shows that PR compared to MBWR leads to 10% and 4% deviation in SEC and COP,
respectively.
... Isothermal P-ρ curves were generated at temperatures of 77 K (pressure range of 0-200 atm) and 298.15 K (pressure range of 0-2000 atm) and the results are compared with experimental data [143,144] in Figures 3.5 and 3.6. For the simulations at 77 K, Feynman-Hibbs quantum corrections [6] were applied to the energetically dominant electronic repulsion/dispersion part of the potential to order 4 via: ...
The emerging field of nanomaterials has raised a number of fascinating scientific questions that remain unanswered. Molecular theory and computer simulation are key tools to unlocking future discoveries in materials science, and various computational techniques and results toward this goal are elucidated here. High-performance computing methods (utilizing the latest supercomputers and codes) have been developed to explore and predict the chemistry and physical properties of systems as diverse as Metal-Organic Frameworks, discrete nanocubes, photoswitch molecules, porphyrins and several interesting enzymes. In addition, highlights of fundamental statistical physics, such as the Feynman-Hibbs effective partition function and generalized ensemble theory, are expounded and upon from the perspective of both research and pedagogy.
... (iii) V m (P int , T) is the molar volume of hydrogen in the space between the graphene sheets at pressure P int and T. P int depends on the externally applied equation (5): charging pressure (P ext) , and the equilibrium constant for the process (K eq ) as shown through equation (4) and where q ads and q free are the activity of the gas in the adsorbed and the free state [18]. V m is calculated from the EoS for hydrogen established by National Institute of Standards and Technology (NIST) [22], K eq is the equilibrium constant for the storage phenomena. ...
The present work provides a comprehensive study of hydrogen uptake and storage in multilayered graphene systems, namely graphene nanoplatelets (GNP), supported by quantitative experimental investigations. For this purpose, a customized Sievert’s Apparatus is fabricated to handle the cryogenic temperatures and pressures up to 5 bar. GNP was characterized using high-resolution transmission electron microscopy, X-ray diffraction and Raman spectroscopy to determine the number of layers and presence of defects. Adsorption studies of molecular hydrogen on GNP have been conducted at three different temperatures of 298K, 243K and 99K, all cases explored upto 2 bar pressure in the adsorption chamber. The maximum gravimetric density of 2.47wt. %. have been observed at temperature of 99K and 2 bar pressure. The nature of hydrogen storage between the GNP layers at different experimental conditions, its bearing on the quantity and stability is analyzed by developing a modified version of the expanded graphite model. Further, the improvement in the performance of the multi-layered graphene system is discussed and correlated experimentally to possible aiding of hydrogen storage through formation of physisorption channel.
... This is straightforward for A-60 where due to nonexistent latent heat and surface tension, droplets are not observed [24]. Oxygen real gas properties are computed from the high ¦delity modi¦ed Benedict WebbRubin equation of state (EoS) of Younglove [25] and stored in a library during a preprocessing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc., are all computed consistently from the real gas EoS. ...
This paper derives from the cooperation between DLR and Airbus within the work package "CFD Modeling of Combustion Chamber Pro-cesses" conducted in the frame of the Propulsion 2020 project. In a joint strategy, DLR Göttingen and Airbus DS Ottobrunn have identified a number of test cases with gradually growing complexity where adequate test data are available for proper successive validation of the computational fluid dynamics (CFD) tools to be used in an industrial environment. This work highlights the simulation results for the Mascotte A-10 and A-60 test cases as presented at the 2nd International Workshop on Rocket Combustion Modeling in Lampoldshausen 2001 by ONERA and SNECMA. These two test cases are characterized by different chamber pressures (10 and 60 bar) and, consequently, by oxygen injection conditions which are subcritical in one case and transcritical in the other case. The test cases are treated with three different CFD codes: the DLR TAU Code (only A-60 case), the Airbus DS in-house tool Rocflam3, and the commercial CFD tool ANSYS CFX incorporating several modeling extensions by Airbus DS. To the knowledge of the authors, this paper is the first one which covers both the A-10 and the A-60 test cases.
... Mole fractions are then converted in Henry constant using equation (2). The fugacity coefficient of hydrogen in vapor phase is calculated with the Soave-Redlich-Kwong equation of state (Soave, 1972) after having checked that this model is able to accurately reproduce pure hydrogen reference compressibility factors (Younglove, 1982). Solubility data ("TPxy" data) are also converted in Henry constants with equation (2) by taking for a given isotherm the smallest available experimental partial pressure to stay as close as possible of the infinite dilution domain. ...
Hydrogen is targeted to have a significant influence on the energy mix in the upcoming years. Its underground injection is an efficient solution for large-scale and long-term storage. Furthermore, natural hydrogen emissions have been proven in several locations of the world, and the potential underground accumulations constitute exciting carbon-free energy sources. In this context, comprehensive models are necessary to better constrain hydrogen behavior in geological formations. In particular, solubility in brines is a key-parameter, as it directly impacts hydrogen reactivity and migration in porous media. In this work, Monte Carlo simulations have been carried out to generate new simulated data of hydrogen solubility in aqueous NaCl solutions in temperature and salinity ranges of interest for geological applications, and for which no experimental data are currently available. For these simulations, molecular models have been selected for hydrogen, water and Na ⁺ and Cl ⁻ to reproduce phase properties of pure components and brine densities. To model solvent-solutes and solutes-solutes interactions, it was shown that the Lorentz-Berthelot mixing rules with a constant interaction binary parameter are the most appropriate to reproduce the experimental hydrogen Henry constants in salted water. With this force field, simulation results match measured solubilities with an average deviation of 6%. Additionally, simulation reproduced the expected behaviors of the H 2 O + H 2 + NaCl system, such as the salting-out effect, a minimum hydrogen solubility close to 57 °C, and a decrease of the Henry constant with increasing temperature. The force field was then used in extrapolation to determine hydrogen Henry constants for temperatures up to 300 °C and salinities up to 2 mol/kg H2O . Using the experimental measures and these new simulated data generated by molecular simulation, a binary interaction parameter of the Soreide and Whiston equation of state has been fitted. The obtained model allows fast and reliable phase equilibrium calculations, and it was applied to illustrative cases relevant for hydrogen geological storage or H 2 natural emissions.
... In general, there is no analytic expression for (8) and (9). This is particularly true for a high-fidelity EOS, e.g., [15][16][17], that can describe liquid and vapor phases within a single formulation. The simplest form of such an EOS is a cubic polynomial as in the van der Waals equation of state. ...
The use of complex multi-parameter equations of state in computational fluid dynamics is limited due to their expensive evaluation. Tabulation methods help to overcome this limitation. We propose in this work a tabulation approach for real equations of state that is also suitable for multi-component flows and multi-phase flows with phase transition based on the homogeneous equilibrium method. The tabulation method is based on piecewise polynomials and allows adaptive refinement in state space, a local variation of the degree of the polynomials and even cut-cells to represent saturation lines. A detailed analysis of the benefits of the chosen tabulation approach is provided showing results of benchmark problems for nitrogen under sub- and trans-critical conditions. The tables are used in numerical simulations based on the finite volume approach. To provide reference solutions, an exact Riemann solver is constructed for the tabulated real EOS. Several numerical flux calculations based on approximate Riemann solutions and flux vector splitting approaches are modified for the tabulated equation of state. Besides the comparison for benchmark problems, two applications are depicted, a shock–bubble interaction and an injection of a trans-critical jet, which demonstrate the applicability of this approach to more complex flow simulations.
... The relevant coolant operative conditions are taken from [14]: overall coolant mass flow rate is _ m ¼ 14:3 kg/s (i.e., 36:7 g/s for a single channel), inlet temperature is T c;in ¼ 53:89 K and inlet pressure is p c;in ¼ 445:5 bar. Coolant thermodynamic and transport properties used in the fluid solver are taken from [31], while the solid-material thermal conductivity, k w ¼ 316 W/m K, is taken from [32] and refers to that of NARloy-Z copper alloy at 533 K. The cooling channels sand grain roughness is an unknown parameter, that, following what already done in [12], is assumed equal to e ¼ 0:23lm to match the pressure drop reported in [14]. ...
The choice of the shape and number of cooling channels is critical when seeking for the best design of a liquid rocket engine thrust chamber. Trade-off has to be considered among the different constraints that must be satisfied in terms of thrust chamber mass and resistance to mechanical and thermal loads, while keeping acceptable the power spent to make the coolant flow in the channels. In this study attention is focused on the phenomenon of thermal stratification that occurs in liquid rocket engine cooling channels due to their asymmetric heating. Its role is studied with a suitable engineering approach that allows to emphasize when rectangular cross section channels become inefficient due to stratification. A parametric analysis is carried out on a reference configuration showing the margins required to satisfy specific wall temperature constraints.
... This is straightforward for A-60 where due to nonexistent latent heat and surface tension, droplets are not observed [24]. Oxygen real gas properties are computed from the high ¦delity modi¦ed Benedict WebbRubin equation of state (EoS) of Younglove [25] and stored in a library during a preprocessing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc., are all computed consistently from the real gas EoS. ...
This paper derives from the cooperation between DLR and Airbus DS within the work package “CFD Modeling of Combustion Chamber Processes” conducted in the frame of the Propulsion 2020 project. In a joint strategy, DLR Göttingen and Airbus DS Ottobrunn have identified a number of test cases with gradually growing complexity where adequate test data are available for proper successive validation of the computational fluid dynamics (CFD) tools to be used in an industrial environment. This work highlights the simulation results for the Mascotte A-10 and A-60 test cases as presented at the 2nd International Workshop on Rocket Combustion Modeling in Lampoldshausen 2001 by ONERA and SNECMA [1]. These two test cases are characterized by different chamber pressures (10 and 60 bar) and, consequently, by oxygen injection conditions which are subcritical in one case and transcritical in the other case. The test cases are treated with three different CFD codes: the DLR TAU Code (only A-60 case), the Airbus DS in-house tool Rocflam3, and the commercial CFD tool ANSYS CFX incorporating several modeling extensions by Airbus DS. To the knowledge of the authors, this paper is the first one which covers both the A-10 and the A-60 test cases.
... It should be noted that the thermal and velocity boundary layers in the chamber consisted of ~20 cells. Material property of 17-4 PH SS, argon and nitrogen gases used in the simulation were obtained from Masoomi et al. [17] and Younglove [18]. More details regarding the simulation conditions can be found in Ref [5]. ...
This study investigates the effect of using either argon or nitrogen as the shielding gas on
the final mechanical properties of additively manufactured (AM) 17-4 PH stainless steel (SS). The difference in thermo-physical properties of shielding gases during the additive manufacturing process can affect part thermal response. Simulations are performed to elucidate the differences in temperature, temperature gradient and cooling rate for argon and nitrogen building environments for the laser-powder bed fusion (L-PBF) process. Mechanical properties of fabricated parts are studied through micro-hardness and tensile tests. Tensile tests are carried out under 0.001 s-1 strain rate at room temperature. Using both numerical and experimental results, the effects of shielding gas type on AM 17-4 PH SS will be presented and discussed.
... (iii) V m (P int , T) is the molar volume of hydrogen in the space between the graphene sheets at pressure P int and T. P int depends on the externally applied equation (5): charging pressure (P ext) , and the equilibrium constant for the process (K eq ) as shown through equation (4) and where q ads and q free are the activity of the gas in the adsorbed and the free state [18]. V m is calculated from the EoS for hydrogen established by National Institute of Standards and Technology (NIST) [22], K eq is the equilibrium constant for the storage phenomena. ...
Recently graphene based systems have generated enormous interest for the energy storage applications. This study focuses on the hydrogen adsorption in graphene nanoplatelets via molecular dynamics simulations and experimental techniques. The graphene nanoplatelets characterized using Raman spectroscopy were found to be 1-4 layered platelets. Experimental characterization of hydrogen adsorption at various temperatures and pressures were conducted using Seiverts apparatus. The sorption-desorption kinetics and the effect of temperature-pressure interrelations in determining the hydrogen adsorption in graphene were established experimentally. However, for the simulation studies a single layered graphene was considered, to capture the detailed mechanism of sorption-desorption phenomena. The interatomic interactions were modeled using AIREBO potential to better understand the chemisorption mode of adsorption and the results were compared with the case considering only Leonard-Jones potential. This work is an attempt to establish a combined experimental–simulation methodology to arrive at an optimal set of experimental conditions to obtain the desired adsorption capacity.
... Here the ideal gas equation of state is solved for H 2 ,H,O,OH and H 2 O, and a real gas equation of state is solved for O 2 . The real gas properties of oxygen are computed form the high fidelity modified Benedict-Webb-Rubin(MBWR) equation of state of Younglove described in [22]. ...
... For cryogenic transcritical injection, real fluid effects are confined to the oxygen stream [26,38,39]. MFM takes advantage of this by tabulating a high accuracy equation of state (here Younglove's modified Benedict-Webb-Rubin equation [40]) for oxygen. All flow outside of the dense core can be treated as ideal. ...
... The utilized temperature-dependent properties of argon [35], as well as solid and liquid properties of Ti-6Al-4 V [36], are presented in Figs. 4 and 5, respectively. For all simulations it was assumed that there was zero oxygen content in the chamber. ...
... A key ingredient in this equation is the molar volume V molar (P,T), which is given by the equation of state, EOS, of hydrogen. Starting from the experimental information available [39,40], we have built an accurate parameterization of the EOS of hydrogen [28,29]. From Eq. (4) one obtains P int for given values of P ext and T, and finally the molar volume of the adsorbed hydrogen phase, V mol (P int , T), is obtained from the EOS. ...
An efficient storage of hydrogen is a crucial requirement for its use as a fuel in the cars of the future. Experimental and theoretical work has revealed that porous carbons are promising materials for storing molecular hydrogen, adsorbed on the surfaces of the pores. The microstructure of porous carbons is not well known, and we have investigated a class of porous carbons, the carbide-derived carbons, by computer simulation, showing that these materials exhibit a structure of connected pores of nanometric size, with graphitic-like walls. We then apply a thermodynamical model of hydrogen storage in planar and curved pores. The model accounts for the quantum effects of the motion of the molecules in the confining potential of the pores. The optimal pore sizes yielding the highest storage capacities depend mainly on the shape of the pore, and slightly on temperature and pressure. At 300 K and 10 MPa, the optimal widths of the pores lie in the range 6-10 Å. The theoretical predictions are consistent with experiments for activated carbons. The calculated storage capacities of those materials at room temperature fall below the targets. This is a consequence of an insufficiently strong attractive interaction between the hydrogen molecules and the walls of carbon pores. Recent work indicates the beneficial effect of metallic doping of the porous carbons in enhancing the binding energy of H<sub>2</sub> to the pore walls, and then the hydrogen storage.
... Higher temperatures identify gases in II, that cannot be compressed to a liquid state (Atkins & de Paula 2010). When instead the pressure is raised, the fluid state in quadrant IV has been referred to as compressed liquid (Oefelein et al. 2012), compressible liquid (Bolmatov et al. 2014), transcritical fluid (Oschwald et al. 2006;Candel et al. 2006), liquid (Younglove 1982), or a supercritical fluid (Bellan 2000). When both pressure and temperature exceed the fluid critical values, fluids are commonly considered supercritical. ...
... For Nitrogen, the National Institute of Standards and Technology (NIST) provides such reference data. These data, however, are not real measurement data but are based on a very complex EoS [14] with two additional models [15,16]. The uncertainty regarding the density (and hence also the volume) of the data provided by NIST for nitrogen is very low and reaches for high pressures (≥ 1GPa) values of up to 0.6%. ...
Many technical applications require accurate predictions of the thermodynamical state of the process fluid, which can be estimated from mathematical equations of state (EoS). Though the existing EoS are sufficiently accurate in the wide operating ranges for various technical fluids, they differ in terms of the complexity, and thus in computation costs. Therefore, for modeling and simulation of large technical systems, preferably simple and sufficiently accurate EoS are desired. The proposed approach presents a methodological support for the selection of appropriate EoS not only considering its accuracy but also its complexity. Furthermode, a cryogenic application involving nitrogen is used to demonstrate the proposed approach.
... In this new model, cryogenic oxygen is treated as an Eulerian continuum. Real gas properties are computed from the high fidelity modified Benedict-Webb-Rubin (MBWR) equation of state (EOS) of Younglove 15 and stored in a library during a pre-processing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc. are all computed consistently from the real gas EOS. ...
... Here, an ideal gas equation is solved for each of the species H 2 , OH, H 2 O, O, H, and a real-gas equation of state is used for O 2 . The real gas properties of oxygen are computed from the high fidelity modified Benedict-Webb-Rubin (MBWR) equation of state (EOS) of Younglove [34] and stored in a library during a pre-processing step. Thermodynamic state variables, such as pressure, enthalpy, heat capacities, speed of sound, etc. are all computed consistently from the real gas EOS. ...
... on their respective crystallization lines.66,67 The conditions cover the temperature ranges: 15 ≤ T /K ≤ 33 for para-H 2 and 24.55 ≤ T /K ≤ 40 for neon. ...
The problem of the equilibrium triplet structures in fluids with quantum behavior is discussed. Theoretical questions of interest to the real space structures are addressed by studying the three types of structures that can be determined via path integrals (instantaneous, centroid, and total thermalized-continuous linear response). The cases of liquid para-H2 and liquid neon on their crystallization lines are examined with path-integral Monte Carlo simulations, the focus being on the instantaneous and the centroid triplet functions (equilateral and isosceles configurations). To analyze the results further, two standard closures, Kirkwood superposition and Jackson-Feenberg convolution, are utilized. In addition, some pilot calculations with path integrals and closures of the instantaneous triplet structure factor of liquid para-H2 are also carried out for the equilateral components. Triplet structural regularities connected to the pair radial structures are identified, a remarkable usefulness of the closures employed is observed (e.g., triplet spatial functions for medium-long distances, triplet structure factors for medium k wave numbers), and physical insight into the role of pair correlations near quantum crystallization is gained.
... For example, work by Perez et al. [59] shows that PR is more suitable than SRK for density of C 5 or higher carbon chain hydrocarbons, SO 2 , benzene and toluene. However, Michelsen & Mollerup [60] observed that the fugacity coefficients calculated by SRK were in much better agreement with those obtained by a modified BWR EoS [61,62] (assumed as experimental) than those predicted by PR. This drawback comes from the improvement in the PR Z c , which decreases to a more realistic value (compared to that of SRK) at the expense of the fugacity coefficient. ...
Since its publication in 1976, the Peng & Robinson equation of state (PR EoS) has become one of the most useful and successfully applied models for thermodynamic and volumetric calculations in both industrial and academic fields. For this reason, we have reviewed this cubic EoS, in order to explore the development around it and some general applications where it has been applied, including its most known modifications. So, a complete time-line of the PR EoS is presented, as a compilation of more than 200 modifications for pure compound applications and about 100 modifications for mixtures.
... To overcome this difficulty, we adjusted the H 2 eH 2 Lennard-Jones potential parameters to predict, with a reasonable accuracy; a) the bulk experimental data of H 2 at different state points b) and the adsorption isotherms in the temperature range 40e100 K. In Fig. 3, we compare experimental bulk fugacity of H 2 [37] as a function of density to simulated data computed by canonical Monte-Carlo. The last data were obtained both from the potential given by Kumar et al. [21] and by using our new set of parameters. ...
Among the different methods to separate hydrogen isotopes one is based on the physisorption at low temperature (below 100 K) where quantum effects induce a particular behavior. In the present work, we study the adsorption of single H2 and D2 on the zeolite NaX by combining experiments (manometry) from 30 to 150 K and molecular dynamics simulations at 40 and 77 K. Simulations also include the adsorption analysis for T2. Adsorption on NaX membranes is simulated and quantum corrections are introduced by using the well-known Feynman–Hibbs approach into the interaction potentials. Experimental adsorption isotherms are reproduced by using the Toth equation and it is shown that the adsorption capacity increases with the molecular weight of the isotopes. Isosteric enthalpies evidence a heterogeneous adsorption process with two type of hydrogen isotopes differently linked to the zeolitic structure. The calculated pair distribution functions at high loadings exhibit a liquid-like structuration in the supercages of NaX, which may explain the different adsorption capacities for H2, D2 and T2 and the heterogeneity of the adsorption process.
... Effective hydrogen density in pores of various sizes at 77 K as a function of equilibrium pressure and pore width. The source for solid and liquid bulk H 2 density is [37]. ...
We report results of vibrational neutron spectroscopy investigation aimed to identify the state of hydrogen adsorbed in ultramicroporous carbon. The mobility of hydrogen confined in carbon pores was probed as a function of temperature and pressure using inelastic neutron scattering, and the molecular translational and rotational motions were studied. At low loading rotation of H2 molecules adsorbed in the smallest carbon pores (∼4–5 Å) is severely hindered, suggesting that the interaction between H2 and the host matrix is anisotropic. At higher loading, H2 molecules behave as a nearly free rotor, implying lower anisotropic interactions with adsorption sites. At 77 K where bulk H2 is a gas, deconvolution of elastic/quasielastic signal provide evidence of pressure-dependent fractions of immobile (solid-like) and partially mobile (liquid-like) hydrogen, which correlate with the excess adsorption isotherm at 77 K. Effective H2 density in pores changes from solid-like to liquid-like with increasing pressure at 77 K. Surprisingly, immobile and partially mobile H2 is present even at temperatures as high as ∼110 K where bulk hydrogen exists only in gas form.
As a clean energy source, hydrogen has attracted much attention due to its high thermal conversion efficiency, recyclability and non-polluting properties. Recently, hydrogen fuel cell vehicles have become a global research hotspot, and the number of hydrogen refueling stations is steadily increasing. But the biggest problem holding them back is that the filling of high-pressure hydrogen causes a rapid increase in the internal temperature of the storage tank. In order to make hydrogen fuel cell vehicles fully popular, the principle of temperature rise is systematically elucidated, the influence of refueling parameters on the tank state is summarized and appropriate mitigation measures and solutions to limit or mitigate the effects of temperature rise are proposed in this review, such as pre-cooling the hydrogen in advance, reducing the initial hydrogen content in the tank and ensuring that the ambient temperature and the initial tank temperature are at a low level. In addition, a number of safe refueling strategies and methods are presented. Through the comprehensive study in this paper, the important relationship between the refueling parameters and the temperature rise in the tank is refined, which is very useful in promoting the development of new refueling strategies and hydrogen fuel cell vehicles.
The NIST REFPROP software program is a powerful tool for calculating thermophysical properties of industrially important fluids, and this manuscript describes the models implemented in, and features of, this software. REFPROP implements the most accurate models available for selected pure fluids and their mixtures that are valid over the entire fluid range including gas, liquid, and supercritical states, with the goal of uncertainties approaching the level of the underlying experimental data. The equations of state for thermodynamic properties are primarily of the Helmholtz energy form; a variety of models are implemented for the transport properties. We document the models for the 147 fluids included in the current version. A graphical user interface generates tables and provides extensive plotting capabilities. Properties can also be accessed through third-party apps or user-written code via the core property subroutines compiled into a shared library. REFPROP disseminates international standards in both the natural gas and refrigeration industries, as well as standards for water/steam. © Not subject to U.S.
Compared to existing technologies, thermodynamic cycles based on supercritical carbon dioxide (sCO2) are leading to higher efficiencies and reduced component sizes. However, it is possible to further improve the performance of sCO2 power cycles by using mixtures of CO2 with suitable additives, as also discussed in the literature for different applications.
This work investigates the potential to optimize the characteristics of sCO2 power cycles by selectively adding different substances in varying amounts to CO2. A new methodology is proposed: By using the reference equation of state for CO2 in combination with a multi-fluid mixture model, a theoretical screening of suitable additives was done. In the literature, studies were mainly limited to mixtures for which adjusted mixture models are available. By contrast, in this work the use of a predictive mixture model, which was recently developed at our institute, also allows to include fluids, for which no adjusted models are available. Applied to two thermodynamic cycles, changes in efficiency compared to the use of pure CO2 have been evaluated. Several promising mixture candidates have been identified. Additionally, individual effects on the cycle characteristics as well as shifts of the critical points have been investigated and are discussed.
A closed-form multi-parameter fluid equation of state (EoS) is proposed and tested with empirical pressure isotherms of water and hydrogen. The EoS is non-algebraic but elementary, applicable in the full temperature range above the melting point, and remains accurate at high pressure. The critical-point conditions (vanishing density-derivatives of pressure) are exactly implemented in the exponential attractive term of the EoS. The singular repulsive term is structured similar to the Carnahan-Starling EoS and depends on five substance-specific parameters, which can be regressed from the critical isotherm. The temperature evolution of the EoS above the critical temperature is regressed from supercritical isotherms. In the subcritical regime above the melting point, the temperature-dependent scale factors of the EoS are inferred from the empirical coexistence curve, which is fully implemented in the EoS. The pressure singularity occurs at a limit density that is noticeably higher than predicted by universal cubic EoSs such as the Peng-Robinson EoS. The parameters of the analytic and non-perturbative EoSs of water and hydrogen are derived from high-pressure data sets.
In this paper, a quantum effect of hydrogen molecules (uncertainties of each atomic nuclear position and momentum) on the bubble nucleation rate was investigated. The homogeneous bubble nucleation analyses were performed using a density functional theory (DFT) reflecting equations of state (EOSs) constructed to reproduce the thermophysical properties of hydrogen obtained from a classical molecular dynamics (MD) method and a quantum MD method. The results showed that the quantum nature of liquid hydrogen decreases the bubble nucleation rate when compared in the same reduced temperature and reduced superheat ratio condition. Further, it was indicated that the results might be caused by the increase of the energy barrier arising from the difference of the density profile and its position at the critical bubble (in other words, the differences of the critical bubble size and the liquid–vapor interface thickness). Furthermore, the DFT analysis was validated through the evaluation of the bubble nucleation rate using the classical MD method and the quantum MD method made as numerical experiments, and qualitatively the same result was obtained between the DFT and the MD simulations.
Deep neural networks have found their way into a wide range of applications, with astound- ing success. Deeper and more complex networks are being developed, with hundreds of layers and intricate architectures. In this paper, we evaluate the opposite: how small can artificial neural networks (ANN) be and still accurately capture fluid properties that are classically provided in computational fluid dynamics (CFD) using segmented polynomial curve fits? Using a combination of JANAF curve fits and NIST data, ANN are found to accurately represent heat capacity data over a wide temperature range up to 5000 K in a single representation, using as few as four tanh units (or ‘neurons’) where the ANN computational cost is of the order of the JANAF fits. By representing fluid data as a function of energy rather than temperature, iteration during CFD runtime can be avoided when the temperature is to be determined from solver-provided density and energy and the ANN representation outperforms curve fits. This is even more pronounced for real fluid properties. ANN provide a number of structural advantages for a solver: a single function in the CFD solver can be used to decode ANN for arbitrary data; logical forks can be avoided by removing temperature ranges in curve fits; every evaluation costs the same, simplifying load balancing for parallelization; the desired accuracy can be arbitrarily adjusted by adding or removing neural units, without being bound by a functional form. Finally, ANN parameters are provided for oxygen heat capacity for ready application in CFD solvers.
The materials of the combustion chamber wall of rocket engines have to withstand extreme thermal and mechanical loadings, which are managed by efficient cooling. For an optimal design of the cooling system, with minimal hydrodynamic losses, a precise knowledge of the heat transfer is required. The combustion chamber profile imposes some curvatures to the cooling channel, because they follow the nozzle profile of the combustion chamber. These curvatures create dynamical secondary flows inside the channel and bring heat flux modifications through the chamber walls. The experimental project EH3C (Electrical Heated Curved Cooling Channels) has been supported by the german space propulsion center (DLR) in the frame of this PhD. Two test specimens have been designed, manufactured and tested. The first specimen is a single straight cooling channel, presenting a high aspect ratio and the second one is curved, in order to enlighten the curvature effects on the heat transfer and the pressure losses. Numerical simulations have been provided to model the experiments
We report the results of a ring polymer molecular dynamics study of the Kubo velocity autocorrelation function of a quantum fluid as para-hydrogen aimed at the comparison with its classical counterpart. Quite different density conditions were considered for both the classical and quantum cases, in order to compare the two systems before and after the dynamical crossover typically undergone by the velocity autocorrelation function (VAF) of fluids at densities around the triple point, where the shape of the function changes from a monotonic to an oscillatory behavior with a negative minimum. A detailed study of the phase diagram of classical para-hydrogen was necessary for a reasonable choice of the classical states to be taken into consideration, in the spirit of the classical principle of corresponding states. The shape of the quantum and classical VAF was thoroughly analyzed, exhibiting at all studied densities clear differences that might be taken as evidence of quantum effects. We show that these differences are substantially reduced by applying a state-dependent time scaling with respect to a reference time identified with the inverse of the collision rate. An even better coincidence in shape is found by comparing the two systems at slightly non-corresponding reduced densities, suggesting that the quantum system behaves almost like the classical one, but at systematically less dense reduced states of the latter. We also find an unexpected and quite interesting density trend of the collision rate of both classical and quantum para-hydrogen, which accounts for the effectiveness of the scaling throughout the explored density range. The mean kinetic energy and the diffusion coefficients are also discussed in some detail.
In recent years, many researchers have studied on the hydrogen storage properties of metal-organic frameworks (MOFs) by grand canonical Monte Carlo (GCMC) simulation. At present, the GCMC studies of Cu-BTC (BTC: benzene-1,3,5-tricarboxylate) which is a prototypical metal-organic framework mainly adopt the classical force fields, the simulation temperatures are mainly focus on 298K and 77K, and most researchers didn't consider the effects of quantum effects at low temperature. Therefore, we used the quantum effects to correct the classical force fields and the force fields with more accurate simulation results were used to simulate the hydrogen adsorption performances of Cu-BTC in the temperature range of 77K∼298K and the pressure range of 1∼8MPa at each temperature. The results show that the effects of quantum effects on the hydrogen storage of Cu-BTC cannot be neglected and the corrected Dreiding force field can simulate hydrogen adsorption performances of Cu-BTC more accurately at low temperature. This article is protected by copyright. All rights reserved.
The results of the simulation of the glass transition process of argon at cooling rates of 10¹², 10¹³, 10¹⁴, and 10¹⁵ K/s are reported. At temperatures far below the melting point, Tf = 83.8 K, the second maximum of the radial distribution function is split into two peaks, which is connected with the glass transition. In addition, the form of this split changes depending on the cooling rates, which points to different structural states of the system. The calculation of the sound velocity in argon by means of correlation functions gives rise to quite reasonable results in the gaseous, liquid, glass, and crystalline states, including the areas of phase transitions.
This paper presents an experimental investigation of small-scale model airframe noise at various Reynolds numbers up to the real-flight case. The study consists of data acquired with a microphone array in the European Transonic Windtunnel (ETW). The advantage of the ETW is to enable testing simultaneously at cryogenic temperatures and increased pressure levels, which extends the range of achievable Reynolds numbers up to those pertaining to full-scale flight conditions. At the German Aerospace Center (DLR), the microphone-array measurement technique has been further developed to perform measurements under combined cryogenic and pressurized conditions. For this purpose, a microphone-array consisting of 96 microphones was designed and constructed. In this paper, aeroacoustic results are presented for various Reynolds numbers up to the real-flight case on an Airbus K3DY half-model of scale 1:13.6. The results showed significant Reynolds number and Mach number dependency for various sources. Of particular note are various dominant sources appearing on the flap at real-flight Reynolds numbers. To the authors knowledge, this is the first time that airframe noise data for a small-scale model have been acquired at real-flight Reynolds numbers.
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