BADGER v1.0: A Fortran equation of state library

NASA Astrophysics Data System (ADS)

Heltemes, T. A.; Moses, G. A.

2012-12-01

The BADGER equation of state library was developed to enable inertial confinement fusion plasma codes to more accurately model plasmas in the high-density, low-temperature regime. The code had the capability to calculate 1- and 2-T plasmas using the Thomas-Fermi model and an individual electron accounting model. Ion equation of state data can be calculated using an ideal gas model or via a quotidian equation of state with scaled binding energies. Electron equation of state data can be calculated via the ideal gas model or with an adaptation of the screened hydrogenic model with ℓ-splitting. The ionization and equation of state calculations can be done in local thermodynamic equilibrium or in a non-LTE mode using a variant of the Busquet equivalent temperature method. The code was written as a stand-alone Fortran library for ease of implementation by external codes. EOS results for aluminum are presented that show good agreement with the SESAME library and ionization calculations show good agreement with the FLYCHK code. Program summaryProgram title: BADGERLIB v1.0 Catalogue identifier: AEND_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEND_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 41 480 No. of bytes in distributed program, including test data, etc.: 2 904 451 Distribution format: tar.gz Programming language: Fortran 90. Computer: 32- or 64-bit PC, or Mac. Operating system: Windows, Linux, MacOS X. RAM: 249.496 kB plus 195.630 kB per isotope record in memory Classification: 19.1, 19.7. Nature of problem: Equation of State (EOS) calculations are necessary for the accurate simulation of high energy density plasmas. Historically, most EOS codes used in these simulations have relied on an ideal gas model. This model is inadequate for low-temperature, high-density plasma conditions; the gaseous and liquid phases; and the solid phase. The BADGER code was developed to give more realistic EOS data in these regimes. Solution method: BADGER has multiple, user-selectable models to treat the ions, average-atom ionization state and electrons. Ion models are ideal gas and quotidian equation of state (QEOS), ionization models are Thomas-Fermi and individual accounting method (IEM) formulation of the screened hydrogenic model (SHM) with l-splitting, electron ionization models are ideal gas and a Helmholtz free energy minimization method derived from the SHM. The default equation of state and ionization models are appropriate for plasmas in local thermodynamic equilibrium (LTE). The code can calculate non-LTE equation of state (EOS) and ionization data using a simplified form of the Busquet equivalent-temperature method. Restrictions: Physical data are only provided for elements Z=1 to Z=86. Multiple solid phases are not currently supported. Liquid, gas and plasma phases are combined into a generalized "fluid" phase. Unusual features: BADGER divorces the calculation of average-atom ionization from the electron equation of state model, allowing the user to select ionization and electron EOS models that are most appropriate to the simulation. The included ion ideal gas model uses ground-state nuclear spin data to differentiate between isotopes of a given element. Running time: Example provided only takes a few seconds to run.

A notable difference between ideal gas and infinite molar volume limit of van der Waals gas

NASA Astrophysics Data System (ADS)

Liu, Q. H.; Shen, Y.; Bai, R. L.; Wang, X.

2010-05-01

The van der Waals equation of state does not sufficiently represent a gas unless a thermodynamic potential with two proper and independent variables is simultaneously determined. The limiting procedures under which the behaviour of the van der Waals gas approaches that of an ideal gas are letting two van der Waals coefficients be zero rather than letting the molar volume become infinitely large; otherwise, the partial derivative of internal energy with respect to pressure at a fixed temperature does not vanish.

Simple fundamental equation of state for liquid, gas, and fluid of argon, nitrogen, and carbon dioxide

NASA Astrophysics Data System (ADS)

Kaplun, A. B.; Meshalkin, A. B.

2017-07-01

A new fundamental low-parametric equation of state in the form of reduced Helmholtz function for describing thermodynamic properties of normal substances was obtained using the methods and approaches developed earlier by the authors. It allows us to describe the thermal properties of gas, liquid, and fluid in the range from the density in ideal-gas state to the density at a triple point (except the critical region) with sufficiently high accuracy close to the accuracy of experiment. The caloric properties and sound velocity of argon, nitrogen, and carbon dioxide are calculated without involving any caloric data, except the ideal gas enthalpy. The obtained values of isochoric heat capacity, sound velocity, and other thermodynamic properties are in good agreement with experimental (reliable tabular) data.

Compressible flow at high pressure with linear equation of state

NASA Astrophysics Data System (ADS)

Sirignano, William A.

2018-05-01

Compressible flow varies from ideal-gas behavior at high pressures where molecular interactions become important. Density is described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, A and B, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behavior, a closed-form solution is obtained that is valid over a wide range of conditions. An expansion in these molecular-interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behavior. Real-gas modifications in density, enthalpy, and sound speed for a given pressure and temperature lead to variations in many basic compressible flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear-wave propagation, and flow across a shock wave, all for the real gas. Modifications are obtained for allowable mass-flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl's shock relation, and the Rankine-Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and be applied to multicomponent flows or to more-complex flow configurations.

Correction to “Comment on ‘Equilibrium Constants and Rate Constants for Adsorbates: 2D Ideal Gas, 2D Ideal Lattice Gas, and Ideal Hindered Translator Models’”

DOE PAGES

Savara, Aditya

2017-06-28

There was an error in the original Comment. The entropy term arising from 1/N! should be free from dimensional dependence, but also negative. In the original Comment, the nN A arising from 1/N! was inadvertently moved into the dimensional dependent term of Eqs. 2 and 3. To avoid confusion and to keep the same numbering as before, the equations should be as follows.

Heat-flow equation motivated by the ideal-gas shock wave.

PubMed

Holian, Brad Lee; Mareschal, Michel

2010-08-01

We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

Gas-Kinetic Theory Based Flux Splitting Method for Ideal Magnetohydrodynamics

NASA Technical Reports Server (NTRS)

Xu, Kun

1998-01-01

A gas-kinetic solver is developed for the ideal magnetohydrodynamics (MHD) equations. The new scheme is based on the direct splitting of the flux function of the MHD equations with the inclusion of "particle" collisions in the transport process. Consequently, the artificial dissipation in the new scheme is much reduced in comparison with the MHD Flux Vector Splitting Scheme. At the same time, the new scheme is compared with the well-developed Roe-type MHD solver. It is concluded that the kinetic MHD scheme is more robust and efficient than the Roe- type method, and the accuracy is competitive. In this paper the general principle of splitting the macroscopic flux function based on the gas-kinetic theory is presented. The flux construction strategy may shed some light on the possible modification of AUSM- and CUSP-type schemes for the compressible Euler equations, as well as to the development of new schemes for a non-strictly hyperbolic system.

Numerical estimation of ultrasonic production of hydrogen: Effect of ideal and real gas based models.

PubMed

Kerboua, Kaouther; Hamdaoui, Oualid

2018-01-01

Based on two different assumptions regarding the equation describing the state of the gases within an acoustic cavitation bubble, this paper studies the sonochemical production of hydrogen, through two numerical models treating the evolution of a chemical mechanism within a single bubble saturated with oxygen during an oscillation cycle in water. The first approach is built on an ideal gas model, while the second one is founded on Van der Waals equation, and the main objective was to analyze the effect of the considered state equation on the ultrasonic hydrogen production retrieved by simulation under various operating conditions. The obtained results show that even when the second approach gives higher values of temperature, pressure and total free radicals production, yield of hydrogen does not follow the same trend. When comparing the results released by both models regarding hydrogen production, it was noticed that the ratio of the molar amount of hydrogen is frequency and acoustic amplitude dependent. The use of Van der Waals equation leads to higher quantities of hydrogen under low acoustic amplitude and high frequencies, while employing ideal gas law based model gains the upper hand regarding hydrogen production at low frequencies and high acoustic amplitudes. Copyright © 2017 Elsevier B.V. All rights reserved.

Demonstrating the Gas Laws.

ERIC Educational Resources Information Center

Holko, David A.

1982-01-01

Presents a complete computer program demonstrating the relationship between volume/pressure for Boyle's Law, volume/temperature for Charles' Law, and volume/moles of gas for Avagadro's Law. The programing reinforces students' application of gas laws and equates a simulated moving piston to theoretical values derived using the ideal gas law.…

Modified Van der Waals equation and law of corresponding states

NASA Astrophysics Data System (ADS)

Zhong, Wei; Xiao, Changming; Zhu, Yongkai

2017-04-01

It is well known that the Van der Waals equation is a modification of the ideal gas law, yet it can be used to describe both gas and liquid, and some important messages can be obtained from this state equation. However, the Van der Waals equation is not a precise state equation, and it does not give a good description of the law of corresponding states. In this paper, we expand the Van der Waals equation into its Taylor's series form, and then modify the fourth order expansion by changing the constant Virial coefficients into their analogous ones. Via this way, a more precise result about the law of corresponding states has been obtained, and the law of corresponding states can then be expressed as: in terms of the reduced variables, all fluids should obey the same equation with the analogous Virial coefficients. In addition, the system of 3 He with quantum effects has also been taken into consideration with our modified Van der Waals equation, and it is found that, for a normal system without quantum effect, the modification on ideal gas law from the Van der Waals equation is more significant than the real case, however, for a system with quantum effect, this modification is less significant than the real case, thus a factor is introduced in this paper to weaken or strengthen the modification of the Van der Waals equation, respectively.

Development and Assessment of a Computer-Based Equation of State for Equilibrium Air

DTIC Science & Technology

2013-09-01

for very low energies. However, the ideal gas EOS is appropriate for atmospheric flight at subsonic, transonic, and low supersonic flight speeds...Flow Properties About Blunt Bodies Moving at Supersonic Speeds in an Equilibrium Gas ,” NASA TR R-204, July 1964. 21. Tannehill, John C., and Mugge...changes are made. 15. Subject Terms Air, thermodynamic properties, equation of state, chemical equilibrium, real- gas 16. SECURITY CLASSIFICATION

Analysis of senior high school student understanding on gas kinetic theory material

NASA Astrophysics Data System (ADS)

Anri, Y.; Maknun, J.; Chandra, D. T.

2018-05-01

The purpose of this research conducted to find out student understanding profile about gas kinetic theory. Particularly, on ideal gas law material, ideal gas equations and kinetic energy of ideal gas. This research was conducted on student of class XII in one of the schools in Bandung. This research is a descriptive research. The data of this research collected by using test instrument which was the essay that has been developed by the researcher based on Bloom’s Taxonomy revised. Based on the analysis result to student answer, this research discovered that whole student has low understanding in the material of gas kinetic theory. This low understanding caused of the misconception of the student, student attitude on physic subjects, and teacher teaching method who are less helpful in obtaining clear pictures in material being taught.

On the analysis of shock implosion

NASA Astrophysics Data System (ADS)

Mishkin, Eli A.; Alejaldre, Carlos

1984-06-01

An imploding shock wave, coming from infinity, moves through an ideal gas with the adiabatic constant γ. To define a single-valued self-similar coefficient λ(γ), over the whole classical interval 1 < γ < ∞, its boundary values λ(1), λ(∞) are deduced. The conservation equations, cast in form of quadratics, exhibit their singular points P,M,M‧. At P the pressure is maximum, at M the velocity of the gas U1, minus ξ, equals the speed of sound C, at M‧ there is a linear relationship between U1, U˙1 and C. The representative curve of the compressed gas passes analytically through all of them. The relative position of P, M, M‧ leads to three solutions of the quadratic conservation equations. Representative curves of the state of the imploded gas, at various values of γ, are shown. The errors associated with the idealized models of implosion and explosion are evaluated.

Pressure (Or No Royal Road)

ERIC Educational Resources Information Center

Bradley, J.

1973-01-01

Discusses how difficult the various problems of pressure, partial pressure, gas laws, and vapor pressure are for students. Outlines the evolution of the concept of pressure, the gas equation for a perfect gas, partial pressures, saturated vapor pressure, Avogadro's hypothesis, Raoult's law, and the vapor pressure of ideal solutions. (JR)

Flux Jacobian Matrices For Equilibrium Real Gases

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

Fluctuation theorem for entropy production during effusion of an ideal gas with momentum transfer.

PubMed

Wood, Kevin; Van den Broeck, C; Kawai, R; Lindenberg, Katja

2007-06-01

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Cleuren [Phys. Rev. E 74, 021117 (2006)], we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

Thermodynamics of high temperature, Mie-Gruneisen solids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lemons, Don S.; Lund, Carl M.

1999-12-01

We construct a set of equations of state for condensed matter at temperatures well above the Debye temperature. These equations incorporate the Mie-Gruneisen equation of state and generic properties of high temperature solids. They are simple enough to provide an alternative to the ideal gas and the van der Waals equations of state for illustrating thermodynamic concepts. (c) 1999 American Association of Physics Teachers.

Oscillatory conductive heat transfer for a fiber in an ideal gas

NASA Technical Reports Server (NTRS)

Kuntz, H. L.; Perreira, N. D.

1985-01-01

A description of the thermal effects created by placing a cylindrical fiber in an inviscid, ideal gas, through which an acoustic wave propagates, is presented. The fibers and the gas have finite heat capacities and thermal conductivities. Expressions for the temperature distribution in the gas and in the material are determined. The temperature distribution is caused by pressure oscillations in the gas which, in turn, are caused by the passage of an acoustic wave. The relative value of a dimensionless parameter is found to be indicative of whether the exact or approximate equations should be used in the solution. This parameter is a function of the thermal conductivities and heat capacities of the fiber and gas, the acoustic frequency, and the fiber diameter.

Unified first principles description from warm dense matter to ideal ionized gas plasma: electron-ion collisions induced friction.

PubMed

Dai, Jiayu; Hou, Yong; Yuan, Jianmin

2010-06-18

Electron-ion interactions are central to numerous phenomena in the warm dense matter (WDM) regime and at higher temperature. The electron-ion collisions induced friction at high temperature is introduced in the procedure of ab initio molecular dynamics using the Langevin equation based on density functional theory. In this framework, as a test for Fe and H up to 1000 eV, the equation of state and the transition of electronic structures of the materials with very wide density and temperature can be described, which covers a full range of WDM up to high energy density physics. A unified first principles description from condensed matter to ideal ionized gas plasma is constructed.

Modeling shock waves in an ideal gas: combining the Burnett approximation and Holian's conjecture.

PubMed

He, Yi-Guang; Tang, Xiu-Zhang; Pu, Yi-Kang

2008-07-01

We model a shock wave in an ideal gas by combining the Burnett approximation and Holian's conjecture. We use the temperature in the direction of shock propagation rather than the average temperature in the Burnett transport coefficients. The shock wave profiles and shock thickness are compared with other theories. The results are found to agree better with the nonequilibrium molecular dynamics (NEMD) and direct simulation Monte Carlo (DSMC) data than the Burnett equations and the modified Navier-Stokes theory.

Defining relative humidity in terms of water activity. Part 1: definition

NASA Astrophysics Data System (ADS)

Feistel, Rainer; Lovell-Smith, Jeremy W.

2017-08-01

Relative humidity (RH) is a quantity widely used in various fields such as metrology, meteorology, climatology or engineering. However, RH is neither uniformly defined, nor do some definitions properly account for deviations from ideal-gas properties, nor is the application range of interest fully covered. In this paper, a new full-range definition of RH is proposed that is based on the thermodynamics of activities in order to include deviations from ideal-gas behaviour. Below the critical point of pure water, at pressures p  <  22.064 MPa and temperatures T  <  647.096 K, RH is rigorously defined as the relative activity (or relative fugacity) of water in humid air. For this purpose, reference states of the relative activity are specified appropriately. Asymptotically, the ideal-gas limit of the new definition is consistent with de-facto standard RH definitions published previously and recommended internationally. Virial approximations are reported for estimating small corrections to the ideal-gas equations.

Hyperpolarized (129) Xe imaging of the rat lung using spiral IDEAL.

PubMed

Doganay, Ozkan; Wade, Trevor; Hegarty, Elaine; McKenzie, Charles; Schulte, Rolf F; Santyr, Giles E

2016-08-01

To implement and optimize a single-shot spiral encoding strategy for rapid 2D IDEAL projection imaging of hyperpolarized (Hp) (129) Xe in the gas phase, and in the pulmonary tissue (PT) and red blood cells (RBCs) compartments of the rat lung, respectively. A theoretical and experimental point spread function analysis was used to optimize the spiral k-space read-out time in a phantom. Hp (129) Xe IDEAL images from five healthy rats were used to: (i) optimize flip angles by a Bloch equation analysis using measured kinetics of gas exchange and (ii) investigate the feasibility of the approach to characterize the exchange of Hp (129) Xe. A read-out time equal to approximately 1.8 × T2* was found to provide the best trade-off between spatial resolution and signal-to-noise ratio (SNR). Spiral IDEAL approaches that use the entire dissolved phase magnetization should give an SNR improvement of a factor of approximately three compared with Cartesian approaches with similar spatial resolution. The IDEAL strategy allowed imaging of gas, PT, and RBC compartments with sufficient SNR and temporal resolution to permit regional gas exchange measurements in healthy rats. Single-shot spiral IDEAL imaging of gas, PT and RBC compartments and gas exchange is feasible in rat lung using Hp (129) Xe. Magn Reson Med 76:566-576, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

The compressibility and the capacitance coefficient of helium-oxygen atmospheres.

PubMed

Imbert, G; Dejours, P; Hildwein, G

1982-12-01

The capacitance coefficient beta of an ideal gas mixture depends only on its temperature T, and its value is derived from the ideal gas law (i.e., beta = 1/RT, R being the ideal gas constant). But real gases behave as ideal gases only at low pressures, and this would not be the case in deep diving. High pressures of helium-oxygen are used in human and animal experimental dives (up to 7 or 12 MPa or more, respectively). At such pressures deviations from the ideal gas law cannot be neglected in hyperbaric atmospheres with respect to current accuracy of measuring instruments. As shown both theoretically and experimentally by this study, the non-ideal nature of helium-oxygen has a significant effect on the capacitance coefficient of hyperbaric atmospheres. The theoretical study is based on interaction energy in either homogeneous (He-He and O2-O2) or heterogeneous (He-O2) molecular pairs, and on the virial equation of state for gas mixtures. The experimental study is based on weight determination of samples of known volume of binary helium-oxygen mixtures, which are prepared in well-controlled pressure and temperature conditions. Our experimental results are in good agreement with theoretical predictions. 1) The helium compressibility factor ZHe increases linearly with pressure [ZHe = 1 + 0.0045 P (in MPa) at 30 degrees C]; and 2) in same temperature and pressure conditions (T = 303 K and P = 0.1 to 15 MPa), the same value for Z is valid for a helium-oxygen binary mixture and for pure helium. As derived from the equation of state of real gases, the capacitance coefficient is inversely related to Z (beta = 1/ZRT); therefore, for helium-oxygen mixtures, this coefficient would decrease with increasing pressure. A table is given for theoretical values of helium-oxygen capacitance coefficient, at pressures ranging from 0.1 to 15.0 MPa and at temperatures ranging from 25 degrees C to 37 degrees C.

Similarity Laws for the Lines of Ideal Free Energy and Chemical Potential in Supercritical Fluids.

PubMed

Apfelbaum, E M; Vorob'ev, V S

2017-09-21

We have found the curves on the density-temperature plane, along which the values of free energy and chemical potential correspond to ideal gas quantities. At first, we have applied the van der Waals equation to construct them and to derive their equations. Then we have shown that the same lines for real substances (Ar, N 2 , CH 4 , SF 6 , H 2 , H 2 O) and for the model Lennard-Jones system constructed on the basis of the measurements data and calculations are well matched with the derived equations. The validity and deviations from the obtained similarity laws are discussed.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

NASA Technical Reports Server (NTRS)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

High Order Filter Methods for the Non-ideal Compressible MHD Equations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjoegreen, Bjoern

2003-01-01

The generalization of a class of low-dissipative high order filter finite difference methods for long time wave propagation of shock/turbulence/combustion compressible viscous gas dynamic flows to compressible MHD equations for structured curvilinear grids has been achieved. The new scheme is shown to provide a natural and efficient way for the minimization of the divergence of the magnetic field numerical error. Standard divergence cleaning is not required by the present filter approach. For certain non-ideal MHD test cases, divergence free preservation of the magnetic fields has been achieved.

An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas

NASA Astrophysics Data System (ADS)

Nagata, Shoichi

2018-03-01

An expression for the entropy of a monoatomic classical ideal gas is known as the Sackur-Tetrode equation. This pioneering investigation about 100 years ago incorporates quantum considerations. The purpose of this paper is to provide an alternative expression for the entropy in terms of the Heisenberg uncertainty relation. The analysis is made on the basis of fluctuation theory, for a canonical system in thermal equilibrium at temperature T. This new formula indicates manifestly that the entropy of macroscopic world is recognized as a measure of uncertainty in microscopic quantum world. The entropy in the Sackur-Tetrode equation can be re-interpreted from a different perspective viewpoint. The emphasis is on the connection between the entropy and the uncertainty relation in quantum consideration.

A low-parametric state equation for calculating the thermodynamic properties of substances in liquid and gaseous state

NASA Astrophysics Data System (ADS)

Kaplun, A. B.; Meshalkin, A. B.

2013-08-01

Using methods and approaches developed by the authors, a new low-parametric state equation for describing the thermal properties of normal substances is obtained that allows us to describe the thermal properties of gases, liquids, and fluids over a range of densities from the ideal gas state to the triple point, except for a critical region, with a high degree of accuracy close to that of an experiment. The caloric properties and speed of sound are calculated for argon, nitrogen, and carbon dioxide without using any caloric data except for the enthalpy of an ideal gas. It is established that the calculated values of enthalpy, heat capacity, the speed of speed of sound, etc., are in good agreement with the experimental (reliably tabulated) data.

Four-fluid MHD simulations of the plasma and neutral gas environment of comet 67P/Churyumov-Gerasimenko near perihelion

NASA Astrophysics Data System (ADS)

Huang, Zhenguang; Tóth, Gábor; Gombosi, Tamas I.; Jia, Xianzhe; Rubin, Martin; Fougere, Nicolas; Tenishev, Valeriy; Combi, Michael R.; Bieler, Andre; Hansen, Kenneth C.; Shou, Yinsi; Altwegg, Kathrin

2016-05-01

The neutral and plasma environment is critical in understanding the interaction of the solar wind and comet 67P/Churyumov-Gerasimenko (CG), the target of the European Space Agency's Rosetta mission. To serve this need and support the Rosetta mission, we have developed a 3-D four-fluid model, which is based on BATS-R-US (Block-Adaptive Tree Solarwind Roe-type Upwind Scheme) within SWMF (Space Weather Modeling Framework) that solves the governing multifluid MHD equations and the Euler equations for the neutral gas fluid. These equations describe the behavior and interactions of the cometary heavy ions, the solar wind protons, the electrons, and the neutrals. This model incorporates different mass loading processes, including photoionization and electron impact ionization, charge exchange, dissociative ion-electron recombination, and collisional interactions between different fluids. We simulated the plasma and neutral gas environment near perihelion in three different cases: an idealized comet with a spherical body and uniform neutral gas outflow, an idealized comet with a spherical body and illumination-driven neutral gas outflow, and comet CG with a realistic shape model and illumination-driven neutral gas outflow. We compared the results of the three cases and showed that the simulations with illumination-driven neutral gas outflow have magnetic reconnection, a magnetic pileup region and nucleus directed plasma flow inside the nightside reconnection region, which have not been reported in the literature.

40 CFR 1065.645 - Amount of water in an ideal gas.

Code of Federal Regulations, 2014 CFR

2014-07-01

... vapor pressure of water in paragraph (a) of this section or another appropriate equation and, depending... converting the last term in each equation. (a) Vapor pressure of water. Calculate the vapor pressure of water... use a different relationship of the vapor pressure of water to a given saturation temperature...

Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions

NASA Technical Reports Server (NTRS)

Bursik, J. W.; Hall, R. M.

1980-01-01

The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.

Conical flow near singular rays. [shock generation in ideal gas

NASA Technical Reports Server (NTRS)

Zahalak, G. I.; Myers, M. K.

1974-01-01

The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.

Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

NASA Astrophysics Data System (ADS)

Hyhlík, Tomáš

2018-06-01

The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

Carbon Footprint Calculations: An Application of Chemical Principles

ERIC Educational Resources Information Center

Treptow, Richard S.

2010-01-01

Topics commonly taught in a general chemistry course can be used to calculate the quantity of carbon dioxide emitted into the atmosphere by various human activities. Each calculation begins with the balanced chemical equation for the reaction that produces the CO[subscript 2] gas. Stoichiometry, thermochemistry, the ideal gas law, and dimensional…

CFD analysis of thermally induced thermodynamic losses in the reciprocating compression and expansion of real gases

NASA Astrophysics Data System (ADS)

Taleb, Aly I.; Sapin, Paul; Barfuß, Christoph; Fabris, Drazen; Markides, Christos N.

2017-03-01

The efficiency of expanders is of prime importance in determining the overall performance of a variety of thermodynamic power systems, with reciprocating-piston expanders favoured at intermediate-scales of application (typically 10-100 kW). Once the mechanical losses in reciprocating machines are minimized (e.g. through careful valve design and operation), losses due to the unsteady thermal-energy exchange between the working fluid and the solid walls of the containing device can become the dominant loss mechanism. In this work, gas-spring devices are investigated numerically in order to focus explicitly on the thermodynamic losses that arise due to this unsteady heat transfer. The specific aim of the study is to investigate the behaviour of real gases in gas springs and to compare this to that of ideal gases in order to attain a better understanding of the impact of real-gas effects on the thermally induced losses in reciprocating expanders and compressors. A CFD-model of a gas spring is developed in OpenFOAM. Three different fluid models are compared: (1) an ideal-gas model with constant thermodynamic and transport properties; (2) an ideal-gas model with temperature-dependent properties; and (3) a real-gas model using the Peng-Robinson equation-of-state with temperature and pressure-dependent properties. Results indicate that, for simple, mono- and diatomic gases, like helium or nitrogen, there is a negligible difference in the pressure and temperature oscillations over a cycle between the ideal and real-gas models. However, when considering heavier (organic) molecules, such as propane, the ideal-gas model tends to overestimate the pressure compared to the real-gas model, especially if the temperature and pressure dependency of the thermodynamic properties is not taken into account. In fact, the ideal-gas model predicts higher pressures by as much as 25% (compared to the real-gas model). Additionally, both ideal-gas models underestimate the thermally induced loss compared to the real-gas model for heavier gases. This discrepancy is most pronounced at rotational speeds where the losses are highest. The real-gas model predicts a peak loss of 8.9% of the compression work, while the ideal-gas model predicts a peak loss of 5.7%. These differences in the work loss are due to the fact that the gas behaves less ideally during expansion than during compression, with the compressibility factor being lower during compression. This behaviour cannot be captured with the ideal-gas law. It is concluded that real-gas effects must be taken into account in order to predict accurately the thermally induced loss mechanism when using heavy fluid molecules in such devices.

Boltzmann's "H"-Theorem and the Assumption of Molecular Chaos

ERIC Educational Resources Information Center

Boozer, A. D.

2011-01-01

We describe a simple dynamical model of a one-dimensional ideal gas and use computer simulations of the model to illustrate two fundamental results of kinetic theory: the Boltzmann transport equation and the Boltzmann "H"-theorem. Although the model is time-reversal invariant, both results predict that the behaviour of the gas is time-asymmetric.…

Free Volume of the Hard Spheres Gas

ERIC Educational Resources Information Center

Shutler, P. M. E.; Martinez, J. C.; Springham, S. V.

2007-01-01

The Enskog factor [chi] plays a central role in the theory of dense gases, quantifying how the finite size of molecules causes many physical quantities, such as the equation of state, the mean free path, and the diffusion coefficient, to deviate from those of an ideal gas. We suggest an intuitive but rigorous derivation of this fact by showing how…

Advantages of using a logarithmic scale in pressure-volume diagrams for Carnot and other heat engine cycles

NASA Astrophysics Data System (ADS)

Shieh, Lih-Yir; Kan, Hung-Chih

2014-04-01

We demonstrate that plotting the P-V diagram of an ideal gas Carnot cycle on a logarithmic scale results in a more intuitive approach for deriving the final form of the efficiency equation. The same approach also facilitates the derivation of the efficiency of other thermodynamic engines that employ adiabatic ideal gas processes, such as the Brayton cycle, the Otto cycle, and the Diesel engine. We finally demonstrate that logarithmic plots of isothermal and adiabatic processes help with visualization in approximating an arbitrary process in terms of an infinite number of Carnot cycles.

Thermodynamic Properties of Nitrogen Including Liquid and Vapor Phases from 63K to 2000K with Pressures to 10,000 Bar

NASA Technical Reports Server (NTRS)

Jacobsen, Richard T.; Stewart, Richard B.

1973-01-01

Tables of thermodynamic properties of nitrogen are presented for the liquid and vapor phases for temperatures from the freezing line to 2000K and pressures to 10,000 bar. The tables include values of density, internal energy, enthalpy, entropy, isochoric heat capacity, isobaric heat capacity velocity of sound, the isotherm derivative, and the isochor derivative. The thermodynamic property tables are based on an equation of state, P=P (p,T), which accurately represents liquid and gaseous nitrogen for the range of pressures and temperatures covered by the tables. Comparisons of property values calculated from the equation of state with measured values for P-p-T, heat capacity, enthalpy, latent heat, and velocity of sound are included to illustrate the agreement between the experimental data and the tables of properties presented here. The coefficients of the equation of state were determined by a weighted least squares fit to selected P-p-T data and, simultaneously, to isochoric heat capacity data determined by corresponding states analysis from oxygen data, and to data which define the phase equilibrium criteria for the saturated liquid and the saturated vapor. The vapor pressure equation, melting curve equation, and an equation to represent the ideal gas heat capacity are also presented. Estimates of the accuracy of the equation of state, the vapor pressure equation, and the ideal gas heat capacity equation are given. The equation of state, derivatives of the equation, and the integral functions for calculating derived thermodynamic properties are included.

Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of state

NASA Astrophysics Data System (ADS)

Babajanova, Gulmira; Matrasulov, Jasur; Nakamura, Katsuhiro

2018-04-01

With use of the scheme of fast forward which realizes quasistatic or adiabatic dynamics in shortened timescale, we investigate a thermally isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size L =L (t ) . In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity (L ˙) and acceleration (L ̈) of L besides rapidly changing state variables like effective temperature (T ) and L itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of L and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number (N ) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.

New generalized Noh solutions for HEDP hydrocode verification

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.; Tangri, V.

2017-10-01

The classic Noh solution describing stagnation of a cold ideal gas in a strong accretion shock wave has been the workhorse of compressible hydrocode verification for over three decades. We describe a number of its generalizations available for HEDP code verification. First, for an ideal gas, we have obtained self-similar solutions that describe adiabatic convergence either of a finite-pressure gas into an empty cavity or of a finite-amplitude sound wave into a uniform resting gas surrounding the center or axis of symmetry. At the moment of collapse such a flow produces a uniform gas whose velocity at each point is constant and directed towards the axis or the center, i. e. the initial condition similar to the classic solution but with a finite pressure of the converging gas. After that, a constant-velocity accretion shock propagates into the incident gas whose pressure and velocity profiles are not flat, in contrast with the classic solution. Second, for an arbitrary equation of state, we demonstrate the existence of self-similar solutions of the Noh problem in cylindrical and spherical geometry. Examples of such solutions with a three-term equation of state that includes cold, thermal ion/lattice, and thermal electron contributions are presented for aluminum and copper. These analytic solutions are compared to our numerical simulation results as an example of their use for code verification. Work supported by the US DOE/NNSA.

The Gaseous State. Independent Learning Project for Advanced Chemistry (ILPAC). Unit P1.

ERIC Educational Resources Information Center

Inner London Education Authority (England).

This unit on the gaseous state is one of 10 first year units produced by the Independent Learning Project for Advanced Chemistry (ILPAC). The unit consists of two levels. Level one deals with the distinctive characteristics of gases, then considers the gas laws, in particular the ideal gas equation and its applications. Level two concentrates on…

Steady Secondary Flows Generated by Periodic Compression and Expansion of an Ideal Gas in a Pulse Tube

NASA Technical Reports Server (NTRS)

Lee, Jeffrey M.

1999-01-01

This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.

Monopole excitations of a harmonically trapped one-dimensional Bose gas from the ideal gas to the Tonks-Girardeau regime.

PubMed

Choi, S; Dunjko, V; Zhang, Z D; Olshanii, M

2015-09-11

Using a time-dependent modified nonlinear Schrödinger equation (MNLSE)-where the conventional chemical potential proportional to the density is replaced by the one inferred from Lieb-Liniger's exact solution-we study frequencies of the collective monopole excitations of a one-dimensional Bose gas. We find that our method accurately reproduces the results of a recent experimental study [E. Haller et al., Science 325, 1224 (2009)] in the full spectrum of interaction regimes from the ideal gas, through the mean-field regime, through the mean-field Thomas-Fermi regime, all the way to the Tonks-Giradeau gas. While the former two are accessible by the standard time-dependent NLSE and inaccessible by the time-dependent local density approximation, the situation reverses in the latter case. However, the MNLSE is shown to treat all these regimes within a single numerical method.

A mass-balanced definition of corrected retention volume in gas chromatography.

PubMed

Kurganov, A

2007-05-25

The mass balance equation of a chromatographic system using a compressible moving phase has been compiled for mass flow of the mobile phase instead of traditional volumetric flow allowing solution of the equation in an analytical form. The relation obtained correlates retention volume measured under ambient conditions with the partition coefficient of the solute. Compared to the relation in the ideal chromatographic system the equation derived contains an additional correction term accounting for the compressibility of the moving phase. When the retention volume is measured under the mean column pressure and column temperature the correction term is reduced to unit and the relation is simplified to those known for the ideal system. This volume according to International Union of Pure and Applied Chemistry (IUPAC) is called the corrected retention volume.

Chemical Potential for the Interacting Classical Gas and the Ideal Quantum Gas Obeying a Generalized Exclusion Principle

ERIC Educational Resources Information Center

Sevilla, F. J.; Olivares-Quiroz, L.

2012-01-01

In this work, we address the concept of the chemical potential [mu] in classical and quantum gases towards the calculation of the equation of state [mu] = [mu](n, T) where n is the particle density and "T" the absolute temperature using the methods of equilibrium statistical mechanics. Two cases seldom discussed in elementary textbooks are…

Foundations of radiation hydrodynamics

NASA Astrophysics Data System (ADS)

Mihalas, D.; Mihalas, B. W.

This book is the result of an attempt, over the past few years, to gather the basic tools required to do research on radiating flows in astrophysics. The microphysics of gases is discussed, taking into account the equation of state of a perfect gas, the first and second law of thermodynamics, the thermal properties of a perfect gas, the distribution function and Boltzmann's equation, the collision integral, the Maxwellian velocity distribution, Boltzmann's H-theorem, the time of relaxation, and aspects of classical statistical mechanics. Other subjects explored are related to the dynamics of ideal fluids, the dynamics of viscous and heat-conducting fluids, relativistic fluid flow, waves, shocks, winds, radiation and radiative transfer, the equations of radiation hydrodynamics, and radiating flows. Attention is given to small-amplitude disturbances, nonlinear flows, the interaction of radiation and matter, the solution of the transfer equation, acoustic waves, acoustic-gravity waves, basic concepts of special relativity, and equations of motion and energy.

GCKP84-general chemical kinetics code for gas-phase flow and batch processes including heat transfer effects

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1984-01-01

A general chemical kinetics code is described for complex, homogeneous ideal gas reactions in any chemical system. The main features of the GCKP84 code are flexibility, convenience, and speed of computation for many different reaction conditions. The code, which replaces the GCKP code published previously, solves numerically the differential equations for complex reaction in a batch system or one dimensional inviscid flow. It also solves numerically the nonlinear algebraic equations describing the well stirred reactor. A new state of the art numerical integration method is used for greatly increased speed in handling systems of stiff differential equations. The theory and the computer program, including details of input preparation and a guide to using the code are given.

FY06 NRL DoD High Performance Computing Modernization Program Annual Reports

DTIC Science & Technology

2007-10-31

our simulations yield important new information on the amount and form of the energy that is released by these explosive events. These results...coupled with the ideal-gas equation of state and a one-step Arrhenuis kinetics of energy release. The equations are solved using the explicit...practical applications, including hydrogen safety and pulse -detonation engines (PDE). For example, the results summarizing the effect of obstacle

An Alternative Treatment of Heat Flow for Charge Transport in Semiconductor Devices (Postprint)

DTIC Science & Technology

2010-07-01

is tantamount to treating them as ideal gases. A three-dimensional ideal Fermi gas is spherically symmetric in momentum space, and its distribution in...the first mo- ment of the Boltzmann equation using the momentum relax- ation time and effective mass approximations.13 Neglecting any magnetic field and...where the integral is over all momentum vectors k, v is electron velocity, k is the momentum relaxation time, and kf denotes the gradient in momentum

The "Sadly Cannot" Thermodynamic Cycle Revisited.

ERIC Educational Resources Information Center

Mills, David S.; Huston, Craig S.

1991-01-01

An exercise that gives students a chance to use the equations of state for both an ideal gas and for an adiabatic process in determining the points at which heat flow reverses direction and at which the working substance reaches its maximum temperature is demonstrated. (KR)

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

Finite-Difference Solution for Laminar or Turbulent Boundary Layer Flow over Axisymmetric Bodies with Ideal Gas, CF4, or Equilibrium Air Chemistry

NASA Technical Reports Server (NTRS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-01-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Finite-difference solution for laminar or turbulent boundary layer flow over axisymmetric bodies with ideal gas, CF4, or equilibrium air chemistry

NASA Astrophysics Data System (ADS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-12-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Magnetogasdynamic spherical shock wave in a non-ideal gas under gravitational field with conductive and radiative heat fluxes

NASA Astrophysics Data System (ADS)

Nath, G.; Vishwakarma, J. P.

2016-11-01

Similarity solutions are obtained for the flow behind a spherical shock wave in a non-ideal gas under gravitational field with conductive and radiative heat fluxes, in the presence of a spatially decreasing azimuthal magnetic field. The shock wave is driven by a piston moving with time according to power law. The radiation is considered to be of the diffusion type for an optically thick grey gas model and the heat conduction is expressed in terms of Fourier's law for heat conduction. Similarity solutions exist only when the surrounding medium is of constant density. The gas is assumed to have infinite electrical conductivity and to obey a simplified van der Waals equation of state. It is shown that an increase of the gravitational parameter or the Alfven-Mach number or the parameter of the non-idealness of the gas decreases the compressibility of the gas in the flow-field behind the shock, and hence there is a decrease in the shock strength. The pressure and density vanish at the inner surface (piston) and hence a vacuum is formed at the center of symmetry. The shock waves in conducting non-ideal gas under gravitational field with conductive and radiative heat fluxes can be important for description of shocks in supernova explosions, in the study of a flare produced shock in the solar wind, central part of star burst galaxies, nuclear explosion etc. The solutions obtained can be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.

Supersonic flow of chemically reacting gas-particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A numerical solution for chemically reacting supersonic gas-particle flows in rocket nozzles and exhaust plumes was described. The gas-particle flow solution is fully coupled in that the effects of particle drag and heat transfer between the gas and particle phases are treated. Gas and particles exchange momentum via the drag exerted on the gas by the particles. Energy is exchanged between the phases via heat transfer (convection and/or radiation). Thermochemistry calculations (chemical equilibrium, frozen or chemical kinetics) were shown to be uncoupled from the flow solution and, as such, can be solved separately. The solution to the set of governing equations is obtained by utilizing the method of characteristics. The equations cast in characteristic form are shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The particle distribution is represented in the numerical solution by a finite distribution of particle sizes.

Supersonic Flow of Chemically Reacting Gas-Particle Mixtures. Volume 2: RAMP - A Computer Code for Analysis of Chemically Reacting Gas-Particle Flows

NASA Technical Reports Server (NTRS)

Penny, M. M.; Smith, S. D.; Anderson, P. G.; Sulyma, P. R.; Pearson, M. L.

1976-01-01

A computer program written in conjunction with the numerical solution of the flow of chemically reacting gas-particle mixtures was documented. The solution to the set of governing equations was obtained by utilizing the method of characteristics. The equations cast in characteristic form were shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The characteristic directions for the gas-particle system are found to be the conventional gas Mach lines, the gas streamlines and the particle streamlines. The basic mesh construction for the flow solution is along streamlines and normals to the streamlines for axisymmetric or two-dimensional flow. The analysis gives detailed information of the supersonic flow and provides for a continuous solution of the nozzle and exhaust plume flow fields. Boundary conditions for the flow solution are either the nozzle wall or the exhaust plume boundary.

A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S."bala"

2016-11-01

The explosive dispersal of particles is an example of a complex multiphase and multi-species fluid flow problem. This problem has many engineering applications including particle-laden explosives. In these flows, the detonation products of the explosive cannot be treated as a perfect gas so a real gas equation of state is used to close the governing equations (unlike air, which uses the ideal gas equation for closure). As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both of the state equations must be satisfied. One of the more accurate, yet computationally expensive, methods to deal with this is a scheme that iterates between the two equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work strives to create a multi-fidelity surrogate model of this process. We then study the performance of the model with respect to the iterative method by performing both gas-only and particle laden flow simulations using an Eulerian-Lagrangian approach with a finite volume code. Specifically, the model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel modeling approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Ballistically Initiated Fire Ball Generation Using M&S: Innovation Grant (Briefing Charts)

DTIC Science & Technology

2012-01-26

isotropic in nature Phenomenological models for explosives initiation. – HVRB, forest fire etc. Equation of state – Ideal gas, Mie-Gruneisen, JWL ...perfectly plastic description • EOS • Mie Gruneisen • JWL for explosive • Phenomenological Model for EFP • High Explosive input for programmed burn

Splitting of inviscid fluxes for real gases

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Vanleer, Bram; Shuen, Jian-Shun

1988-01-01

Flux-vector and flux-difference splittings for the inviscid terms of the compressible flow equations are derived under the assumption of a general equation of state for a real gas in equilibrium. No necessary assumptions, approximations or auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and readily apply to curvilinear coordinates. Applications of the formulas in a TVD algorithm to one-dimensional shock-tube and nozzle problems show their quality and robustness.

Splitting of inviscid fluxes for real gases

NASA Technical Reports Server (NTRS)

Liou, Meng-Sing; Van Leer, Bram; Shuen, Jian-Shun

1990-01-01

Flux-vector and flux-difference splittings for the inviscid terms of the compressible flow equations are derived under the assumption of a general equation of state for a real gas in equilibrium. No necessary assumptions, approximations for auxiliary quantities are introduced. The formulas derived include several particular cases known for ideal gases and readily apply to curvilinear coordinates. Applications of the formulas in a TVD algorithm to one-dimensional shock-tube and nozzle problems show their quality and robustness.

Real-Gas Effects on Binary Mixing Layers

NASA Technical Reports Server (NTRS)

Okong'o, Nora; Bellan, Josette

2003-01-01

This paper presents a computational study of real-gas effects on the mean flow and temporal stability of heptane/nitrogen and oxygen/hydrogen mixing layers at supercritical pressures. These layers consist of two counterflowing free streams of different composition, temperature, and density. As in related prior studies reported in NASA Tech Briefs, the governing conservation equations were the Navier-Stokes equations of compressible flow plus equations for the conservation of total energy and of chemical- species masses. In these equations, the expressions for heat fluxes and chemical-species mass fluxes were derived from fluctuation-dissipation theory and incorporate Soret and Dufour effects. Similarity equations for the streamwise velocity, temperature, and mass fractions were derived as approximations to the governing equations. Similarity profiles showed important real-gas, non-ideal-mixture effects, particularly for temperature, in departing from the error-function profile, which is the similarity solution for incompressible flow. The temperature behavior was attributed to real-gas thermodynamics and variations in Schmidt and Prandtl numbers. Temporal linear inviscid stability analyses were performed using the similarity and error-function profiles as the mean flow. For the similarity profiles, the growth rates were found to be larger and the wavelengths of highest instability shorter, relative to those of the errorfunction profiles and to those obtained from incompressible-flow stability analysis. The range of unstable wavelengths was found to be larger for the similarity profiles than for the error-function profiles

Dynamic water behaviour due to one trapped air pocket in a laboratory pipeline apparatus

NASA Astrophysics Data System (ADS)

Bergant, A.; Karadžić, U.; Tijsseling, A.

2016-11-01

Trapped air pockets may cause severe operational problems in hydropower and water supply systems. A locally isolated air pocket creates distinct amplitude, shape and timing of pressure pulses. This paper investigates dynamic behaviour of a single trapped air pocket. The air pocket is incorporated as a boundary condition into the discrete gas cavity model (DGCM). DGCM allows small gas cavities to form at computational sections in the method of characteristics (MOC). The growth of the pocket and gas cavities is described by the water hammer compatibility equation(s), the continuity equation for the cavity volume, and the equation of state of an ideal gas. Isentropic behaviour is assumed for the trapped gas pocket and an isothermal bath for small gas cavities. Experimental investigations have been performed in a laboratory pipeline apparatus. The apparatus consists of an upstream end high-pressure tank, a horizontal steel pipeline (total length 55.37 m, inner diameter 18 mm), four valve units positioned along the pipeline including the end points, and a downstream end tank. A trapped air pocket is captured between two ball valves at the downstream end of the pipeline. The transient event is initiated by rapid opening of the upstream end valve; the downstream end valve stays closed during the event. Predicted and measured results for a few typical cases are compared and discussed.

Buoyancy of gas-filled bladders at great depth

NASA Astrophysics Data System (ADS)

Priede, Imants G.

2018-02-01

At high hydrostatic pressures exceeding 20 MPa or 200 bar, equivalent to depths exceeding ca.2000 m, the behaviour of gases deviates significantly from the predictions of standard equations such as Boyle's Law, the Ideal Gas Law and Van der Waals equation. The predictions of these equations are compared with experimental data for nitrogen, oxygen and air at 0 °C and 15 °C, at pressures up to 1100 bar (110 MPa) equivalent to full ocean depth of ca. 11000 m. Owing to reduced compressibility of gases at high pressures, gas-filled bladders at full ocean depth have a density of 847 kg m-3 for Oxygen, 622 kg m-3 for Nitrogen and 660 kg m-3 for air providing potentially useful buoyancy comparable with that available from man-made materials. This helps explain why some of the deepest-living fishes at ca. 7000 m depth (700 bar or 70 MPa) have gas-filled swim bladders. A table is provided of the density and buoyancy of oxygen, nitrogen and air at 0 °C and 15 °C from 100 to 1100 bar.

On determining absolute entropy without quantum theory or the third law of thermodynamics

NASA Astrophysics Data System (ADS)

Steane, Andrew M.

2016-04-01

We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the third law of thermodynamics. The Gibbs-Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.

Vorticity and symplecticity in multi-symplectic, Lagrangian gas dynamics

NASA Astrophysics Data System (ADS)

Webb, G. M.; Anco, S. C.

2016-02-01

The Lagrangian, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the Lagrangian fluid labels, m i (the Lagrangian mass coordinates) and time t are the independent variables, and in which the Eulerian position of the fluid element {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the Lagrangian map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the Lagrangian map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The Lagrangian is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the Lagrangian energy conservation law with respect to the Lagrangian mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.

Analytical Phase Equilibrium Function for Mixtures Obeying Raoult's and Henry's Laws

NASA Astrophysics Data System (ADS)

Hayes, Robert

When a mixture of two substances exists in both the liquid and gas phase at equilibrium, Raoults and Henry's laws (ideal solution and ideal dilute solution approximations) can be used to estimate the gas and liquid mole fractions at the extremes of either very little solute or solvent. By assuming that a cubic polynomial can reasonably approximate the intermediate values to these extremes as a function of mole fraction, the cubic polynomial is solved and presented. A closed form equation approximating the pressure dependence on mole fraction of the constituents is thereby obtained. As a first approximation, this is a very simple and potentially useful means to estimate gas and liquid mole fractions of equilibrium mixtures. Mixtures with an azeotrope require additional attention if this type of approach is to be utilized. This work supported in part by federal Grant NRC-HQ-84-14-G-0059.

Master equation for a kinetic model of a trading market and its analytic solution

NASA Astrophysics Data System (ADS)

Chatterjee, Arnab; Chakrabarti, Bikas K.; Stinchcombe, Robin B.

2005-08-01

We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index ν exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases.

Master equation for a kinetic model of a trading market and its analytic solution.

PubMed

Chatterjee, Arnab; Chakrabarti, Bikas K; Stinchcombe, Robin B

2005-08-01

We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index nu exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases.

Noether symmetries and stability of ideal gas solutions in Galileon cosmology

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Jamal, Sameerah; Leon, Genly; Paliathanasis, Andronikos

2017-03-01

A class of generalized Galileon cosmological models, which can be described by a pointlike Lagrangian, is considered in order to utilize Noether's theorem to determine conservation laws for the field equations. In the Friedmann-Lemaître-Robertson-Walker universe, the existence of a nontrivial conservation law indicates the integrability of the field equations. Because of the complexity of the latter, we apply the differential invariants approach in order to construct special power-law solutions and study their stability.

40 CFR 1065.645 - Amount of water in an ideal gas.

Code of Federal Regulations, 2010 CFR

2010-07-01

... vapor pressure of water in paragraph (a) of this section or another appropriate equation and, depending...) or (c) of this section. (a) Vapor pressure of water. Calculate the vapor pressure of water for a... different relationship of the vapor pressure of water to a given saturation temperature condition: (1) For...

Simulations of Neon Pellets for Plasma Disruption Mitigation in Tokamaks

NASA Astrophysics Data System (ADS)

Bosviel, Nicolas; Samulyak, Roman; Parks, Paul

2017-10-01

Numerical studies of the ablation of neon pellets in tokamaks in the plasma disruption mitigation parameter space have been performed using a time-dependent pellet ablation model based on the front tracking code FronTier-MHD. The main features of the model include the explicit tracking of the solid pellet/ablated gas interface, a self-consistent evolving potential distribution in the ablation cloud, JxB forces, atomic processes, and an improved electrical conductivity model. The equation of state model accounts for atomic processes in the ablation cloud as well as deviations from the ideal gas law in the dense, cold layers of neon gas near the pellet surface. Simulations predict processes in the ablation cloud and pellet ablation rates and address the sensitivity of pellet ablation processes to details of physics models, in particular the equation of state.

Investigating the effects of critical phenomena in premixed methane-oxygen flames at cryogenic conditions

NASA Astrophysics Data System (ADS)

Gopal, Abishek; Yellapantula, Shashank; Larsson, Johan

2017-11-01

Methane is increasingly becoming viable as a rocket fuel in the latest generation of launch vehicles. In liquid rocket engines, fuel and oxidizer are injected under cryogenic conditions into the combustion chamber. At high pressures, typical of rocket combustion chambers, the propellants exist in supercritical states where the ideal gas thermodynamics are no longer valid. We investigate the effects of real-gas thermodynamics on transcritical laminar premixed methane-oxygen flames. The effect of the real-gas cubic equations of state and high-pressure transport properties on flame dynamics is presented. We also study real-gas effects on the extinction limits of the methane-oxygen flame.

On real statistics of relaxation in gases

NASA Astrophysics Data System (ADS)

Kuzovlev, Yu. E.

2016-02-01

By example of a particle interacting with ideal gas, it is shown that the statistics of collisions in statistical mechanics at any value of the gas rarefaction parameter qualitatively differ from that conjugated with Boltzmann's hypothetical molecular chaos and kinetic equation. In reality, the probability of collisions of the particle in itself is random. Because of that, the relaxation of particle velocity acquires a power-law asymptotic behavior. An estimate of its exponent is suggested on the basis of simple kinematic reasons.

Van der Waals equation of state revisited: importance of the dispersion correction.

PubMed

de Visser, Sam P

2011-04-28

One of the most basic equations of state describing nonideal gases and liquids is the van der Waals equation of state, and as a consequence, it is generally taught in most first year undergraduate chemistry courses. In this work, we show that the constants a and b in the van der Waals equation of state are linearly proportional to the polarizability volume of the molecules in a gas or liquid. Using this information, a new thermodynamic one-parameter equation of state is derived that contains experimentally measurable variables and physics constants only. This is the first equation of state apart from the Ideal Gas Law that contains experimentally measurable variables and physics constants only, and as such, it may be a very useful and practical equation for the description of dilute gases and liquids. The modified van der Waals equation of state describes pV as the sum of repulsive and attractive intermolecular interaction energies that are represented by an exponential repulsion function between the electron clouds of the molecules and a London dispersion component, respectively. The newly derived equation of state is tested against experimental data for several gas and liquid examples, and the agreement is satisfactory. The description of the equation of state as a one-parameter function also has implications on other thermodynamic functions, such as critical parameters, virial coefficients, and isothermal compressibilities. Using our modified van der Waals equation of state, we show that all of these properties are a function of the molecular polarizability volume. Correlations of experimental data confirm the derived proportionalities.

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I. P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

NASA Technical Reports Server (NTRS)

Shih, T. I-P.; Yang, S. L.; Schock, H. J.

1986-01-01

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Strong imploding shock - The representative curve

NASA Astrophysics Data System (ADS)

Mishkin, E. A.; Alejaldre, C.

1981-02-01

The representative curve of the ideal gas behind the front of a spherically or cylindrically asymmetric strong imploding shock is derived. The partial differential equations of mass, momentum and energy conservation are reduced to a set of ordinary differential equations by the method of quasi-separation of variables, following which the reduced pressure and density as functions of the radius with respect to the shock front are explicit functions of coordinates defining the phase plane of the self-similar solution. The curve in phase space representing the state of the imploded gas behind the shock front is shown to pass through the point where the reduced pressure is maximum, which is located somewhat behind the shock front and ahead of the tail of the shock.

Analytic Modeling of the Hydrodynamic, Thermal, and Structural Behavior of Foil Thrust Bearings

NASA Technical Reports Server (NTRS)

Bruckner, Robert J.; DellaCorte, Christopher; Prahl, Joseph M.

2005-01-01

A simulation and modeling effort is conducted on gas foil thrust bearings. A foil bearing is a self acting hydrodynamic device capable of separating stationary and rotating components of rotating machinery by a film of air or other gaseous lubricant. Although simple in appearance these bearings have proven to be complicated devices in analysis. They are sensitive to fluid structure interaction, use a compressible gas as a lubricant, may not be in the fully continuum range of fluid mechanics, and operate in the range where viscous heat generation is significant. These factors provide a challenge to the simulation and modeling task. The Reynolds equation with the addition of Knudsen number effects due to thin film thicknesses is used to simulate the hydrodynamics. The energy equation is manipulated to simulate the temperature field of the lubricant film and combined with the ideal gas relationship, provides density field input to the Reynolds equation. Heat transfer between the lubricant and the surroundings is also modeled. The structural deformations of the bearing are modeled with a single partial differential equation. The equation models the top foil as a thin, bending dominated membrane whose deflections are governed by the biharmonic equation. A linear superposition of hydrodynamic load and compliant foundation reaction is included. The stiffness of the compliant foundation is modeled as a distributed stiffness that supports the top foil. The system of governing equations is solved numerically by a computer program written in the Mathematica computing environment. Representative calculations and comparisons with experimental results are included for a generation I gas foil thrust bearing.

An Undergraduate Exercise in the First Law of Relativistic Thermodynamics

ERIC Educational Resources Information Center

Guemez, J.

2010-01-01

The isothermal compression of an ideal gas is analysed using a relativistic thermodynamics formalism based on the principle of inertia of energy (Einstein's equation) and the asynchronous formulation (Cavalleri and Salgarelli 1969 "Nuovo Cimento" 42 722-54), which is similar to the formalism developed by van Kampen (1968 "Phys. Rev." 173 295-301)…

SOIL-AIR PERMEABILITY MEASUREMENT WITH A TRANSIENT PRESSURE BUILDUP METHOD

EPA Science Inventory

An analytical solution for transient pressure change in a single venting well was derived from mass conservation of air, Darcy's law of flow in porous media, and the ideal gas law equation of state. Slopes of plots of Pw2 against ln (t+Δt)/Δt similar to Homer's plot were used to ...

A Graphical Representation for the Fugacity of a Pure Substance

ERIC Educational Resources Information Center

Book, Neil L.; Sitton, Oliver C.

2010-01-01

The thermodynamic equations used to define and compute the fugacity of a pure substance are depicted as processes on a semi-logarithmic plot of pressure vs. molar Gibbs energy (PG diagram) with isotherms for the substance behaving as an ideal gas superimposed. The PG diagram clearly demonstrates the physical basis for the definitions and the…

A Simple Method for Determination of the Density of Granular Materials

ERIC Educational Resources Information Center

Tsutsumanova, G. G.; Kirilov, K. M.; Russev, S. C.

2012-01-01

A simple experiment using low cost equipment for the determination of the density of granular materials, without immersing them in a liquid, is presented. It is based only on the ideal gas state equation, so it is a good experimental task for undergraduate and high school students. (Contains 2 tables and 5 figures.)

Simulation of hot spots formation and evolution in HMX

NASA Astrophysics Data System (ADS)

Wang, Cheng; Yang, Tonghui

2017-06-01

In order to study the formation and evolution of hot spots under shock loading, HMX explosives were selected as the object of study for the two-dimensional finite difference numerical simulation. A fifth order finite difference weighted essentially non-oscillatory (WENO) scheme and a third order TVD Runge-Kutta method are utilized for the spatial discretization and the time advance, respectively. The governing equations are based on the fluid elasto-plastic control equations. The Mie-Gruneisen equation of state and the ideal gas equation of state are selected to use in the state equation of the solid explosives and gas material. In order to simplify the calculation of the model, the reaction can be considered to complete in one step. The calculated area is [ 3.0 ×10-5 m ] × [ 3.0 ×10-5 m ] . The radius is 0.6 ×10-5 m, and the internal gas is not involved in the reaction. The calculation area is divided into 300×300 grids and 10 grids are selected from the bottom of each column to give the particle velocity u as the initial condition. In the selected grid, different initial velocity 100m/s and 200m/s are loaded respectively to study the influence of hot spot formation and evolution in different impact intensity.

Quasiconservation laws for compressible three-dimensional Navier-Stokes flow.

PubMed

Gibbon, J D; Holm, D D

2012-10-01

We formulate the quasi-Lagrangian fluid transport dynamics of mass density ρ and the projection q=ω·∇ρ of the vorticity ω onto the density gradient, as determined by the three-dimensional compressible Navier-Stokes equations for an ideal gas, although the results apply for an arbitrary equation of state. It turns out that the quasi-Lagrangian transport of q cannot cross a level set of ρ. That is, in this formulation, level sets of ρ (isopycnals) are impermeable to the transport of the projection q.

Implementation of ECIRR model based on virtual simulation media to reduce students’ misconception on kinetic theory of gases

NASA Astrophysics Data System (ADS)

Prastiwi, A. C.; Kholiq, A.; Setyarsih, W.

2018-03-01

The purposed of this study are to analyse reduction of students’ misconceptions after getting ECIRR with virtual simulation. The design of research is the pre-experimental design with One Group Pretest-Posttest Design. Subjects of this research were 36 students of class XI MIA-5 SMAN 1 Driyorejo Gresik 2015/2016 school year. Students misconceptions was determined by Three-tier Diagnostic Test. The result shows that the average percentage of misconceptions reduced on topics of ideal gas law, equation of ideal gases and kinetic theory of gases respectively are 38%, 34% and 38%.

Quantifying real-gas effects on a laminar n-dodecane - air premixed flame

NASA Astrophysics Data System (ADS)

Gopal, Abishek; Yellapantula, Shashank; Larsson, Johan

2015-11-01

With the increasing demand for higher efficiencies in aircraft gas-turbine engines, there has been a progressive march towards high pressure-ratio cycles. Under these conditions, the aviation fuel, Jet A, is injected into the combustor at supercritical pressures. In this work, we study and quantify the effects of transcriticality on a 1D freely propagating laminar n-dodecane - air premixed flame. The impact of the constitutive state relations arising from the Ideal Gas equation of state(EOS) and Peng-Robinson EOS on flame structure and propagation is presented. The effects of real-gas models of transport properties, such as viscosity on laminar flame speed, are also presented.

A 3D Model for Gas Transfer, Storage and Resulting Displacement in a Permeable Volcanic Edifice

NASA Astrophysics Data System (ADS)

Collinson, Amy; Neuberg, Jurgen

2014-05-01

The total volume of gas in a magma, dissolved and subsequently exsolved, greatly influences the degree of explosiveness of a volcanic system. There is a marked contrast between the behaviour of a volcano in an open system compared to one which is closed. Whilst gas release is evident from surface gas emission measurements, gas storage is also thought to play an important role, as evidenced by large gas emissions after some large dome collapse events, suggesting gas may be stored in large volumes at shallow depths within the dome and edifice. Consequently, it is essential to understand degassing, to appreciate how much gas may be stored and where, and under what conditions it may be transferred or emitted to the atmosphere. We use previous experimental data on permeabilities to create 3D numerical models to investigate gas transport and storage in a permeable volcanic edifice. We combine the continuity equation, Darcy's law and the ideal gas law to derive a partial differential equation which is solved using a finite element method to obtain the gas pressure. The associated pressure gradient is then used within Darcy's law to calculate the gas velocity. In addition, we use the momentum equation to investigate how the presence of gas and variations in permeability influence the rate and degree of deformation in the volcanic edifice. Hence this provides two important surface constraints: gas emissions and surface displacement. Geometries are created to simulate the topography of actual volcanoes and the pressure and permeabilities incorporated into the model as boundary and domain conditions, respectively. This method is applied to investigate a variety of volcanological phenomena affecting gas, for example regions of high permeability due to fractures, or low permeability due to sealing.

One-dimensional flows of an imperfect diatomic gas

NASA Technical Reports Server (NTRS)

1959-01-01

With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author)

Design of structure and simulation of the three-zone gasifier of dense layer of the inverted process

NASA Astrophysics Data System (ADS)

Zagrutdinov, R. Sh; Negutorov, V. N.; Maliykhin, D. G.; Nikishanin, M. S.; Senachin, P. K.

2017-11-01

Experts of LLC “New Energy Technologies” have developed gasifiers designs, with the implementation of the three-zone gasification method, which satisfy the following conditions: 1) the generated gas must be free from tar, soot and hydrocarbons, with a given ratio of CO/H2; 2) to use as the fuel source a wide range of low-grade low-value solid fuels, including biomass and various kinds of carbonaceous wastes; 3) have high reliability in operation, do not require qualified operating personnel, be relatively inexpensive to produce and use steam-air blowing instead of expensive steam-oxygen one; 4) the line of standard sizes should be sufficiently wide (with a single unit capacity of fuel from 1 to 50-70 MW). Two models of gas generators of the inverted gasification process with three combustion zones operating under pressure have been adopted for design: 1) gas generator with a remote combustion chamber type GOP-VKS (two-block version) and 2) a gas generator with a common combustion chamber of the GOP-OK type (single-block version), which is an almost ideal model for increasing the unit capacity. There have been worked out various schemes for the preparation of briquettes from practically the entire spectrum of low-grade fuel: high-ash and high-moisture coals, peat and biomass, including all types of waste - solid household waste, crop, livestock, poultry, etc. In the gas generators there are gasified the cylindrical briquettes with a diameter of 20-25 mm and a length of 25-35 mm. There have been developed a mathematical model and computer code for numerical simulation of synthesis gas generation processes in a gasifier of a dense layer of inverted process during a steam-air blast, including: continuity equations for the 8 gas phase components and for the solid phase; the equation of the heat balance for the entire heterogeneous system; the Darcy law equation (for porous media); equation of state for 8 components of the gas phase; equations for the rates of 3 gas-phase and 4 heterogeneous reactions; macro kinetics law of coke combustion; other equations and boundary conditions.

SIERRA/Aero Theory Manual Version 4.46.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal/Fluid Team

2017-09-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, themore » governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.« less

SIERRA/Aero Theory Manual Version 4.44

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal /Fluid Team

2017-04-01

SIERRA/Aero is a two and three dimensional, node-centered, edge-based finite volume code that approximates the compressible Navier-Stokes equations on unstructured meshes. It is applicable to inviscid and high Reynolds number laminar and turbulent flows. Currently, two classes of turbulence models are provided: Reynolds Averaged Navier-Stokes (RANS) and hybrid methods such as Detached Eddy Simulation (DES). Large Eddy Simulation (LES) models are currently under development. The gas may be modeled either as ideal, or as a non-equilibrium, chemically reacting mixture of ideal gases. This document describes the mathematical models contained in the code, as well as certain implementation details. First, themore » governing equations are presented, followed by a description of the spatial discretization. Next, the time discretization is described, and finally the boundary conditions. Throughout the document, SIERRA/ Aero is referred to simply as Aero for brevity.« less

Mixing of the Interstellar and Solar Plasmas at the Heliospheric Interface

DOE PAGES

Pogorelov, N. V.; Borovikov, S. N.

2015-10-12

From the ideal MHD perspective, the heliopause is a tangential discontinuity that separates the solar wind plasma from the local interstellar medium plasma. There are physical processes, however, that make the heliopause permeable. They can be subdivided into kinetic and MHD categories. Kinetic processes occur on small length and time scales, and cannot be resolved with MHD equations. On the other hand, MHD instabilities of the heliopause have much larger scales and can be easily observed by spacecraft. The heliopause may also be a subject of magnetic reconnection. In this paper, we discuss mechanisms of plasma mixing at the heliopausemore » in the context of Voyager 1 observations. Numerical results are obtained with a Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS), which is a package of numerical codes capable of performing adaptive mesh refinement simulations of complex plasma flows in the presence of discontinuities and charge exchange between ions and neutral atoms. The flow of the ionized component is described with the ideal MHD equations, while the transport of atoms is governed either by the Boltzmann equation or multiple Euler gas dynamics equations. The code can also treat nonthermal ions and turbulence produced by them.« less

Use of 'ideal' alveolar air equations and corrected end-tidal PCO2 to estimate arterial PCO2 and physiological dead space during exercise in patients with heart failure.

PubMed

Van Iterson, Erik H; Olson, Thomas P

2018-01-01

Arterial CO 2 tension (PaCO 2 ) and physiological dead space (V D ) are not routinely measured during clinical cardiopulmonary exercise testing (CPET). Abnormal changes in PaCO 2 accompanied by increased V D directly contribute to impaired exercise ventilatory function in heart failure (HF). Because arterial catheterization is not standard practice during CPET, this study tested the construct validity of PaCO 2 and V D prediction models using 'ideal' alveolar air equations and basic ventilation and gas-exchangegas exchange measurements during CPET in HF. Forty-seven NYHA class II/III HF (LVEF=21±7%; age=55±9years; male=89%; BMI=28±5kg/m 2 ) performed step-wise cycle ergometry CPET to volitional fatigue. Breath-by-breath ventilation and gas exchange were measured continuously. Steady-state PaCO 2 was measured at rest and peak exercise via radial arterial catheterization. Criterion V D was calculated via 'ideal' alveolar equations, whereas PaCO 2 or V D models were based on end-tidal CO 2 tension (P ET CO 2 ), tidal volume (V T ), and/or weight. Criterion measurements of PaCO 2 (38±5 vs. 33±5mmHg, P<0.01) and V D (0.26±0.07 vs. 0.41±0.15L, P<0.01) differed at rest vs. peak exercise, respectively. The equation, 5.5+0.90×P ET CO 2 -0.0021×V T , was the strongest predictor of PaCO 2 at rest and peak exercise (bias±95%LOA=-3.24±6.63 and -0.98±5.76mmHg; R 2 =0.57 and 0.75, P<0.001, respectively). This equation closely predicted V D at rest and peak exercise (bias±95%LOA=-0.03±0.06 and -0.02±0.13L; R 2 =0.86 and 0.83, P<0.001, respectively). These data suggest predicted PaCO 2 and V D based on breath-by-breath gas exchange and ventilatory responses demonstrate acceptable agreement with criterion measurements at peak exercise in HF patients. Routine assessment of PaCO 2 and V D can be used to improve interpretability of exercise ventilatory responses in HF. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

The Osher scheme for real gases

NASA Technical Reports Server (NTRS)

Suresh, Ambady; Liou, Meng-Sing

1990-01-01

An extension of Osher's approximate Riemann solver to include gases with an arbitrary equation of state is presented. By a judicious choice of thermodynamic variables, the Riemann invariats are reduced to quadratures which are then approximated numerically. The extension is rigorous and does not involve any further assumptions or approximations over the ideal gas case. Numerical results are presented to demonstrate the feasibility and accuracy of the proposed method.

COED Transactions, Vol. 8, No. 10, October 1976. The Computer Generation of Thermodynamic Phase Diagrams.

ERIC Educational Resources Information Center

Jolls, Kenneth R.; And Others

A technique is described for the generation of perspective views of three-dimensional models using computer graphics. The technique is applied to models of familiar thermodynamic phase diagrams and the results are presented for the ideal gas and van der Waals equations of state as well as the properties of liquid water and steam from the Steam…

Structural characterization/correlation of calorimetric properties of coal fluids: Final report, September 1, 1985--August 31, 1988

DOE Office of Scientific and Technical Information (OSTI.GOV)

Starling, K.E.; Mallinson, R.G.; Li, M.H.

The objective of this research is to examine the relationship between the calorimetric properties of coal fluids and their molecular functional group composition. Coal fluid samples which have had their calorimetric properties measured are characterized using proton NMR, IR, and elemental analysis. These characterizations are then used in a chemical structural model to determine the composition of the coal fluid in terms of the important molecular functional groups. These functional groups are particularly important in determining the intramolecular based properties of a fluid, such as ideal gas heat capacities. Correlational frameworks for ideal gas heat capacities are then examined withinmore » an existing equation of state methodology to determine an optimal correlation. The optimal correlation for obtaining the characterization/chemical structure information and the sensitivity of the correlation to the characterization and structural model is examined. 8 refs.« less

Structural characterization/correlation of calorimetric properties of coal fluids: Second annual report, September 1, 1986-August 31, 1987

DOE Office of Scientific and Technical Information (OSTI.GOV)

Starling, K.E.; Mallinson, R.G.; Li, M.H.

The objective of this research is to examine the relationship between the calorimetric properties of coal fluids and their molecular functional group composition. Coal fluid samples which have had their calorimetric properties measured are characterized using proton NMR, ir, and elemental analysis. These characterizations are then used in a chemical structural model to determine the composition of the coal fluid in terms of the important molecular functional groups. These functional groups are particularly important in determining the intramolecular based properties of a fluid, such as ideal gas heat capacities. Correlational frameworks for ideal gas heat capacities are then examined withinmore » an existing equation of state methodology to determine an optimal correlation. The optimal correlation for obtaining the characterization/chemical structure information and the sensitivity of the correlation to the characterization and structural model is examined.« less

New wrinkles on black hole perturbations: Numerical treatment of acoustic and gravitational waves

NASA Astrophysics Data System (ADS)

Tenyotkin, Valery

2009-06-01

This thesis develops two main topics. A full relativistic calculation of quasinormal modes of an acoustic black hole is carried out. The acoustic black hole is formed by a perfect, inviscid, relativistic, ideal gas that is spherically accreting onto a Schwarzschild black hole. The second major part is the calculation of sourceless vector (electromagnetic) and tensor (gravitational) covariant field evolution equations for perturbations on a Schwarzschild background using the relatively recent [Special characters omitted.] decomposition method. Scattering calculations are carried out in Schwarzschild coordinates for electromagnetic and gravitational cases as validation of the method and the derived equations.

Classical and Quantum Thermal Physics

NASA Astrophysics Data System (ADS)

Prasad, R.

2016-11-01

List of figures; List of tables; Preface; Acknowledgement; Dedication; 1. The kinetic theory of gases; 2. Ideal to real gas, viscosity, conductivity and diffusion; 3. Thermodynamics: definitions and Zeroth law; 4. First Law of Thermodynamics and some of its applications; 5. Second Law of Thermodynamics and some of its applications; 6. TdS equations and their applications; 7. Thermodynamic functions, potentials, Maxwell equations, the Third Law and equilibrium; 8. Some applications of thermodynamics to problems of physics and engineering; 9. Application of thermodynamics to chemical reactions; 10. Quantum thermodynamics; 11. Some applications of quantum thermodynamics; 12. Introduction to the thermodynamics of irreversible processes; Index.

Effect of minimal length uncertainty on the mass-radius relation of white dwarfs

NASA Astrophysics Data System (ADS)

Mathew, Arun; Nandy, Malay K.

2018-06-01

Generalized uncertainty relation that carries the imprint of quantum gravity introduces a minimal length scale into the description of space-time. It effectively changes the invariant measure of the phase space through a factor (1 + βp2) - 3 so that the equation of state for an electron gas undergoes a significant modification from the ideal case. It has been shown in the literature (Rashidi 2016) that the ideal Chandrasekhar limit ceases to exist when the modified equation of state due to the generalized uncertainty is taken into account. To assess the situation in a more complete fashion, we analyze in detail the mass-radius relation of Newtonian white dwarfs whose hydrostatic equilibria are governed by the equation of state of the degenerate relativistic electron gas subjected to the generalized uncertainty principle. As the constraint of minimal length imposes a severe restriction on the availability of high momentum states, it is speculated that the central Fermi momentum cannot have values arbitrarily higher than pmax ∼β - 1 / 2. When this restriction is imposed, it is found that the system approaches limiting mass values higher than the Chandrasekhar mass upon decreasing the parameter β to a value given by a legitimate upper bound. Instead, when the more realistic restriction due to inverse β-decay is considered, it is found that the mass and radius approach the values 1.4518 M⊙ and 601.18 km near the legitimate upper bound for the parameter β.

A pressure relaxation closure model for one-dimensional, two-material Lagrangian hydrodynamics based on the Riemann problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamm, James R; Shashkov, Mikhail J

2009-01-01

Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on the problem of closing a system of equations for a two-material cell under the assumption of a single velocity model. There are several existing models and approaches, each possessing different levels of fidelity to the underlying physics and each exhibiting unique features in the computed solutions. We consider the case in which the change in heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast asmore » four equations in four unknowns, comprised of the updated values of the specific internal energy and the specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which the updated values of the sub-cell, relaxing-toward-equilibrium constituent pressures are related to a local Riemann problem through an optimization principle. This approach couples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the framework of a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equations of state and compare these results to those computed with the method of Tipton and with corresponding pure-material calculations.« less

Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization

NASA Astrophysics Data System (ADS)

Pu, Shi; Roy, Victor; Rezzolla, Luciano; Rischke, Dirk H.

2016-04-01

We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a nonzero magnetization. First, we assume a constant magnetic susceptibility χm and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with χm>0 ), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with χm<0 ), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time τ with a power law ˜τ-a, two distinct solutions can be found depending on the values of a and χm. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the nonvanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. It is only for magnetic fields about an order of magnitude larger than expected for heavy-ion collisions that the system is substantially reheated and the lifetime of the quark phase might be extended.

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Application of a flux-split algorithm to chemically relaxing, hypervelocity blunt-body flows

NASA Technical Reports Server (NTRS)

Balakrishnan, A.

1987-01-01

Viscous, nonequilibrium, hypervelocity flow fields over two axisymmetric configurations are numerically simulated using a factored, implicit, flux-split algorithm. The governing gas-dynamic and species-continuity equations for laminar flow are presented. The gas-dynamics/nonequilibrium-chemistry coupling procedure is developed as part of the solution procedure and is described in detail. Numerical solutions are presented for hypervelocity flows over a hemisphere and over an axisymmetric aeroassisted orbital transfer vehicle using three different chemistry models. The gas models considered are those for an ideal gas, for a frozen gas, and for chemically relaxing air consisting of five species. The calculated results are compared with existing numerical solutions in the literature along the stagnation line of the hemisphere. The effects of free-stream Reynolds number on the nonequilibrium flow field are discussed.

Active ideal sedimentation: exact two-dimensional steady states.

PubMed

Hermann, Sophie; Schmidt, Matthias

2018-02-28

We consider an ideal gas of active Brownian particles that undergo self-propelled motion and both translational and rotational diffusion under the influence of gravity. We solve analytically the corresponding Smoluchowski equation in two space dimensions for steady states. The resulting one-body density is given as a series, where each term is a product of an orientation-dependent Mathieu function and a height-dependent exponential. A lower hard wall is implemented as a no-flux boundary condition. Numerical evaluation of the suitably truncated analytical solution shows the formation of two different spatial regimes upon increasing Peclet number. These regimes differ in their mean particle orientation and in their variation of the orientation-averaged density with height.

Analysis of a Multi-Fidelity Surrogate for Handling Real Gas Equations of State

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Rollin, Bertrand; Balachandar, S.

2017-06-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the detonation products of the explosive must be treated as real gas while the ideal gas equation of state is used for the surrounding air. As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both state equations must be satisfied. One of the most accurate, yet computationally expensive, methods to handle this problem is an algorithm that iterates between both equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work aims to use a multi-fidelity surrogate model to replace this process. A Kriging model is used to produce a curve fit which interpolates selected data from the iterative algorithm using Bayesian statistics. We study the model performance with respect to the iterative method in simulations using a finite volume code. The model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel approach. Also, optimizing the combination of model accuracy and computational speed through the choice of sampling points is explained. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program as a Cooperative Agreement under the Predictive Science Academic Alliance Program under Contract No. DE-NA0002378.

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Denicol, Gabriel S.; Noronha, Jorge

2018-03-01

We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with an ideal gas equation of state and a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.

Shock implosion of a small homogeneous pellet

NASA Astrophysics Data System (ADS)

Fujimoto, Yasuichi; Mishkin, Eli A.; Alejaldre, Carlos

1985-10-01

A small spherical, or cylindrical, pellet is imploded by an intensive, evenly distributed, short energy pulse. At the surface of the pellet the matter ionizes, its temperature and pressure rapidly rise, and the ablated plasma, by reaction, implodes the inner nucleus of the pellet. The involved structure of the energy absorbing zone is idealized and a sharp deflagration front is considered. With an almost square energy pulse, slightly dropping with time, the solution of the mass, momentum, and energy conservation equations of the compressed matter, is self-similar. The differential equation of the nondimensional position of the deflagration front, its integral, and the magnitude and shape of the outside energy pulse are derived. The process of ablation is shown to depend solely on the nondimensional velocity of the gas just ahead of the deflagration front, minus the speed of sound, or the ratio of the gas densities across the deflagration front.

A Two-moment Radiation Hydrodynamics Module in ATHENA Using a Godunov Method

NASA Astrophysics Data System (ADS)

Skinner, M. A.; Ostriker, E. C.

2013-04-01

We describe a module for the Athena code that solves the grey equations of radiation hydrodynamics (RHD) using a local variable Eddington tensor (VET) based on the M1 closure of the two-moment hierarchy of the transfer equation. The variables are updated via a combination of explicit Godunov methods to advance the gas and radiation variables including the non-stiff source terms, and a local implicit method to integrate the stiff source terms. We employ the reduced speed of light approximation (RSLA) with subcycling of the radiation variables in order to reduce computational costs. The streaming and diffusion limits are well-described by the M1 closure model, and our implementation shows excellent behavior for problems containing both regimes simultaneously. Our operator-split method is ideally suited for problems with a slowly-varying radiation field and dynamical gas flows, in which the effect of the RSLA is minimal.

Linear dependence of surface expansion speed on initial plasma temperature in warm dense matter

DOE PAGES

Bang, Woosuk; Albright, Brian James; Bradley, Paul Andrew; ...

2016-07-12

Recent progress in laser-driven quasi-monoenergetic ion beams enabled the production of uniformly heated warm dense matter. Matter heated rapidly with this technique is under extreme temperatures and pressures, and promptly expands outward. While the expansion speed of an ideal plasma is known to have a square-root dependence on temperature, computer simulations presented here show a linear dependence of expansion speed on initial plasma temperature in the warm dense matter regime. The expansion of uniformly heated 1–100 eV solid density gold foils was modeled with the RAGE radiation-hydrodynamics code, and the average surface expansion speed was found to increase linearly withmore » temperature. The origin of this linear dependence is explained by comparing predictions from the SESAME equation-of-state tables with those from the ideal gas equation-of-state. In conclusion, these simulations offer useful insight into the expansion of warm dense matter and motivate the application of optical shadowgraphy for temperature measurement.« less

Toward Better Modeling of Supercritical Turbulent Mixing

NASA Technical Reports Server (NTRS)

Selle, Laurent; Okongo'o, Nora; Bellan, Josette; Harstad, Kenneth

2008-01-01

study was done as part of an effort to develop computational models representing turbulent mixing under thermodynamic supercritical (here, high pressure) conditions. The question was whether the large-eddy simulation (LES) approach, developed previously for atmospheric-pressure compressible-perfect-gas and incompressible flows, can be extended to real-gas non-ideal (including supercritical) fluid mixtures. [In LES, the governing equations are approximated such that the flow field is spatially filtered and subgrid-scale (SGS) phenomena are represented by models.] The study included analyses of results from direct numerical simulation (DNS) of several such mixing layers based on the Navier-Stokes, total-energy, and conservation- of-chemical-species governing equations. Comparison of LES and DNS results revealed the need to augment the atmospheric- pressure LES equations with additional SGS momentum and energy terms. These new terms are the direct result of high-density-gradient-magnitude regions found in the DNS and observed experimentally under fully turbulent flow conditions. A model has been derived for the new term in the momentum equation and was found to perform well at small filter size but to deteriorate with increasing filter size. Several alternative models were derived for the new SGS term in the energy equation that would need further investigations to determine if they are too computationally intensive in LES.

NEW APPROACHES: A hot air balloon from dustbin liners

NASA Astrophysics Data System (ADS)

Weaver, Nicholas

1998-07-01

This article describes how a simple hot air balloon, inflated by a hair dryer, can be made out of household bin liners and Sellotape. It can be used at sixth-form level as an application of the ideal gas equation, = constant, and is rather more exciting than heated pistons. It gives a taste of a simple engineering design process, although the students do have to be reasonably adept at geometry and algebra.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions.

PubMed

Latella, Ivan; Pérez-Madrid, Agustín

2013-10-01

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Supersonic beams at high particle densities: model description beyond the ideal gas approximation.

PubMed

Christen, Wolfgang; Rademann, Klaus; Even, Uzi

2010-10-28

Supersonic molecular beams constitute a very powerful technique in modern chemical physics. They offer several unique features such as a directed, collision-free flow of particles, very high luminosity, and an unsurpassed strong adiabatic cooling during the jet expansion. While it is generally recognized that their maximum flow velocity depends on the molecular weight and the temperature of the working fluid in the stagnation reservoir, not a lot is known on the effects of elevated particle densities. Frequently, the characteristics of supersonic beams are treated in diverse approximations of an ideal gas expansion. In these simplified model descriptions, the real gas character of fluid systems is ignored, although particle associations are responsible for fundamental processes such as the formation of clusters, both in the reservoir at increased densities and during the jet expansion. In this contribution, the various assumptions of ideal gas treatments of supersonic beams and their shortcomings are reviewed. It is shown in detail that a straightforward thermodynamic approach considering the initial and final enthalpy is capable of characterizing the terminal mean beam velocity, even at the liquid-vapor phase boundary and the critical point. Fluid properties are obtained using the most accurate equations of state available at present. This procedure provides the opportunity to naturally include the dramatic effects of nonideal gas behavior for a large variety of fluid systems. Besides the prediction of the terminal flow velocity, thermodynamic models of isentropic jet expansions permit an estimate of the upper limit of the beam temperature and the amount of condensation in the beam. These descriptions can even be extended to include spinodal decomposition processes, thus providing a generally applicable tool for investigating the two-phase region of high supersaturations not easily accessible otherwise.

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

One-dimensional model and solutions for creeping gas flows in the approximation of uniform pressure

NASA Astrophysics Data System (ADS)

Vedernikov, A.; Balapanov, D.

2016-11-01

A model, along with analytical and numerical solutions, is presented to describe a wide variety of one-dimensional slow flows of compressible heat-conductive fluids. The model is based on the approximation of uniform pressure valid for the flows, in which the sound propagation time is much shorter than the duration of any meaningful density variation in the system. The energy balance is described by the heat equation that is solved independently. This approach enables the explicit solution for the fluid velocity to be obtained. Interfacial and volumetric heat and mass sources as well as boundary motion are considered as possible sources of density variation in the fluid. A set of particular tasks is analyzed for different motion sources in planar, axial, and central symmetries in the quasistationary limit of heat conduction (i.e., for large Fourier number). The analytical solutions are in excellent agreement with corresponding numerical solutions of the whole system of the Navier-Stokes equations. This work deals with the ideal gas. The approach is also valid for other equations of state.

Axisymmetric ideal MHD stellar wind flow

NASA Technical Reports Server (NTRS)

Heinemann, M.; Olbert, S.

1978-01-01

The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.

Simplified combustion noise theory yielding a prediction of fluctuating pressure level

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The first order equations for the conservation of mass and momentum in differential form are combined for an ideal gas to yield a single second order partial differential equation in one dimension and time. Small perturbation analysis is applied. A Fourier transformation is performed that results in a second order, constant coefficient, nonhomogeneous equation. The driving function is taken to be the source of combustion noise. A simplified model describing the energy addition via the combustion process gives the required source information for substitution in the driving function. This enables the particular integral solution of the nonhomogeneous equation to be found. This solution multiplied by the acoustic pressure efficiency predicts the acoustic pressure spectrum measured in turbine engine combustors. The prediction was compared with the overall sound pressure levels measured in a CF6-50 turbofan engine combustor and found to be in excellent agreement.

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

NASA Astrophysics Data System (ADS)

Drivas, Theodore D.; Eyink, Gregory L.

2017-12-01

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

Sizes of nanobubbles from nucleation rate measurements

NASA Astrophysics Data System (ADS)

Wilemski, G.

2003-03-01

In homogeneous bubble nucleation, the critical nucleus typically has nanometer dimensions. The volume V of a critical bubble can be determined from the simple equation (partial W/partial p)_T=V, where W is the reversible work of nucleus formation and p is the ambient pressure of the liquid phase in which bubble formation is occurring. The relation, W/kT=-ln J+ln A, where J is the steady state nucleation rate and A is the weakly pressure-dependent kinetic prefactor, allows V to be determined from rate measurements. The original derivation of this equation for V from the nucleation theorem was limited to one-component, ideal gas bubbles with a gas density much smaller than that of the ambient liquid. [D. Kashchiev, Nucleation: basic theory with applications (Butterworth-Heinemann, Oxford, 2000) p. 226.] The result is actually much more general, and it will be shown that it applies to multi-component, nonideal gas bubbles, provided the same density inequality holds. When the bubble phase and liquid densities are comparable, a more complicated, but also general and rigorous result is found.

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

PubMed Central

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

MCDU-8-A Computer Code for One-Dimensional Blast Wave Problems

DTIC Science & Technology

1975-07-01

medium surrounding the explosion is assuned to be air obeying an ideal gas equation of state with a constant specific heat ratio, y2, of 1.4. The...characteristics Explosive blast Pentolite spheres ■ 20.\\ASSTRACT (Continue on reverie eld* II neceeemry end Identify by block number) he method...INVOLVING THE. SUDDEN RELEASE OF A HIGHLY COMPRESSED AIR SPHERE 11 V. A SAMPLE PROBLEM INVOLVING A BLAST WAVE RESULTING FROM THE DETONATION OF A

A Modified Benedict-Webb-Rubin Equation of State for the Thermodynamic Properties of R152a (1,1-difluoroethane)

NASA Astrophysics Data System (ADS)

Outcalt, Stephanie L.; McLinden, Mark O.

1996-03-01

A modified Benedict-Webb-Rubin (MBWR) equation of state has been developed for R152a (1,1-difluoroethane). The correlation is based on a selection of available experimental thermodynamic property data. Single-phase pressure-volume-temperature (PVT), heat capacity, and sound speed data, as well as second virial coefficient, vapor pressure, and saturated liquid and saturated vapor density data, were used with multi-property linear least-squares fitting to determine the 32 adjustable coefficients of the MBWR equation. Ancillary equations representing the vapor pressure, saturated liquid and saturated vapor densities, and the ideal gas heat capacity were determined. Coefficients for the equation of state and the ancillary equations are given. Experimental data used in this work covered temperatures from 162 K to 453 K and pressures to 35 MPa. The MBWR equation established in this work may be used to predict thermodynamic properties of R152a from the triple-point temperature of 154.56 K to 500 K and for pressures up to 60 MPa except in the immediate vicinity of the critical point.

Use of the Digamma Function in Statistical Astrophysics Distributions

NASA Astrophysics Data System (ADS)

Cahill, Michael

2017-06-01

Relaxed astrophysical statistical distributions may be constructed by using the inverse of a most probable energy distribution equation giving the energy ei of each particle in cell i in terms of the cell’s particle population Ni. The digamma mediated equation is A + Bei = Ψ(1+ Ni), where the constants A & B are Lagrange multipliers and Ψ is the digamma function given by Ψ(1+x) = dln(x!)/dx. Results are discussed for a Monatomic Ideal Gas, Atmospheres of Spherical Planets or Satellites and for Spherical Globular Clusters. These distributions are self-terminating even if other factors do not cause a cutoff. The examples are discussed classically but relativistic extensions are possible.

Tendency towards maximum complexity in a nonequilibrium isolated system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Calbet, Xavier; Lopez-Ruiz, Ricardo

2001-06-01

The time evolution equations of a simplified isolated ideal gas, the {open_quotes}tetrahedral{close_quotes} gas, are derived. The dynamical behavior of the Lopez-Ruiz{endash}Mancini{endash}Calbet complexity [R. Lopez-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A >209, 321 (1995)] is studied in this system. In general, it is shown that the complexity remains within the bounds of minimum and maximum complexity. We find that there are certain restrictions when the isolated {open_quotes}tetrahedral{close_quotes} gas evolves towards equilibrium. In addition to the well-known increase in entropy, the quantity called disequilibrium decreases monotonically with time. Furthermore, the trajectories of the system in phase space approach themore » maximum complexity path as it evolves toward equilibrium.« less

First and second sound in cylindrically trapped gases.

PubMed

Bertaina, G; Pitaevskii, L; Stringari, S

2010-10-08

We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wavelength limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wavelengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a nondissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.

Filamentation effect in a gas attenuator for high-repetition-rate X-ray FELs.

PubMed

Feng, Yiping; Krzywinski, Jacek; Schafer, Donald W; Ortiz, Eliazar; Rowen, Michael; Raubenheimer, Tor O

2016-01-01

A sustained filamentation or density depression phenomenon in an argon gas attenuator servicing a high-repetition femtosecond X-ray free-electron laser has been studied using a finite-difference method applied to the thermal diffusion equation for an ideal gas. A steady-state solution was obtained by assuming continuous-wave input of an equivalent time-averaged beam power and that the pressure of the entire gas volume has reached equilibrium. Both radial and axial temperature/density gradients were found and describable as filamentation or density depression previously reported for a femtosecond optical laser of similar attributes. The effect exhibits complex dependence on the input power, the desired attenuation, and the geometries of the beam and the attenuator. Time-dependent simulations were carried out to further elucidate the evolution of the temperature/density gradients in between pulses, from which the actual attenuation received by any given pulse can be properly calculated.

Navier-Stokes simulation of real gas flows in nozzles

NASA Technical Reports Server (NTRS)

Nagaraj, N.; Lombard, C. K.

1987-01-01

Air flow in a hypersonic nozzle causes real gas effects due to reaction among the species constituting air. Such reactions may be in chemical equilibrium or in chemical nonequilibrium. Here using the CSCM upwind scheme for the compressible Navier-Stokes equations, the real gas flowfield in an arcjet nozzle is computed for both the equilibrium case and the nonequilibrium case. A hypersonic nozzle flow arising from a pebble bed heated plenum is also computed for the equilibrium situation. Between the equilibrium cases, the chemistry is treated by two different schemes and comments are made as to computational complexity. For the nonequilibrium case, a full set of seventeen reactions and full implicit coupling of five species with gasdynamics is employed to compute the flowfield. For all cases considered here the gas is assumed to be a calorically imperfect mixture of ideal gases in thermal equilibrium.

Thermodynamic Properties of Low-Density {}^{132}Xe Gas in the Temperature Range 165-275 K

NASA Astrophysics Data System (ADS)

Akour, Abdulrahman

2018-01-01

The method of static fluctuation approximation was used to calculate selected thermodynamic properties (internal energy, entropy, energy capacity, and pressure) for xenon in a particularly low-temperature range (165-270 K) under different conditions. This integrated microscopic study started from an initial basic assumption as the main input. The basic assumption in this method was to replace the local field operator with its mean value, then numerically solve a closed set of nonlinear equations using an iterative method, considering the Hartree-Fock B2-type dispersion potential as the most appropriate potential for xenon. The results are in very good agreement with those of an ideal gas.

Phase equilibrium of methane and nitrogen at low temperatures - Application to Titan

NASA Technical Reports Server (NTRS)

Kouvaris, Louis C.; Flasar, F. M.

1991-01-01

Since the vapor phase composition of Titan's methane-nitrogen lower atmosphere is uniquely determined as a function of the Gibbs phase rule, these data are presently computed via integration of the Gibbs-Duhem equation. The thermodynamic consistency of published measurements and calculations of the vapor phase composition is then examined, and the saturated mole fraction of gaseous methane is computed as a function of altitude up to the 700-mbar level. The mole fraction is found to lie approximately halfway between that computed from Raoult's law, for a gas in equilibrium with an ideal solution of liquid nitrogen and methane, and that for a gas in equilibrium with pure liquid methane.

Chemical potentials and thermodynamic characteristics of ideal Bose- and Fermi-gases in the region of quantum degeneracy

NASA Astrophysics Data System (ADS)

Sotnikov, A. G.; Sereda, K. V.; Slyusarenko, Yu. V.

2017-01-01

Calculations of chemical potentials for ideal monatomic gases with Bose-Einstein and Fermi-Dirac statistics as functions of temperature, across the temperature region that is typical for the collective quantum degeneracy effect, are presented. Numerical calculations are performed without any additional approximations, and explicit dependences of the chemical potentials on temperature are constructed at a fixed density of gas particles. Approximate polynomial dependences of chemical potentials on temperature are obtained that allow for the results to be used in further studies without re-applying the involved numerical methods. The ease of using the obtained representations is demonstrated on examples of deformation of distribution for a population of energy states at low temperatures, and on the impact of quantum statistics (exchange interaction) on the equations of state for ideal gases and some of the thermodynamic properties thereof. The results of this study essentially unify two opposite limiting cases in an intermediate region that are used to describe the equilibrium states of ideal gases, which are well known from university courses on statistical physics, thus adding value from an educational point of view.

Solubility modeling of refrigerant/lubricant mixtures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Michels, H.H.; Sienel, T.H.

1996-12-31

A general model for predicting the solubility properties of refrigerant/lubricant mixtures has been developed based on applicable theory for the excess Gibbs energy of non-ideal solutions. In our approach, flexible thermodynamic forms are chosen to describe the properties of both the gas and liquid phases of refrigerant/lubricant mixtures. After an extensive study of models for describing non-ideal liquid effects, the Wohl-suffix equations, which have been extensively utilized in the analysis of hydrocarbon mixtures, have been developed into a general form applicable to mixtures where one component is a POE lubricant. In the present study we have analyzed several POEs wheremore » structural and thermophysical property data were available. Data were also collected from several sources on the solubility of refrigerant/lubricant binary pairs. We have developed a computer code (NISC), based on the Wohl model, that predicts dew point or bubble point conditions over a wide range of composition and temperature. Our present analysis covers mixtures containing up to three refrigerant molecules and one lubricant. The present code can be used to analyze the properties of R-410a and R-407c in mixtures with a POE lubricant. Comparisons with other models, such as the Wilson or modified Wilson equations, indicate that the Wohl-suffix equations yield more reliable predictions for HFC/POE mixtures.« less

Improving Students' Understanding of the Connections between the Concepts of Real-Gas Mixtures, Gas Ideal-Solutions, and Perfect-Gas Mixtures

ERIC Educational Resources Information Center

Privat, Romain; Jaubert, Jean-Noël; Moine, Edouard

2016-01-01

In many textbooks of chemical-engineering thermodynamics, a gas mixture obeying the fundamental law pV[subscript m] = RT is most often called ideal-gas mixture (in some rare cases, the term perfect-gas mixture can be found). These textbooks also define the fundamental concept of ideal solution which in theory, can be applied indifferently to…

Thermodynamic properties of seven gaseous halogenated hydrocarbons from acoustic measurements: CHClFCF3, CHF2 CF3, CF3 CH3, CHF2CH3, CF3CHFCHF2, CF3CH2CF3, and CHF2CF2CH2F

NASA Astrophysics Data System (ADS)

Gillis, K. A.

1997-01-01

Measurements of the speed of sound in seven halogenated hydrocarbons are presented. The compounds in this study are 1-chloro-1,2,2,2-tetrafluoroethane (CHClFCF3 or HCFC-124), pentafluoroethane (CHF2 CF3 or HFC-125), 1,1,1-trifluoroethane (CF3CH3 or HFC-143a), 1,1-difluoroethane (CHF2CH3 or HFC-152a), 1,1,1,2,3,3-hexafluoropropane (CF3CHFCHF2 or HFC-236ea), 1,1,1,3,3,3-hexafluoropropane (CF3CH2CF3 or HFC-236fa), and 1,1,2,2,3-pentafluoropropane (CHF2CF2CH2F or HFC-245ca). The measurements were performed with a cylindrical resonator at temperatures between 240 and 400 K and at pressures up to 1.0 MPa. Ideal-gas heat capacities and acoustic virial coefficients were directly deduced from the data. The ideal-gas heat capacity of HFC-125 from this work differs from spectroscopic calculations by less than 0.2% over the measurement range. The coefficients for virial equations of state were obtained from the acoustic data and hard-core square-well intermolecular potentials. Gas densities that were calculated from the virial equations of state for HCFC-124 and HFC-125 differ from independent density measurements by at most 0.15%, for the ranges of temperature and pressure over which both acoustic and Burnett data exist. The uncertainties in the derived properties for the other five compounds are comparable to those for HCFC-124 and HFC-125.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

PubMed

Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

2008-02-01

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald ripening (only one hole survives at the end), and we report a particular regime where the "hole ripening" statistics exhibits a simple dynamic scaling behavior.

Non-invasive measurement of the mean alveolar O(2) tension from the oxygen uptake versus tidal volume curve.

PubMed

Jordanoglou, J; Latsi, P; Chroneou, A; Koulouris, N G

2007-10-01

The classical equations for measuring the mean and the ideal alveolar O(2) tension are based on assumptions, which are shown to be invalid. So we thought to develop a new, non-invasive method for measuring the mean alveolar P,O(2) within the volume domain (PA,O(2(Bohr))). This method is based on the oxygen uptake vs. tidal volume curve (VO(2) vs. VT) obtained during tidal breathing of room air and/or air enriched with oxygen. PA,O(2(Bohr)) and the ideal alveolar PO(2) (PA,O(2(ideal))) were simultaneously measured in 10 healthy subjects and 34 patients suffering from chronic obstructive pulmonary disease (COPD) breathing tidally room air at rest. Additionally, 10 subjects (three healthy subjects and seven COPD patients) were studied while breathing initially room air and subsequently air enriched with oxygen. According to the results, PA,O(2(Bohr)) considerably differed from PA,O(2(ideal)) (P = 0.004). The cause of the difference, at the individual's R, is: (1) the difference between the arterial and Bohr's alveolar CO(2) tension, mainly in COPD patients, and (2) the inequality between Bohr's alveolar part of the tidal volume for CO(2) and O(2). Furthermore, end-tidal gas tension (PET,CO(2) and PET,O(2)) differed from Pa,CO(2) and PA,O(2(Bohr)) respectively. The deviation of PA,O(2(Bohr)) from PA,O(2(ideal)) has a definite impact on Bohr's dead space ratio for O(2) and CO(2), and on the alveolar-arterial O(2) difference. The difference (PA,O(2(Bohr)) - PA,O(2(ideal))) is not related to the pathology of the disease. So, gas exchange within the lungs should be assessed at the subject's R from PA,O(2(Bohr)) and PA,CO(2(Bohr)) but not from PA,O(2(ideal)) nor Pa,CO(2).

DOE Office of Scientific and Technical Information (OSTI.GOV)

Remming, Ian S.; Khokhlov, Alexei M.

We present general equations for non-ideal, reactive flow magnetohydrodynamics (RFMHD) in the form best suited for describing thermonuclear combustion in high-density degenerate matter of SNe Ia. The relative importance of various non-ideal effects is analyzed as a function of characteristic spatial and temporal scales of the problem. From the general RFMHD equations, we derive the one-dimensional ordinary differential equations describing the steady-state propagation of a planar thermonuclear flame front in a magnetic field. The physics of the flame is first studied qualitatively using a simple case of one-step Arrhenius kinetics, a perfect gas equation of state (EOS), and constant thermalmore » conductivity coefficients. After that, the equations are solved, the internal flame front structure is calculated, and the flame velocity, S {sub l} , and flame thickness, δ {sub l} , are found for carbon–oxygen degenerate material of supernovae using a realistic EOS, transport properties, and detailed nuclear kinetics. The magnetic field changes the flame behavior significantly, both qualitatively and quantitatively, as compared to the non-magnetic case of classical combustion. (1) The magnetic field influences the evolutionarity of a flame front and makes it impossible for a flame to propagate steadily in a wide range of magnetic field strengths and orientations relative to the front. (2) When the flame moves steadily, it can propagate in several distinct modes, the most important being the slow C {sub S} and super-Alfvénic C {sub sup} modes. (3) The speed of the flame can be diminished or enhanced by up to several factors relative to the non-magnetic laminar flame speed.« less

Multi-d CFD Modeling of a Free-piston Stirling Convertor at NASA Glenn

NASA Technical Reports Server (NTRS)

Wilson, Scott D.; Dyson, Rodger W.; Tew, Roy C.; Ibrahim, Mounir B.

2004-01-01

A high efficiency Stirling Radioisotope Generator (SRG) is being developed for possible use in long duration space science missions. NASA s advanced technology goals for next generation Stirling convertors include increasing the Carnot efficiency and percent of Carnot efficiency. To help achieve these goals, a multidimensional Computational Fluid Dynamics (CFD) code is being developed to numerically model unsteady fluid flow and heat transfer phenomena of the oscillating working gas inside Stirling convertors. Simulations of the Stirling convertors for the SRG will help characterize the thermodynamic losses resulting from fluid flow and heat transfer between the working gas and solid walls. The current CFD simulation represents approximated 2-dimensional convertor geometry. The simulation solves the Navier Stokes equations for an ideal helium gas oscillating at low speeds. The current simulation results are discussed.

Multi channel thermal hydraulic analysis of gas cooled fast reactor using genetic algorithm

NASA Astrophysics Data System (ADS)

Drajat, R. Z.; Su'ud, Z.; Soewono, E.; Gunawan, A. Y.

2012-05-01

There are three analyzes to be done in the design process of nuclear reactor i.e. neutronic analysis, thermal hydraulic analysis and thermodynamic analysis. The focus in this article is the thermal hydraulic analysis, which has a very important role in terms of system efficiency and the selection of the optimal design. This analysis is performed in a type of Gas Cooled Fast Reactor (GFR) using cooling Helium (He). The heat from nuclear fission reactions in nuclear reactors will be distributed through the process of conduction in fuel elements. Furthermore, the heat is delivered through a process of heat convection in the fluid flow in cooling channel. Temperature changes that occur in the coolant channels cause a decrease in pressure at the top of the reactor core. The governing equations in each channel consist of mass balance, momentum balance, energy balance, mass conservation and ideal gas equation. The problem is reduced to finding flow rates in each channel such that the pressure drops at the top of the reactor core are all equal. The problem is solved numerically with the genetic algorithm method. Flow rates and temperature distribution in each channel are obtained here.

The effect of intraocular gas and fluid volumes on intraocular pressure.

PubMed

Simone, J N; Whitacre, M M

1990-02-01

Large increases in the intraocular pressure (IOP) of postoperative gas-containing eyes may require the removal of gas or fluid to reduce the IOP to the normal range. Application of the ideal gas law to Friedenwald's equation provides a mathematical model of the relationship between IOP, intraocular gas and fluid volumes, and the coefficient of scleral rigidity. This mathematic model shows that removal of a given volume of gas or fluid produces an identical decrease in IOP and that the more gas an eye contains, the greater the volume reduction necessary to reduce the pressure. Application of the model shows that the effective coefficient of scleral rigidity is low (mean K, 0.0021) in eyes with elevated IOP that have undergone vitrectomy and retinal cryopexy and very low (mean K, 0.0013) in eyes with elevated IOP that have undergone placement of a scleral buckle and band. By using the appropriate mean coefficient of rigidity, the volume of material to be aspirated to produce a given decrease in IOP can be predicted with clinically useful accuracy.

Cellular Analysis of Boltzmann Most Probable Ideal Gas Statistics

NASA Astrophysics Data System (ADS)

Cahill, Michael E.

2018-04-01

Exact treatment of Boltzmann's Most Probable Statistics for an Ideal Gas of Identical Mass Particles having Translational Kinetic Energy gives a Distribution Law for Velocity Phase Space Cell j which relates the Particle Energy and the Particle Population according toB e(j) = A - Ψ(n(j) + 1)where A & B are the Lagrange Multipliers and Ψ is the Digamma Function defined byΨ(x + 1) = d/dx ln(x!)A useful sufficiently accurate approximation for Ψ is given byΨ(x +1) ≈ ln(e-γ + x)where γ is the Euler constant (≈.5772156649) & so the above distribution equation is approximatelyB e(j) = A - ln(e-γ + n(j))which can be inverted to solve for n(j) givingn(j) = (eB (eH - e(j)) - 1) e-γwhere B eH = A + γ& where B eH is a unitless particle energy which replaces the parameter A. The 2 approximate distribution equations imply that eH is the highest particle energy and the highest particle population isnH = (eB eH - 1) e-γwhich is due to the facts that population becomes negative if e(j) > eH and kinetic energy becomes negative if n(j) > nH.An explicit construction of Cells in Velocity Space which are equal in volume and homogeneous for almost all cells is shown to be useful in the analysis.Plots for sample distribution properties using e(j) as the independent variable are presented.

Collisions of ideal gas molecules with a rough/fractal surface. A computational study.

PubMed

Panczyk, Tomasz

2007-02-01

The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).

Test of a new heat-flow equation for dense-fluid shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2010-09-21

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.

Compressible convection in geophysical fluids: comparison of anelastic, anelastic liquid and full numerical simulations

NASA Astrophysics Data System (ADS)

Curbelo, Jezabel; Alboussiere, Thierry; Labrosse, Stephane; Dubuffet, Fabien; Ricard, Yanick

2015-11-01

In this talk we describe the numerical method implemented to study convection in a fully compressible two-dimensional model, which may be reduced to the different simplifications such as the anelastic approximation and the anelastic liquid approximation. Various equations of state are considered, from the ideal gas equation to equations related to liquid or solid condensed matter. We are particularly interested in the total value and spatial distribution of viscous dissipation. We analyze the solutions obtained with each approximation in a wide range of dimensionless parameters and compare the domain of validity of each of them. The authors are grateful to the LABEX Lyon Institute of Origins (ANR-10-LABX-0066) of the Universite de Lyon for its financial support ``Investissements d'Avenir'' (ANR-11-IDEX-0007) of the French government operated by the National Research Agency (ANR).

Compression of turbulent magnetized gas in giant molecular clouds

NASA Astrophysics Data System (ADS)

Birnboim, Yuval; Federrath, Christoph; Krumholz, Mark

2018-01-01

Interstellar gas clouds are often both highly magnetized and supersonically turbulent, with velocity dispersions set by a competition between driving and dissipation. This balance has been studied extensively in the context of gases with constant mean density. However, many astrophysical systems are contracting under the influence of external pressure or gravity, and the balance between driving and dissipation in a contracting, magnetized medium has yet to be studied. In this paper, we present three-dimensional magnetohydrodynamic simulations of compression in a turbulent, magnetized medium that resembles the physical conditions inside molecular clouds. We find that in some circumstances the combination of compression and magnetic fields leads to a rate of turbulent dissipation far less than that observed in non-magnetized gas, or in non-compressing magnetized gas. As a result, a compressing, magnetized gas reaches an equilibrium velocity dispersion much greater than would be expected for either the hydrodynamic or the non-compressing case. We use the simulation results to construct an analytic model that gives an effective equation of state for a coarse-grained parcel of the gas, in the form of an ideal equation of state with a polytropic index that depends on the dissipation and energy transfer rates between the magnetic and turbulent components. We argue that the reduced dissipation rate and larger equilibrium velocity dispersion has important implications for the driving and maintenance of turbulence in molecular clouds and for the rates of chemical and radiative processes that are sensitive to shocks and dissipation.

A complete equation of state for non-ideal condensed phase explosives

NASA Astrophysics Data System (ADS)

Wilkinson, S. D.; Braithwaite, M.; Nikiforakis, N.; Michael, L.

2017-12-01

The objective of this work is to improve the robustness and accuracy of numerical simulations of both ideal and non-ideal explosives by introducing temperature dependence in mechanical equations of state for reactants and products. To this end, we modify existing mechanical equations of state to appropriately approximate the temperature in the reaction zone. Mechanical equations of state of the Mie-Grüneisen form are developed with extensions, which allow the temperature to be evaluated appropriately and the temperature equilibrium condition to be applied robustly. Furthermore, the snow plow model is used to capture the effect of porosity on the reactant equation of state. We apply the methodology to predict the velocity of compliantly confined detonation waves. Once reaction rates are calibrated for unconfined detonation velocities, simulations of confined rate sticks and slabs are performed, and the experimental detonation velocities are matched without further parameter alteration, demonstrating the predictive capability of our simulations. We apply the same methodology to both ideal (PBX9502, a high explosive with principal ingredient TATB) and non-ideal (EM120D, an ANE or ammonium nitrate based emulsion) explosives.

Multicomponent lattice Boltzmann model from continuum kinetic theory.

PubMed

Shan, Xiaowen

2010-04-01

We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.

Ideal gas thermodynamic properties for the phenyl, phenoxy, and o-biphenyl radicals

NASA Technical Reports Server (NTRS)

Burcat, A.; Zeleznik, F. J.; Mcbride, B. J.

1985-01-01

Ideal gas thermodynamic properties of the phenyl and o-biphenyl radicals, their deuterated analogs and the phenoxy radical were calculated to 5000 K using estimated vibrational frequencies and structures. The ideal gas thermodynamic properties of benzene, biphenyl, their deuterated analogs and phenyl were also calculated.

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

Fragility Analysis of a Concrete Gravity Dam Embedded in Rock and Its System Response Curve Computed by the Analytical Program GDLAD_Foundation

DTIC Science & Technology

2012-06-01

According to the Bernoulli equation for ideal flows, i.e. steady, frictionless, incompressible flows, the total head, H, at any point can be determined...centerline and using the Bernoulli equation for ideal flow with an assumption that the velocity is small, the total head equals the pressure head...the Bernoulli equation for ideal flows, i.e. steady, frictionless, incompressible flows, the total head, H, at any point can be determined by

Bose-Einstein condensation of paraxial light

NASA Astrophysics Data System (ADS)

Klaers, J.; Schmitt, J.; Damm, T.; Vewinger, F.; Weitz, M.

2011-10-01

Photons, due to the virtually vanishing photon-photon interaction, constitute to very good approximation an ideal Bose gas, but owing to the vanishing chemical potential a (free) photon gas does not show Bose-Einstein condensation. However, this is not necessarily true for a lower-dimensional photon gas. By means of a fluorescence induced thermalization process in an optical microcavity one can achieve a thermal photon gas with freely adjustable chemical potential. Experimentally, we have observed thermalization and subsequently Bose-Einstein condensation of the photon gas at room temperature. In this paper, we give a detailed description of the experiment, which is based on a dye-filled optical microcavity, acting as a white-wall box for photons. Thermalization is achieved in a photon number-conserving way by photon scattering off the dye molecules, and the cavity mirrors both provide an effective photon mass and a confining potential-key prerequisites for the Bose-Einstein condensation of photons. The experimental results are in good agreement with both a statistical and a simple rate equation model, describing the properties of the thermalized photon gas.

Measurement of blood flow from an assist ventricle by computation of pneumatic driving parameters.

PubMed

Qian, K X

1992-03-01

The measurement of blood flow from an assist ventricle is important but sometimes difficult in artificial heart experiments. Along with the development of a pneumatic cylinder-piston driver coupled with a ventricular assist device, a simplified method for measuring pump flow was established. From driving parameters such as the piston (or cylinder) displacement and air pressure, the pump flow could be calculated by the use of the equation of state for an ideal gas. The results of this method are broadly in agreement with electromagnetic and Doppler measurements.

Statistical mechanics of light elements at high pressure. V Three-dimensional Thomas-Fermi-Dirac theory. [relevant to Jovian planetary interiors

NASA Technical Reports Server (NTRS)

Macfarlane, J. J.; Hubbard, W. B.

1983-01-01

A numerical technique for solving the Thomas-Fermi-Dirac (TED) equation in three dimensions, for an array of ions obeying periodic boundary conditions, is presented. The technique is then used to calculate deviations from ideal mixing for an alloy of hydrogen and helium at zero temperature and high presures. Results are compared with alternative models which apply perturbation theory to calculation of the electron distribution, based upon the assumption of weak response of the electron gas to the ions. The TFD theory, which permits strong electron response, always predicts smaller deviations from ideal mixing than would be predicted by perturbation theory. The results indicate that predicted phase separation curves for hydrogen-helium alloys under conditions prevailing in the metallic zones of Jupiter and Saturn are very model dependent.

Simple equations to simulate closed-loop recycling liquid-liquid chromatography: Ideal and non-ideal recycling models.

PubMed

Kostanyan, Artak E

2015-12-04

The ideal (the column outlet is directly connected to the column inlet) and non-ideal (includes the effects of extra-column dispersion) recycling equilibrium-cell models are used to simulate closed-loop recycling counter-current chromatography (CLR CCC). Simple chromatogram equations for the individual cycles and equations describing the transport and broadening of single peaks and complex chromatograms inside the recycling closed-loop column for ideal and non-ideal recycling models are presented. The extra-column dispersion is included in the theoretical analysis, by replacing the recycling system (connecting lines, pump and valving) by a cascade of Nec perfectly mixed cells. To evaluate extra-column contribution to band broadening, two limiting regimes of recycling are analyzed: plug-flow, Nec→∞, and maximum extra-column dispersion, Nec=1. Comparative analysis of ideal and non-ideal models has shown that when the volume of the recycling system is less than one percent of the column volume, the influence of the extra-column processes on the CLR CCC separation may be neglected. Copyright © 2015 Elsevier B.V. All rights reserved.

Using Rubber-Elastic Material-Ideal Gas Analogies To Teach Introductory Thermodynamics. Part II: The Laws of Thermodynamics.

ERIC Educational Resources Information Center

Smith, Brent

2002-01-01

Describes the laws of thermodynamics as a supplement to an introductory thermodynamics undergraduate course. Uses rubber-elastic materials (REM) which have strong analogies to the concept of ideal gas. Provides examples of the analogies between ideal gas and REM and mathematical analogies. (YDS)

Condensate statistics and thermodynamics of weakly interacting Bose gas: Recursion relation approach

NASA Astrophysics Data System (ADS)

Dorfman, K. E.; Kim, M.; Svidzinsky, A. A.

2011-03-01

We study condensate statistics and thermodynamics of weakly interacting Bose gas with a fixed total number N of particles in a cubic box. We find the exact recursion relation for the canonical ensemble partition function. Using this relation, we calculate the distribution function of condensate particles for N=200. We also calculate the distribution function based on multinomial expansion of the characteristic function. Similar to the ideal gas, both approaches give exact statistical moments for all temperatures in the framework of Bogoliubov model. We compare them with the results of unconstraint canonical ensemble quasiparticle formalism and the hybrid master equation approach. The present recursion relation can be used for any external potential and boundary conditions. We investigate the temperature dependence of the first few statistical moments of condensate fluctuations as well as thermodynamic potentials and heat capacity analytically and numerically in the whole temperature range.

Equation-of-State Scaling Factors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scannapieco, Anthony J.

2016-06-28

Equation-of-State scaling factors are needed when using a tabular EOS in which the user de ned material isotopic fractions di er from the actual isotopic fractions used by the table. Additionally, if a material is dynamically changing its isotopic structure, then an EOS scaling will again be needed, and will vary in time and location. The procedure that allows use of a table to obtain information about a similar material with average atomic mass Ms and average atomic number Zs is described below. The procedure is exact for a fully ionized ideal gas. However, if the atomic number is replacemore » by the e ective ionization state the procedure can be applied to partially ionized material as well, which extends the applicability of the scaling approximation continuously from low to high temperatures.« less

Development of comprehensive numerical schemes for predicting evaporating gas-droplets flow processes of a liquid-fueled combustor

NASA Technical Reports Server (NTRS)

Chen, C. P.

1990-01-01

An existing Computational Fluid Dynamics code for simulating complex turbulent flows inside a liquid rocket combustion chamber was validated and further developed. The Advanced Rocket Injector/Combustor Code (ARICC) is simplified and validated against benchmark flow situations for laminar and turbulent flows. The numerical method used in ARICC Code is re-examined for incompressible flow calculations. For turbulent flows, both the subgrid and the two equation k-epsilon turbulence models are studied. Cases tested include idealized Burger's equation in complex geometries and boundaries, a laminar pipe flow, a high Reynolds number turbulent flow, and a confined coaxial jet with recirculations. The accuracy of the algorithm is examined by comparing the numerical results with the analytical solutions as well as experimented data with different grid sizes.

Thermodynamics and kinetics of binary nucleation in ideal-gas mixtures.

PubMed

Alekseechkin, Nikolay V

2015-08-07

The nonisothermal single-component theory of droplet nucleation [N. V. Alekseechkin, Physica A 412, 186 (2014)] is extended to binary case; the droplet volume V, composition x, and temperature T are the variables of the theory. An approach based on macroscopic kinetics (in contrast to the standard microscopic model of nucleation operating with the probabilities of monomer attachment and detachment) is developed for the droplet evolution and results in the derived droplet motion equations in the space (V, x, T)—equations for V̇≡dV/dt, ẋ, and Ṫ. The work W(V, x, T) of the droplet formation is obtained in the vicinity of the saddle point as a quadratic form with diagonal matrix. Also, the problem of generalizing the single-component Kelvin equation for the equilibrium vapor pressure to binary case is solved; it is presented here as a problem of integrability of a Pfaffian equation. The equation for Ṫ is shown to be the first law of thermodynamics for the droplet, which is a consequence of Onsager's reciprocal relations and the linked-fluxes concept. As an example of ideal solution for demonstrative numerical calculations, the o-xylene-m-xylene system is employed. Both nonisothermal and enrichment effects are shown to exist; the mean steady-state overheat of droplets and their mean steady-state enrichment are calculated with the help of the 3D distribution function. Some qualitative peculiarities of the nucleation thermodynamics and kinetics in the water-sulfuric acid system are considered in the model of regular solution. It is shown that there is a small kinetic parameter in the theory due to the small amount of the acid in the vapor and, as a consequence, the nucleation process is isothermal.

Investigation of Dalton and Amagat's laws for gas mixtures with shock propagation

NASA Astrophysics Data System (ADS)

Wayne, Patrick; Trueba Monje, Ignacio; Yoo, Jason H.; Truman, C. Randall; Vorobieff, Peter

2016-11-01

Two common models describing gas mixtures are Dalton's Law and Amagat's Law (also known as the laws of partial pressures and partial volumes, respectively). Our work is focused on determining the suitability of these models to prediction of effects of shock propagation through gas mixtures. Experiments are conducted at the Shock Tube Facility at the University of New Mexico (UNM). To validate experimental data, possible sources of uncertainty associated with experimental setup are identified and analyzed. The gaseous mixture of interest consists of a prescribed combination of disparate gases - helium and sulfur hexafluoride (SF6). The equations of state (EOS) considered are the ideal gas EOS for helium, and a virial EOS for SF6. The values for the properties provided by these EOS are then used used to model shock propagation through the mixture in accordance with Dalton's and Amagat's laws. Results of the modeling are compared with experiment to determine which law produces better agreement for the mixture. This work is funded by NNSA Grant DE-NA0002913.

Filamentation effect in a gas attenuator for high-repetition-rate X-ray FELs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Yiping; Krzywinski, Jacek; Schafer, Donald W.

A sustained filamentation or density depression phenomenon in an argon gas attenuator servicing a high-repetition femtosecond X-ray free-electron laser has been studied using a finite-difference method applied to the thermal diffusion equation for an ideal gas. A steady-state solution was obtained by assuming continuous-wave input of an equivalent time-averaged beam power and that the pressure of the entire gas volume has reached equilibrium. Both radial and axial temperature/density gradients were found and describable as filamentation or density depression previously reported for a femtosecond optical laser of similar attributes. The effect exhibits complex dependence on the input power, the desired attenuation,more » and the geometries of the beam and the attenuator. Time-dependent simulations were carried out to further elucidate the evolution of the temperature/density gradients in between pulses, from which the actual attenuation received by any given pulse can be properly calculated.« less

Effects of real fluid properties on axial turbine meanline design and off-design analysis

NASA Astrophysics Data System (ADS)

MacLean, Cameron

The effects of real fluid properties on axial turbine meanline analysis have been investigated employing two meanline analysis codes, namely Turbine Meanline Design (TMLD) and Turbine Meanline Off-Design (TMLO). The previously developed TMLD code assumed the working fluid was an ideal gas. Therefore it was modified to use real fluid properties. TMLO was then developed from TMLD Both codes can be run using either the ideal gas assumption or real fluid properties. TMLD was employed for the meanline design of several axial turbines for a range of inlet conditions, using both the ideal gas assumption and real fluid properties. The resulting designs were compared to see the effects of real fluid properties. Meanline designs, generated using the ideal gas assumption, were then analysed with TMLO using real fluid properties. This was done over a range of inlet conditions that correspond to varying degrees of departure from ideal gas conditions. The goal was to show how machines designed with the ideal gas assumption would perform with the real working fluid. The working fluid used in both investigations was supercritical carbon dioxide. Results from the investigation show that real fluid properties had a strong effect on the gas path areas of the turbine designs as well as the performance of turbines designed using the ideal gas assumption. Specifically, power output and the velocities of the working fluid were affected. It was found that accounting for losses tended to lessen the effects of the real fluid properties.

40 CFR 1065.645 - Amount of water in an ideal gas.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 40 Protection of Environment 34 2012-07-01 2012-07-01 false Amount of water in an ideal gas. 1065.645 Section 1065.645 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR POLLUTION CONTROLS ENGINE-TESTING PROCEDURES Calculations and Data Requirements § 1065.645 Amount of water in an ideal gas. This section describes how to...

40 CFR 1065.645 - Amount of water in an ideal gas.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 40 Protection of Environment 34 2013-07-01 2013-07-01 false Amount of water in an ideal gas. 1065.645 Section 1065.645 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR POLLUTION CONTROLS ENGINE-TESTING PROCEDURES Calculations and Data Requirements § 1065.645 Amount of water in an ideal gas. This section describes how to...

40 CFR 1065.645 - Amount of water in an ideal gas.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 33 2011-07-01 2011-07-01 false Amount of water in an ideal gas. 1065.645 Section 1065.645 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR POLLUTION CONTROLS ENGINE-TESTING PROCEDURES Calculations and Data Requirements § 1065.645 Amount of water in an ideal gas. This section describes how to...

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity,more » the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.« less

A Comparison of Grid-based and SPH Binary Mass-transfer and Merger Simulations

DOE PAGES

Motl, Patrick M.; Frank, Juhan; Staff, Jan; ...

2017-03-29

There is currently a great amount of interest in the outcomes and astrophysical implications of mergers of double degenerate binaries. In a commonly adopted approximation, the components of such binaries are represented by polytropes with an index of n = 3/2. We present detailed comparisons of stellar mass-transfer and merger simulations of polytropic binaries that have been carried out using two very different numerical algorithms—a finite-volume "grid" code and a smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in both the ultimate outcomes of the evolutions and the intermediate stages if the initial conditions for each code aremore » chosen to match as closely as possible. We find that even with closely matching initial setups, the time it takes to reach a concordant evolution differs between the two codes because the initial depth of contact cannot be matched exactly. There is a general tendency for SPH to yield higher mass transfer rates and faster evolution to the final outcome. Here, we also present comparisons of simulations calculated from two different energy equations: in one series, we assume a polytropic equation of state and in the other series an ideal gas equation of state. In the latter series of simulations, an atmosphere forms around the accretor, which can exchange angular momentum and cause a more rapid loss of orbital angular momentum. In the simulations presented here, the effect of the ideal equation of state is to de-stabilize the binary in both SPH and grid simulations, but the effect is more pronounced in the grid code.« less

MINIMUM CORE MASSES FOR GIANT PLANET FORMATION WITH REALISTIC EQUATIONS OF STATE AND OPACITIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Piso, Ana-Maria A.; Murray-Clay, Ruth A.; Youdin, Andrew N., E-mail: apiso@cfa.harvard.edu

2015-02-20

Giant planet formation by core accretion requires a core that is sufficiently massive to trigger runaway gas accretion in less than the typical lifetime of protoplanetary disks. We explore how the minimum required core mass, M {sub crit}, depends on a non-ideal equation of state (EOS) and on opacity changes due to grain growth across a range of stellocentric distances from 5-100 AU. This minimum M {sub crit} applies when planetesimal accretion does not substantially heat the atmosphere. Compared to an ideal gas polytrope, the inclusion of molecular hydrogen (H{sub 2}) dissociation and variable occupation of H{sub 2} rotational statesmore » increases M {sub crit}. Specifically, M {sub crit} increases by a factor of ∼2 if the H{sub 2} spin isomers, ortho- and parahydrogen, are in thermal equilibrium, and by a factor of ∼2-4 if the ortho-to-para ratio is fixed at 3:1. Lower opacities due to grain growth reduce M {sub crit}. For a standard disk model around a Solar mass star, we calculate M {sub crit} ∼ 8 M {sub ⊕} at 5 AU, decreasing to ∼5 M {sub ⊕} at 100 AU, for a realistic EOS with an equilibrium ortho-to-para ratio and for grain growth to centimeter-sizes. If grain coagulation is taken into account, M {sub crit} may further reduce by up to one order of magnitude. These results for the minimum critical core mass are useful for the interpretation of surveys that find exoplanets at a range of orbital distances.« less

Use of Jackknifing to Evaluate Effects of Anchor Item Selection on Equating with the Nonequivalent Groups with Anchor Test (NEAT) Design. Research Report. ETS RR-15-10

ERIC Educational Resources Information Center

Lu, Ru; Haberman, Shelby; Guo, Hongwen; Liu, Jinghua

2015-01-01

In this study, we apply jackknifing to anchor items to evaluate the impact of anchor selection on equating stability. In an ideal world, the choice of anchor items should have little impact on equating results. When this ideal does not correspond to reality, selection of anchor items can strongly influence equating results. This influence does not…

Revisiting Maxwell’s accommodation coefficient: A study of nitrogen flow in a silica microtube across all flow regimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lei, Wenwen, E-mail: wlei@physics.usyd.edu.au; McKenzie, David R., E-mail: d.mckenzie@physics.usyd.edu.au

2014-12-15

Gas flows have been studied quantitatively for more than a hundred years and have relevance in modern fields such as the control of gas inputs to processes, the measurement of leak rates and the separation of gaseous species. Cha and McCoy have derived a convenient formula for the flow of an ideal gas applicable across a wide range of Knudsen numbers (Kn) that approaches the Navier–Stokes equations at small Kn and the Smoluchowski extension of the Knudsen flow equation at large Kn. Smoluchowski’s result relies on the Maxwell definition of the tangential momentum accommodation coefficient α, recently challenged by Aryamore » et al. We measure the flow rate of nitrogen gas in a smooth walled silica tube across a wide range of Knudsen numbers from 0.0048 to 12.4583. We find that the nitrogen flow obeys the Cha and McCoy equation with a large value of α, unlike carbon nanotubes which show flows consistent with a small value of α. Silica capillaries are therefore not atomically smooth. The flow at small Kn has α=0.91 and at large Kn has α close to one, consistent with the redefinition of accommodation coefficient by Arya et al., which also resolves a problem in the literature where there are many observations of α of less than one at small Kn and many equal to one at large Kn. Silica capillaries are an excellent choice for an accurate flow control system. - Highlights: • First experimental study on flow rate across all flow regimes in a well-defined microtube. • Extend Cha and McCoy theory for molecular flow regime. • Demonstrate the Maxwell accommodation coefficient is different in the slip and molecular flow regimes.« less

Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates

NASA Astrophysics Data System (ADS)

Kuropatenko, V. F.; Shestakovskaya, E. S.

2016-10-01

It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.

Constructive methods for the ground-state energy of fully interacting fermion gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilera Navarro, V.C.; Baker G.A. Jr.; Benofy, L.P.

1987-11-01

A perturbation scheme based not on the ideal gas but on a system of purely repulsive cores is applied to a typical fully interacting fermion gas. This is ''neutron matter'' interacting via (a) the repulsive ''Bethe homework-problem'' potential, (b) a hard-core--plus--square-well potential, and (c) the Baker-Hind-Kahane modification of the latter, suitable for describing a more accurate two-nucleon potential. Pade extrapolation techniques and generalizations thereof are employed to represent both the density dependence as well as the attractive coupling dependence of the perturbation expansion. Equations of state are constructed and compared with Jastrow--Monte Carlo calculations as well as expectations based onmore » semiempirical mass formulas. Excellent agreement is found with the latter.« less

Two-Dimensional Homogeneous Fermi Gases

NASA Astrophysics Data System (ADS)

Hueck, Klaus; Luick, Niclas; Sobirey, Lennart; Siegl, Jonas; Lompe, Thomas; Moritz, Henning

2018-02-01

We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.

Inhomogeneous Oxygen Vacancy Distribution in Semiconductor Gas Sensors: Formation, Migration and Determination on Gas Sensing Characteristics

PubMed Central

Liu, Jianqiao; Gao, Yinglin; Wu, Xu; Jin, Guohua; Zhai, Zhaoxia; Liu, Huan

2017-01-01

The density of oxygen vacancies in semiconductor gas sensors was often assumed to be identical throughout the grain in the numerical discussion of the gas-sensing mechanism of the devices. In contrast, the actual devices had grains with inhomogeneous distribution of oxygen vacancy under non-ideal conditions. This conflict between reality and discussion drove us to study the formation and migration of the oxygen defects in semiconductor grains. A model of the gradient-distributed oxygen vacancy was proposed based on the effects of cooling rate and re-annealing on semiconductive thin films. The model established the diffusion equations of oxygen vacancy according to the defect kinetics of diffusion and exclusion. We described that the steady-state and transient-state oxygen vacancy distributions, which were used to calculate the gas-sensing characteristics of the sensor resistance and response to reducing gases under two different conditions. The gradient-distributed oxygen vacancy model had the applications in simulating the sensor performances, such as the power law, the grain size effect and the effect of depletion layer width. PMID:28796167

Inhomogeneous Oxygen Vacancy Distribution in Semiconductor Gas Sensors: Formation, Migration and Determination on Gas Sensing Characteristics.

PubMed

Liu, Jianqiao; Gao, Yinglin; Wu, Xu; Jin, Guohua; Zhai, Zhaoxia; Liu, Huan

2017-08-10

The density of oxygen vacancies in semiconductor gas sensors was often assumed to be identical throughout the grain in the numerical discussion of the gas-sensing mechanism of the devices. In contrast, the actual devices had grains with inhomogeneous distribution of oxygen vacancy under non-ideal conditions. This conflict between reality and discussion drove us to study the formation and migration of the oxygen defects in semiconductor grains. A model of the gradient-distributed oxygen vacancy was proposed based on the effects of cooling rate and re-annealing on semiconductive thin films. The model established the diffusion equations of oxygen vacancy according to the defect kinetics of diffusion and exclusion. We described that the steady-state and transient-state oxygen vacancy distributions, which were used to calculate the gas-sensing characteristics of the sensor resistance and response to reducing gases under two different conditions. The gradient-distributed oxygen vacancy model had the applications in simulating the sensor performances, such as the power law, the grain size effect and the effect of depletion layer width.

A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.

2018-03-01

Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.

Numerical modeling of underground storage system for natural gas

NASA Astrophysics Data System (ADS)

Ding, J.; Wang, S.

2017-12-01

Natural gas is an important type of base-load energy, and its supply needs to be adjusted according to different demands in different seasons. For example, since natural gas is increasingly used to replace coal for winter heating, the demand for natural gas in winter is much higher than that in other seasons. As storage systems are the essential tools for balancing seasonal supply and demand, the design and simulation of natural gas storage systems form an important research direction. In this study, a large-scale underground storage system for natural gas is simulated based on theoretical analysis and finite element modeling.It is proven that the problem of axi-symmetric Darcy porous flow of ideal gas is governed by the Boussinesq equation. In terms of the exact solution to the Boussinesq equation, the basic operating characteristics of the underground storage system is analyzed, and it is demonstrated that the propagation distance of the pore pressure is proportional to the 1/4 power of the mass flow rate and to the 1/2 power of the propagation time. This quantitative relationship can be used to guide the overall design of natural gas underground storage systems.In order to fully capture the two-way coupling between pore pressure and elastic matrix deformation, a poro-elastic finite element model for natural gas storage is developed. Based on the numerical model, the dynamic processes of gas injection, storage and extraction are simulated, and the corresponding time-dependent surface deformations are obtained. The modeling results not only provide a theoretical basis for real-time monitoring for the operating status of the underground storage system through surface deformation measurements, but also demonstrate that a year-round balance can be achieved through periodic gas injection and extraction.This work is supported by the CAS "100 talents" Program and the National Natural Science Foundation of China (41371090).

Positron kinetics in an idealized PET environment

PubMed Central

Robson, R. E.; Brunger, M. J.; Buckman, S. J.; Garcia, G.; Petrović, Z. Lj.; White, R. D.

2015-01-01

The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the ‘gas-phase’ assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations. PMID:26246002

Experimental and Numerical Investigation of Adsorption/Desorption in Packed Sorption Beds Under Ideal and Non-Ideal Flows

NASA Technical Reports Server (NTRS)

Mohamadinejad, H.; Knox, J. C.; Smith, James E.

1999-01-01

The importance of the wall effect on packed beds in the adsorption and desorption of carbon dioxide, nitrogen, and water on molecular sieve 5A of 0.127 cm in radius is examined experimentally and with one-dimensional computer simulations. Experimental results are presented for a 22.5-cm long by 4.5-cm diameter cylindrical column with concentration measurements taken at various radial locations. The set of partial differential equations are solved using finite differences and Newman's method. Comparison of test data with the axial-dispersed, non-isothermal, linear driving force model suggests that a two-dimensional model (submitted to Separation Science and Technology) is required for accurate simulation of the average column breakthrough concentration. Additional comparisons of test data with the model provided information on the interactive effects of carrier gas coadsorption with CO2, as well as CO2-H2O interactions.

Observations of density fluctuations in an elongated Bose gas: ideal gas and quasicondensate regimes.

PubMed

Esteve, J; Trebbia, J-B; Schumm, T; Aspect, A; Westbrook, C I; Bouchoule, I

2006-04-07

We report in situ measurements of density fluctuations in a quasi-one-dimensional 87Rb Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected "bunching" for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.

3-D simulation of gases transport under condition of inert gas injection into goaf

NASA Astrophysics Data System (ADS)

Liu, Mao-Xi; Shi, Guo-Qing; Guo, Zhixiong; Wang, Yan-Ming; Ma, Li-Yang

2016-12-01

To prevent coal spontaneous combustion in mines, it is paramount to understand O2 gas distribution under condition of inert gas injection into goaf. In this study, the goaf was modeled as a 3-D porous medium based on stress distribution. The variation of O2 distribution influenced by CO2 or N2 injection was simulated based on the multi-component gases transport and the Navier-Stokes equations using Fluent. The numerical results without inert gas injection were compared with field measurements to validate the simulation model. Simulations with inert gas injection show that CO2 gas mainly accumulates at the goaf floor level; however, a notable portion of N2 gas moves upward. The evolution of the spontaneous combustion risky zone with continuous inert gas injection can be classified into three phases: slow inerting phase, rapid accelerating inerting phase, and stable inerting phase. The asphyxia zone with CO2 injection is about 1.25-2.4 times larger than that with N2 injection. The efficacy of preventing and putting out mine fires is strongly related with the inert gas injecting position. Ideal injections are located in the oxidation zone or the transitional zone between oxidation zone and heat dissipation zone.

Modeling Solar Wind Flow with the Multi-Scale Fluid-Kinetic Simulation Suite

DOE PAGES

Pogorelov, N.V.; Borovikov, S. N.; Bedford, M. C.; ...

2013-04-01

Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS) is a package of numerical codes capable of performing adaptive mesh refinement simulations of complex plasma flows in the presence of discontinuities and charge exchange between ions and neutral atoms. The flow of the ionized component is described with the ideal MHD equations, while the transport of atoms is governed either by the Boltzmann equation or multiple Euler gas dynamics equations. We have enhanced the code with additional physical treatments for the transport of turbulence and acceleration of pickup ions in the interplanetary space and at the termination shock. In this article, we present themore » results of our numerical simulation of the solar wind (SW) interaction with the local interstellar medium (LISM) in different time-dependent and stationary formulations. Numerical results are compared with the Ulysses, Voyager, and OMNI observations. Finally, the SW boundary conditions are derived from in-situ spacecraft measurements and remote observations.« less

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

NASA Technical Reports Server (NTRS)

Gloss, R. J.

1971-01-01

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

Integrability from point symmetries in a family of cosmological Horndeski Lagrangians

NASA Astrophysics Data System (ADS)

Dimakis, N.; Giacomini, Alex; Paliathanasis, Andronikos

2017-07-01

For a family of Horndeski theories, formulated in terms of a generalized Galileon model, we study the integrability of the field equations in a Friedmann-Lemaître-Robertson-Walker space-time. We are interested in point transformations which leave invariant the field equations. Noether's theorem is applied to determine the conservation laws for a family of models that belong to the same general class. The cosmological scenarios with or without an extra perfect fluid with constant equation of state parameter are the two important cases of our study. The de Sitter universe and ideal gas solutions are derived by using the invariant functions of the symmetry generators as a demonstration of our result. Furthermore, we discuss the connection of the different models under conformal transformations while we show that when the Horndeski theory reduces to a canonical field the same holds for the conformal equivalent theory. Finally, we discuss how singular solutions provides nonsingular universes in a different frame and vice versa.

Thermodynamic properties of seven gaseous halogenated hydrocarbons from acoustic measurements: CHClFCF{sub 3}, CHF{sub 2}CF{sub 3}, CF{sub 3}CH{sub 3}, CHF{sub 2}CH{sub 3}, CF{sub 3}CHFCHF{sub 2},CF{sub 3}CH{sub 2}CF{sub 3}, and CHF{sub 2}CF{sub 2}CH{sub 2}F

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gillis, K.A.

1997-01-01

Measurements of the speed of sound in seven halogenated hydrocarbons are presented. The compounds in this study are 1-chloro-,2,2,2-tetrafluoroethane (CHCIFCF{sub 3} or HCFC-124), pentafluoroethane (CHF{sub 2}CF{sub 3} or HFC-125), 1,1,1-trifluoroethane (CF{sub 3}CH{sub 3} or HFC-143a), 1,1-difluoroethane (CHF{sub 2}CH{sub 3} or HFC-152a), 1,1,2,3,3-hexafluoropropane (CF{sub 3}CHFCHF{sub 2} or HFC-236ea), 1,1,1,3,3,3-hexafluoropropane (CF{sub 3}CH{sub 2}CF{sub 3} or HFC-236fa), and 1,1,2,2,3-pentafluoropropane (CHF{sub 2}CF{sub 2}CH{sub 2}F or HFC-245ca). The measurements were performed with a cylindrical resonator at temperatures between 240 and 400 K and at pressures up to 1.0 MPa. Ideal-gas heat capacities and acoustic virial coefficients were directly deduced from the data. The ideal-gas heatmore » capacity of HFC-125 from this work differs from spectroscopic calculations by less than 0.2% over the measurement range. The coefficients for virial equations of state were obtained from the acoustic data and hard-core square-well intermolecular potentials. Gas densities that were calculated from the virial equations of state for HCFC-124 and HFC-125 differ from independent density measurements by at most 0.15%, for the ranges of temperature and pressure over which both acoustic and Burnett data exist. The uncertainties in the derived properties of the other five compounds are comparable to those for HCFC-124 and HFC-125.« less

High School Forum. The Solution: "Derivation of the Ideal Gas Law."

ERIC Educational Resources Information Center

Herron, J. Dudley, Ed.

1980-01-01

Presents responses to an earlier report concerning a procedure for the derivation of the Ideal Gas Law from Charles', Boyle's, and other gas laws. Logic errors and solutions that work are discussed. (CS)

Real-Gas Correction Factors for Hypersonic Flow Parameters in Helium

NASA Technical Reports Server (NTRS)

Erickson, Wayne D.

1960-01-01

The real-gas hypersonic flow parameters for helium have been calculated for stagnation temperatures from 0 F to 600 F and stagnation pressures up to 6,000 pounds per square inch absolute. The results of these calculations are presented in the form of simple correction factors which must be applied to the tabulated ideal-gas parameters. It has been shown that the deviations from the ideal-gas law which exist at high pressures may cause a corresponding significant error in the hypersonic flow parameters when calculated as an ideal gas. For example the ratio of the free-stream static to stagnation pressure as calculated from the thermodynamic properties of helium for a stagnation temperature of 80 F and pressure of 4,000 pounds per square inch absolute was found to be approximately 13 percent greater than that determined from the ideal-gas tabulation with a specific heat ratio of 5/3.

De Sitter and scaling solutions in a higher-order modified teleparallel theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paliathanasis, Andronikos, E-mail: anpaliat@phys.uoa.gr

The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field equations and we reduce the field equationsmore » in an algebraic equation, where in order to demonstrate our result we show how this noncanonical scalar field can reproduce the Hubble function of Λ-cosmology.« less

A Comparison of Grid-based and SPH Binary Mass-transfer and Merger Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Motl, Patrick M.; Frank, Juhan; Clayton, Geoffrey C.

2017-04-01

There is currently a great amount of interest in the outcomes and astrophysical implications of mergers of double degenerate binaries. In a commonly adopted approximation, the components of such binaries are represented by polytropes with an index of n  = 3/2. We present detailed comparisons of stellar mass-transfer and merger simulations of polytropic binaries that have been carried out using two very different numerical algorithms—a finite-volume “grid” code and a smoothed-particle hydrodynamics (SPH) code. We find that there is agreement in both the ultimate outcomes of the evolutions and the intermediate stages if the initial conditions for each code are chosen to matchmore » as closely as possible. We find that even with closely matching initial setups, the time it takes to reach a concordant evolution differs between the two codes because the initial depth of contact cannot be matched exactly. There is a general tendency for SPH to yield higher mass transfer rates and faster evolution to the final outcome. We also present comparisons of simulations calculated from two different energy equations: in one series, we assume a polytropic equation of state and in the other series an ideal gas equation of state. In the latter series of simulations, an atmosphere forms around the accretor, which can exchange angular momentum and cause a more rapid loss of orbital angular momentum. In the simulations presented here, the effect of the ideal equation of state is to de-stabilize the binary in both SPH and grid simulations, but the effect is more pronounced in the grid code.« less

Analysis Tools for CFD Multigrid Solvers

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Diskin, Boris

2004-01-01

Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid solver. These new tools are applicable to general systems of equations and/or discretizations and point to problem areas within an existing multigrid solver. Idealized Relaxation and Idealized Coarse Grid are applied in developing textbook-efficient multigrid solvers for incompressible stagnation flow problems.

Ozone Uptake During Inspiratory Flow in a Model of the Larynx, Trachea and Primary Bronchial Bifurcation

PubMed Central

Padaki, Amit; Ultman, James S.; Borhan, Ali

2009-01-01

Three-dimensional simulations of the transport and uptake of a reactive gas such as O3 were compared between an idealized model of the larynx, trachea, and first bifurcation and a second “control” model in which the larynx was replaced by an equivalent, cylindrical, tube segment. The Navier-Stokes equations, Spalart-Allmaras turbulence equation, and convection-diffusion equation were implemented at conditions reflecting inhalation into an adult human lung. Simulation results were used to analyze axial velocity, turbulent viscosity, local fractional uptake, and regional uptake. Axial velocity data revealed a strong laryngeal jet with a reattachment point in the proximal trachea. Turbulent viscosity data indicated that jet turbulence occurred only at high Reynolds numbers and was attenuated by the first bifurcation. Local fractional uptake data affirmed hotspots previously reported at the first carina, and suggested additional hotspots at the glottal constriction and jet reattachment point in the proximal trachea. These laryngeal effects strongly depended on inlet Reynolds number, with maximal effects (approaching 15%) occurring at maximal inlet flow rates. While the increase in the regional uptake caused by the larynx subsided by the end of the model, the effect of the larynx on cumulative uptake persisted further downstream. These results suggest that with prolonged exposure to a reactive gas, entire regions of the larynx and proximal trachea could show signs of tissue injury. PMID:22949744

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rashidi, Reza, E-mail: reza.rashidi@srttu.edu

The effects of a generalized uncertainty principle on the structure of an ideal white dwarf star is investigated. The equation describing the equilibrium configuration of the star is a generalized form of the Lane–Emden equation. It is proved that the star always has a finite size. It is then argued that the maximum mass of such an ideal white dwarf tends to infinity, as opposed to the conventional case where it has a finite value.

The analytical solution of the problem of a shock focusing in a gas for one-dimensional case

NASA Astrophysics Data System (ADS)

Shestakovskaya, E. S.; Magazov, F. G.

2018-03-01

The analytical solution of the problem of an imploding shock wave in the vessel with an impermeable wall is constructed for the cases of planar, cylindrical and spherical symmetry. The negative velocity is set at the vessel boundary. The velocity of cold ideal gas is zero. At the initial time the shock spreads from this point into the center of symmetry. The boundary moves under the particular law which conforms to the movement of the shock. In Euler variables it moves but in Lagrangian variables its trajectory is a vertical line. Equations that determine the structure of the gas flow between the shock front and the boundary as a function of time and the Lagrangian coordinate as well as the dependence of the entropy on the shock wave velocity are obtained. Self-similar coefficients and corresponding critical values of self-similar coordinates were found for a wide range of adiabatic index. The problem is solved for Lagrangian coordinates.

Simulation of ideal-gas flow by nitrogen and other selected gases at cryogenic temperatures. [transonic flow in cryogenic wind tunnels

NASA Technical Reports Server (NTRS)

Hall, R. M.; Adcock, J. B.

1981-01-01

The real gas behavior of nitrogen, the gas normally used in transonic cryogenic tunnels, is reported for the following flow processes: isentropic expansion, normal shocks, boundary layers, and interactions between shock waves and boundary layers. The only difference in predicted pressure ratio between nitrogen and an ideal gas which may limit the minimum operating temperature of transonic cryogenic wind tunnels occur at total pressures approaching 9 atm and total temperatures 10 K below the corresponding saturation temperature. These pressure differences approach 1 percent for both isentropic expansions and normal shocks. Alternative cryogenic test gases were also analyzed. Differences between air and an ideal diatomic gas are similar in magnitude to those for nitrogen and should present no difficulty. However, differences for helium and hydrogen are over an order of magnitude greater than those for nitrogen or air. It is concluded that helium and cryogenic hydrogen would not approximate the compressible flow of an ideal diatomic gas.

Osmotic Pressure in the Physics Course for Students of the Life Sciences

ERIC Educational Resources Information Center

Hobbie, Russell K.

1974-01-01

Discusses the use of an ideal gas model to explain osmotic equilibrium and nonequilibrium flows through an ideal semipermeable membrane. Included are a justification of the relationship between an ideal gas and a dilute solution, a review of the irreversible thermodynamic flow, and some sample applications to physiology. (CC)

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

DOE PAGES

Pantano, C.; Saurel, R.; Schmitt, T.

2017-02-01

Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-knownmore » pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.« less

An oscillation free shock-capturing method for compressible van der Waals supercritical fluid flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pantano, C.; Saurel, R.; Schmitt, T.

Numerical solutions of the Euler equations using real gas equations of state (EOS) often exhibit serious inaccuracies. The focus here is the van der Waals EOS and its variants (often used in supercritical fluid computations). The problems are not related to a lack of convexity of the EOS since the EOS are considered in their domain of convexity at any mesh point and at any time. The difficulties appear as soon as a density discontinuity is present with the rest of the fluid in mechanical equilibrium and typically result in spurious pressure and velocity oscillations. This is reminiscent of well-knownmore » pressure oscillations occurring with ideal gas mixtures when a mass fraction discontinuity is present, which can be interpreted as a discontinuity in the EOS parameters. We are concerned with pressure oscillations that appear just for a single fluid each time a density discontinuity is present. As a result, the combination of density in a nonlinear fashion in the EOS with diffusion by the numerical method results in violation of mechanical equilibrium conditions which are not easy to eliminate, even under grid refinement.« less

Perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases.

PubMed

Mohammadzadeh, Hosein; Adli, Fereshteh; Nouri, Sahereh

2016-12-01

We investigate perturbative thermodynamic geometry of nonextensive ideal classical, Bose, and Fermi gases. We show that the intrinsic statistical interaction of nonextensive Bose (Fermi) gas is attractive (repulsive) similar to the extensive case but the value of thermodynamic curvature is changed by a nonextensive parameter. In contrary to the extensive ideal classical gas, the nonextensive one may be divided to two different regimes. According to the deviation parameter of the system to the nonextensive case, one can find a special value of fugacity, z^{*}, where the sign of thermodynamic curvature is changed. Therefore, we argue that the nonextensive parameter induces an attractive (repulsive) statistical interaction for zz^{*}) for an ideal classical gas. Also, according to the singular point of thermodynamic curvature, we consider the condensation of nonextensive Boson gas.

Direct numerical simulations of temporally developing hydrocarbon shear flames at elevated pressure: effects of the equation of state and the unity Lewis number assumption

NASA Astrophysics Data System (ADS)

Korucu, Ayse; Miller, Richard

2016-11-01

Direct numerical simulations (DNS) of temporally developing shear flames are used to investigate both equation of state (EOS) and unity-Lewis (Le) number assumption effects in hydrocarbon flames at elevated pressure. A reduced Kerosene / Air mechanism including a semi-global soot formation/oxidation model is used to study soot formation/oxidation processes in a temporarlly developing hydrocarbon shear flame operating at both atmospheric and elevated pressures for the cubic Peng-Robinson real fluid EOS. Results are compared to simulations using the ideal gas law (IGL). The results show that while the unity-Le number assumption with the IGL EOS under-predicts the flame temperature for all pressures, with the real fluid EOS it under-predicts the flame temperature for 1 and 35 atm and over-predicts the rest. The soot mass fraction, Ys, is only under-predicted for the 1 atm flame for both IGL and real gas fluid EOS models. While Ys is over-predicted for elevated pressures with IGL EOS, for the real gas EOS Ys's predictions are similar to results using a non-unity Le model derived from non-equilibrium thermodynamics and real diffusivities. Adopting the unity Le assumption is shown to cause misprediction of Ys, the flame temperature, and the mass fractions of CO, H and OH.

Effect of entropy on anomalous transport in ITG-modes of magneto-plasma

NASA Astrophysics Data System (ADS)

Yaqub Khan, M.; Qaiser Manzoor, M.; Haq, A. ul; Iqbal, J.

2017-04-01

The ideal gas equation and S={{c}v}log ≤ft(P/ρ \\right) (where S is entropy, P is pressure and ρ is the mass density) define the interconnection of entropy with the temperature and density of plasma. Therefore, different phenomena relating to plasma and entropy need to be investigated. By employing the Braginskii transport equations for a nonuniform electron-ion magnetoplasma, two new parameters—the entropy distribution function and the entropy gradient drift—are defined, a new dispersion relation is obtained, and the dependence of anomalous transport on entropy is also proved. Some results, like monotonicity, the entropy principle and the second law of thermodynamics, are proved with a new definition of entropy. This work will open new horizons in fusion processes, not only by controlling entropy in tokamak plasmas—particularly in the pedestal regions of the H-mode and space plasmas—but also in engineering sciences.

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q

2015-01-01

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments is based upon a novel approach that relies on the global momentum conservation of the closed fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. A numerical example illustrates the method's application to prediction of bulk fluid behavior during a spacecraft ullage settling maneuver.

Smoothed Particle Hydrodynamics Simulations of Ultrarelativistic Shocks with Artificial Viscosity

NASA Astrophysics Data System (ADS)

Siegler, S.; Riffert, H.

2000-03-01

We present a fully Lagrangian conservation form of the general relativistic hydrodynamic equations for perfect fluids with artificial viscosity in a given arbitrary background spacetime. This conservation formulation is achieved by choosing suitable Lagrangian time evolution variables, from which the generic fluid variables of rest-mass density, 3-velocity, and thermodynamic pressure have to be determined. We present the corresponding equations for an ideal gas and show the existence and uniqueness of the solution. On the basis of the Lagrangian formulation we have developed a three-dimensional general relativistic smoothed particle hydrodynamics (SPH) code using the standard SPH formalism as known from nonrelativistic fluid dynamics. One-dimensional simulations of a shock tube and a wall shock are presented together with a two-dimensional test calculation of an inclined shock tube. With our method we can model ultrarelativistic fluid flows including shocks with Lorentz factors of even 1000.

Lattice Boltzmann Method for Spacecraft Propellant Slosh Simulation

NASA Technical Reports Server (NTRS)

Orr, Jeb S.; Powers, Joseph F.; Yang, Hong Q.

2015-01-01

A scalable computational approach to the simulation of propellant tank sloshing dynamics in microgravity is presented. In this work, we use the lattice Boltzmann equation (LBE) to approximate the behavior of two-phase, single-component isothermal flows at very low Bond numbers. Through the use of a non-ideal gas equation of state and a modified multiple relaxation time (MRT) collision operator, the proposed method can simulate thermodynamically consistent phase transitions at temperatures and density ratios consistent with typical spacecraft cryogenic propellants, for example, liquid oxygen. Determination of the tank forces and moments relies upon the global momentum conservation of the fluid domain, and a parametric wall wetting model allows tuning of the free surface contact angle. Development of the interface is implicit and no interface tracking approach is required. Numerical examples illustrate the method's application to predicting bulk fluid motion including lateral propellant slosh in low-g conditions.

Derivation of the Ideal Gas Law

ERIC Educational Resources Information Center

Laugier, Alexander; Garai, Jozsef

2007-01-01

Undergraduate and graduate physics and chemistry books usually state that combining the gas laws results in the ideal gas law. Leaving the derivation to the students implies that this should be a simple task, most likely a substitution. Boyle's law, Charles's law, and the Avogadro's principle are given under certain conditions; therefore, direct…

Is the Reaction Equilibrium Composition in Non-ideal Mixtures Uniquely Determined by the Initial Composition?

NASA Astrophysics Data System (ADS)

Sefcik, Jan

1998-05-01

Reaction equilibrium can be mathematically described by the equilibrium equation and the reaction equilibrium composition can be calculated by solving this equation. It can be proved by non-elementary thermodynamic arguments that for a generic system with given initial composition, temperature and pressure there is a unique stable equilibrium state corresponding to the global minimum of the Gibbs free energy function. However, when the concept of equilibrium is introduced in undergraduate chemistry and chemical engineering courses, such arguments are generally not accessible. When there is a single reaction equilibrium among mixture components and the components form an ideal mixture, it has been demonstrated by a simple, elegant mathematical argument that there is a unique composition satisfying the equilibrium equation. It has been also suggested that this particular argument extends to non-ideal mixtures by simply incorporating activity coefficients. We show that the argument extension to non-ideal systems is not generally valid. Increasing non-ideality can result in non-monotonicity of the function crucial for the simple uniqueness argument, and only later it leads to non-uniqueness and hence phase separation. The main feature responsible for this is a composition dependence of activity coefficients in non-ideal mixtures.

General Flow-Solver Code for Turbomachinery Applications

NASA Technical Reports Server (NTRS)

Dorney, Daniel; Sondak, Douglas

2006-01-01

Phantom is a computer code intended primarily for real-fluid turbomachinery problems. It is based on Corsair, an ideal-gas turbomachinery code, developed by the same authors, which evolved from the ROTOR codes from NASA Ames. Phantom is applicable to real and ideal fluids, both compressible and incompressible, flowing at subsonic, transonic, and supersonic speeds. It utilizes structured, overset, O- and H-type zonal grids to discretize flow fields and represent relative motions of components. Values on grid boundaries are updated at each time step by bilinear interpolation from adjacent grids. Inviscid fluxes are calculated to third-order spatial accuracy using Roe s scheme. Viscous fluxes are calculated using second-order-accurate central differences. The code is second-order accurate in time. Turbulence is represented by a modified Baldwin-Lomax algebraic model. The code offers two options for determining properties of fluids: One is based on equations of state, thermodynamic departure functions, and corresponding state principles. The other, which is more efficient, is based on splines generated from tables of properties of real fluids. Phantom currently contains fluid-property routines for water, hydrogen, oxygen, nitrogen, kerosene, methane, and carbon monoxide as well as ideal gases.

Using Improved Equation of State to Model Simultaneous Nucleation and Bubble Growth in Thermoplastic Foams

NASA Astrophysics Data System (ADS)

Khan, Irfan; Costeux, Stephane; Adrian, David; Cristancho, Diego

2013-11-01

Due to environmental regulations carbon-dioxide (CO2) is increasingly being used to replace traditional blowing agents in thermoplastic foams. CO2 is dissolved in the polymer matrix under supercritical conditions. In order to predict the effect of process parameters on foam properties using numerical modeling, the P-V-T relationship of the blowing agents should accurately be represented at the supercritical state. Previous studies in the area of foam modeling have all used ideal gas equation of state to predict the behavior of the blowing agent. In this work the Peng-Robinson equation of state is being used to model the blowing agent during its diffusion into the growing bubble. The model is based on the popular ``Influence Volume Approach,'' which assumes a growing boundary layer with depleted blowing agent surrounds each bubble. Classical nucleation theory is used to predict the rate of nucleation of bubbles. By solving the mass balance, momentum balance and species conservation equations for each bubble, the model is capable of predicting average bubble size, bubble size distribution and bulk porosity. The effect of the improved model on the bubble growth and foam properties are discussed.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

Renyi Entropy of the Ideal Gas in Finite Momentum Intervals

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.

2003-06-01

Coincidence probabilities of multiparticle events, as measured in finite momentum intervals for Bose and Fermi ideal gas, are calculated and compared with the exact expressions given in statistical physics.

Do the Particles of an Ideal Gas Collide?

ERIC Educational Resources Information Center

Lesk, Arthur M.

1974-01-01

Describes the collisional properties as a logically essential component of the ideal gas model since an actual intraparticle process cannot support observable anisotropic velocity distributions without collisions taken into account. (CC)

A high-resolution Godunov method for compressible multi-material flow on overlapping grids

NASA Astrophysics Data System (ADS)

Banks, J. W.; Schwendeman, D. W.; Kapila, A. K.; Henshaw, W. D.

2007-04-01

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform-pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on the Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of a planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.

Development of linear projecting in studies of non-linear flow. Acoustic heating induced by non-periodic sound

NASA Astrophysics Data System (ADS)

Perelomova, Anna

2006-08-01

The equation of energy balance is subdivided into two dynamics equations, one describing evolution of the dominative sound, and the second one responsible for acoustic heating. The first one is the famous KZK equation, and the second one is a novel equation governing acoustic heating. The novel dynamic equation considers both periodic and non-periodic sound. Quasi-plane geometry of flow is supposed. Subdividing is provided on the base of specific links of every mode. Media with arbitrary thermic T(p,ρ) and caloric e(p,ρ) equations of state are considered. Individual roles of thermal conductivity and viscosity in the heating induced by aperiodic sound in the ideal gases and media different from ideal gases are discussed.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Effect of pairwise additivity on finite-temperature behavior of classical ideal gas

NASA Astrophysics Data System (ADS)

Shekaari, Ashkan; Jafari, Mahmoud

2018-05-01

Finite-temperature molecular dynamics simulations have been applied to inquire into the effect of pairwise additivity on the behavior of classical ideal gas within the temperature range of T = 250-4000 K via applying a variety of pair potentials and then examining the temperature dependence of a number of thermodynamical properties. Examining the compressibility factor reveals the most deviation from ideal-gas behavior for the Lennard-Jones system mainly due to the presence of both the attractive and repulsive terms. The systems with either attractive or repulsive intermolecular potentials are found to present no resemblance to real gases, but the most similarity to the ideal one as temperature rises.

Electrical model of dielectric barrier discharge homogenous and filamentary modes

NASA Astrophysics Data System (ADS)

López-Fernandez, J. A.; Peña-Eguiluz, R.; López-Callejas, R.; Mercado-Cabrera, A.; Valencia-Alvarado, R.; Muñoz-Castro, A.; Rodríguez-Méndez, B. G.

2017-01-01

This work proposes an electrical model that combines homogeneous and filamentary modes of an atmospheric pressure dielectric barrier discharge cell. A voltage controlled electric current source has been utilized to implement the power law equation that represents the homogeneous discharge mode, which starts when the gas breakdown voltage is reached. The filamentary mode implies the emergence of electric current conducting channels (microdischarges), to add this phenomenon an RC circuit commutated by an ideal switch has been proposed. The switch activation occurs at a higher voltage level than the gas breakdown voltage because it is necessary to impose a huge electric field that contributes to the appearance of streamers. The model allows the estimation of several electric parameters inside the reactor that cannot be measured. Also, it is possible to appreciate the modes of the DBD depending on the applied voltage magnitude. Finally, it has been recognized a good agreement between simulation outcomes and experimental results.

Astrophysical fluid simulations of thermally ideal gases with non-constant adiabatic index: numerical implementation

NASA Astrophysics Data System (ADS)

Vaidya, B.; Mignone, A.; Bodo, G.; Massaglia, S.

2015-08-01

Context. An equation of state (EoS) is a relation between thermodynamic state variables and it is essential for closing the set of equations describing a fluid system. Although an ideal EoS with a constant adiabatic index Γ is the preferred choice owing to its simplistic implementation, many astrophysical fluid simulations may benefit from a more sophisticated treatment that can account for diverse chemical processes. Aims: In the present work we first review the basic thermodynamic principles of a gas mixture in terms of its thermal and caloric EoS by including effects like ionization, dissociation, and temperature dependent degrees of freedom such as molecular vibrations and rotations. The formulation is revisited in the context of plasmas that are either in equilibrium conditions (local thermodynamic- or collisional excitation-equilibria) or described by non-equilibrium chemistry coupled to optically thin radiative cooling. We then present a numerical implementation of thermally ideal gases obeying a more general caloric EoS with non-constant adiabatic index in Godunov-type numerical schemes. Methods: We discuss the necessary modifications to the Riemann solver and to the conversion between total energy and pressure (or vice versa) routinely invoked in Godunov-type schemes. We then present two different approaches for computing the EoS. The first employs root-finder methods and it is best suited for EoS in analytical form. The second is based on lookup tables and interpolation and results in a more computationally efficient approach, although care must be taken to ensure thermodynamic consistency. Results: A number of selected benchmarks demonstrate that the employment of a non-ideal EoS can lead to important differences in the solution when the temperature range is 500-104 K where dissociation and ionization occur. The implementation of selected EoS introduces additional computational costs although the employment of lookup table methods (when possible) can significantly reduce the overhead by a factor of ~ 3-4.

High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows

NASA Astrophysics Data System (ADS)

Sjögreen, Björn; Yee, H. C.

2018-07-01

The Sjogreen and Yee [31] high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal magnetohydrodynamics (MHD). The basic idea is based on Tadmor's [40] original work for inviscid perfect gas flows. For the MHD four formulations of the MHD are considered: (a) the conservative MHD, (b) the Godunov [14] non-conservative form, (c) the Janhunen [19] - MHD with magnetic field source terms, and (d) a MHD with source terms by Brackbill and Barnes [5]. Three forms of the high order entropy numerical fluxes for the MHD in the finite difference framework are constructed. They are based on the extension of the low order form of Chandrashekar and Klingenberg [9], and two forms with modifications of the Winters and Gassner [49] numerical fluxes. For flows containing discontinuities and multiscale turbulence fluctuations the high order entropy conservative numerical fluxes as the new base scheme under the Yee and Sjogreen [31] and Kotov et al. [21,22] high order nonlinear filter approach is developed. The added nonlinear filter step on the high order centered entropy conservative spatial base scheme is only utilized at isolated computational regions, while maintaining high accuracy almost everywhere for long time integration of unsteady flows and DNS and LES of turbulence computations. Representative test cases for both smooth flows and problems containing discontinuities for the gas dynamics and the ideal MHD are included. The results illustrate the improved stability by using the high order entropy conservative numerical flux as the base scheme instead of the pure high order central scheme.

Equation of State of Ammonium Nitrate

NASA Astrophysics Data System (ADS)

Robbins, David L.; Sheffield, Stephen A.; Dattelbaum, Dana M.; Velisavljevic, Nenad; Stahl, David B.

2009-12-01

Ammonium nitrate (AN) is a widely used fertilizer and mining explosive. AN is commonly used in ammonium nitrate-fuel oil (ANFO), which is a mixture of explosive-grade AN prills and fuel oil in a 94:6 ratio by weight. ANFO is a non-ideal explosive with measured detonation velocities around 4 km/s. The equation of state properties and known initiation behavior of neat AN are limited. We present the results of a series of gas gun-driven plate impact experiments on pressed neat ammonium nitrate at 1.72 g/cm3. No evidence of initiation was observed under shock loading to 22 GPa. High pressure x-ray diffraction experiments in diamond anvil cells provided insight into the high pressure phase behavior over the same pressure range (to 25 GPa), as well as a static isotherm at ambient temperature. From the isotherm and thermodynamic properties at ambient conditions, a preliminary unreacted equation of state (EOS) has been developed based on the Murnaghan isotherm and Helmholtz formalism [1], which compares favorably with the available experimental Hugoniot data on several densities of AN.

A purely Lagrangian method for computing linearly-perturbed flows in spherical geometry

NASA Astrophysics Data System (ADS)

Jaouen, Stéphane

2007-07-01

In many physical applications, one wishes to control the development of multi-dimensional instabilities around a one-dimensional (1D) complex flow. For predicting the growth rates of these perturbations, a general numerical approach is viable which consists in solving simultaneously the one-dimensional equations and their linearized form for three-dimensional perturbations. In Clarisse et al. [J.-M. Clarisse, S. Jaouen, P.-A. Raviart, A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed planar-symmetric flows of gas dynamics, J. Comp. Phys. 198 (2004) 80-105], a class of Godunov-type schemes for planar-symmetric flows of gas dynamics has been proposed. Pursuing this effort, we extend these results to spherically symmetric flows. A new method to derive the Lagrangian perturbation equations, based on the canonical form of systems of conservation laws with zero entropy flux [B. Després, Lagrangian systems of conservation laws. Invariance properties of Lagrangian systems of conservation laws, approximate Riemann solvers and the entropy condition, Numer. Math. 89 (2001) 99-134; B. Després, C. Mazeran, Lagrangian gas dynamics in two dimensions and Lagrangian systems, Arch. Rational Mech. Anal. 178 (2005) 327-372] is also described. It leads to many advantages. First of all, many physical problems we are interested in enter this formalism (gas dynamics, two-temperature plasma equations, ideal magnetohydrodynamics, etc.) whatever is the geometry. Secondly, a class of numerical entropic schemes is available for the basic flow [11]. Last, linearizing and devising numerical schemes for the perturbed flow is straightforward. The numerical capabilities of these methods are illustrated on three test cases of increasing difficulties and we show that - due to its simplicity and its low computational cost - the Linear Perturbations Code (LPC) is a powerful tool to understand and predict the development of hydrodynamic instabilities in the linear regime.

Comparison of five equations for estimating resting energy expenditure in Chinese young, normal weight healthy adults

PubMed Central

2012-01-01

Background Most resting energy expenditure (REE) predictive equations for adults were derived from research conducted in western populations; whether they can also be used in Chinese young people is still unclear. Therefore, we conducted this study to determine the best REE predictive equation in Chinese normal weight young adults. Methods Forty-three (21 male, 22 female) healthy college students between the age of 18 and 25 years were recruited. REE was measured by the indirect calorimetry (IC) method. Harris-Benedict, World Health Organization (WHO), Owen, Mifflin and Liu’s equations were used to predictREE (REEe). REEe that was within 10% of measured REE (REEm) was defined as accurate. Student’s t test, Wilcoxon Signed Ranks Test, McNemar Test and the Bland-Altman method were used for data analysis. Results REEm was significantly lower (P < 0.05 or P < 0.01) than REEe from equations, except for Liu’s, Liu’s-s, Owen, Owen-s and Mifflin in men and Liu’s and Owen in women. REEe calculated by ideal body weight was significantly higher than REEe calculated by current body weight ( P < 0.01), the only exception being Harris-Benedict equation in men. Bland-Altman analysis showed that the Owen equation with current body weight generated the least bias. The biases of REEe from Owen with ideal body weight and Mifflin with both current and ideal weights were also lower. Conclusions Liu’s, Owen, and Mifflin equations are appropriate for the prediction of REE in young Chinese adults. However, the use of ideal body weight did not increase the accuracy of REEe. PMID:22937737

Relativistic neutron star merger simulations with non-zero temperature equations of state. I. Variation of binary parameters and equation of state

NASA Astrophysics Data System (ADS)

Oechslin, R.; Janka, H.-T.; Marek, A.

2007-05-01

An extended set of binary neutron star (NS) merger simulations is performed with an approximative treatment of general relativity to systematically investigate the influence of the nuclear equation of state (EoS), the NS masses, and the NS spin states prior to merging. The general relativistic hydrodynamics simulations are based on a conformally flat approximation to the Einstein equations and a Smoothed Particle Hydrodynamics code for the gas treatment. We employ the two non-zero temperature EoSs of Shen et al. (1998a, Nucl. Phys. A, 637, 435; 1998b, Prog. Theor. Phys., 100, 1013) and Lattimer & Swesty (1991, Nucl. Phys. A, 535, 331), which represent a "harder" and a "softer" behavior, respectively, with characteristic differences in the incompressibility at supernuclear densities and in the maximum mass of nonrotating, cold neutron stars. In addition, we use the cold EoS of Akmal et al. (1998, Phys. Rev. C, 58, 1804) with a simple ideal-gas-like extension according to Shibata & Taniguchi (2006, Phys. Rev. D, 73, 064027), in order to compare with their results, and an ideal-gas EoS with parameters fitted to the supernuclear part of the Shen-EoS. We estimate the mass sitting in a dilute "torus" around the future black hole (BH) by requiring the specific angular momentum of the torus matter to be larger than the angular momentum of the ISCO around a Kerr BH with the mass and spin parameter of the compact central remnant. The dynamics and outcome of the models is found to depend strongly on the EoS and on the binary parameters. Larger torus masses are found for asymmetric systems (up to 0.3 M_⊙ for a mass ratio of 0.55), for large initial NSs, and for a NS spin state which corresponds to a larger total angular momentum. We find that the postmerger remnant collapses either immediately or after a short time when employing the soft EoS of Lattimer& Swesty, whereas no sign of post-merging collapse is found within tens of dynamical timescales for all other EoSs used. The typical temperatures in the torus are found to be about 3{-}10 MeV depending on the strength of the shear motion at the collision interface between the NSs and thus depending on the initial NS spins. About 10-3{-}10-2 M_⊙ of NS matter become gravitationally unbound during or right after the merging process. This matter consists of a hot/high-entropy component from the collision interface and (only in case of asymmetric systems) of a cool/low-entropy component from the spiral arm tips. Appendices are only available in electronic form at http://www.aanda.org

Gravitational Thermodynamics for Interstellar Gas and Weakly Degenerate Quantum Gas

NASA Astrophysics Data System (ADS)

Zhu, Ding Yu; Shen, Jian Qi

2016-03-01

The temperature distribution of an ideal gas in gravitational fields has been identified as a longstanding problem in thermodynamics and statistical physics. According to the principle of entropy increase (i.e., the principle of maximum entropy), we apply a variational principle to the thermodynamical entropy functional of an ideal gas and establish a relationship between temperature gradient and gravitational field strength. As an illustrative example, the temperature and density distributions of an ideal gas in two simple but typical gravitational fields (i.e., a uniform gravitational field and an inverse-square gravitational field) are considered on the basis of entropic and hydrostatic equilibrium conditions. The effect of temperature inhomogeneity in gravitational fields is also addressed for a weakly degenerate quantum gas (e.g., Fermi and Bose gas). The present gravitational thermodynamics of a gas would have potential applications in quantum fluids, e.g., Bose-Einstein condensates in Earth’s gravitational field and the temperature fluctuation spectrum in cosmic microwave background radiation.

Universal equation for estimating ideal body weight and body weight at any BMI1

PubMed Central

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-01-01

Background: Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. Objective: For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. Design: With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Results: Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5–0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Conclusions: Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. PMID:27030535

Universal equation for estimating ideal body weight and body weight at any BMI.

PubMed

Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B

2016-05-01

Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.

Commentary on factors affecting transverse vibration using an idealized theoretical equation

Treesearch

Joseph F. Murphy

2000-01-01

An idealized theoretical equation to calculate flexural stiffness using transverse vibration of a simply end-supported beam is being considered by the American Society of Testing and Materials (ASTM) Wood Committee D07 to determine lumber modulus of elasticity. This commentary provides the user a quantitative view of six factors that affect the accuracy of using the...

Temperature and the Ideal Gas

ERIC Educational Resources Information Center

Daisley, R. E.

1973-01-01

Presents some organized ideas in thermodynamics which are suitable for use with high school (GCE A level or ONC) students. Emphases are placed upon macroscopic observations and intimate connection of the modern definition of temperature with the concept of ideal gas. (CC)

Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations

NASA Astrophysics Data System (ADS)

Derigs, Dominik; Winters, Andrew R.; Gassner, Gregor J.; Walch, Stefanie; Bohm, Marvin

2018-07-01

The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning mechanism in such a way that the resulting model is consistent with the second law of thermodynamics. As a byproduct of these derivations, we show that not all of the commonly used divergence cleaning extensions of the ideal MHD equations are thermodynamically consistent. Secondly, we present a numerical scheme obtained by constructing a specific finite volume discretization that is consistent with the discrete thermodynamic entropy. It includes a mechanism to control the discrete divergence error of the magnetic field by construction and is Galilean invariant. We implement the new high-order MHD solver in the adaptive mesh refinement code FLASH where we compare the divergence cleaning efficiency to the constrained transport solver available in FLASH (unsplit staggered mesh scheme).

Stellar feedback strongly alters the amplification and morphology of galactic magnetic fields

NASA Astrophysics Data System (ADS)

Su, Kung-Yi; Hayward, Christopher C.; Hopkins, Philip F.; Quataert, Eliot; Faucher-Giguère, Claude-André; Kereš, Dušan

2018-01-01

Using high-resolution magnetohydrodynamic simulations of idealized, non-cosmological galaxies, we investigate how cooling, star formation and stellar feedback affect galactic magnetic fields. We find that the amplification histories, saturation values and morphologies of the magnetic fields vary considerably depending on the baryonic physics employed, primarily because of differences in the gas density distribution. In particular, adiabatic runs and runs with a subgrid (effective equation of state) stellar feedback model yield lower saturation values and morphologies that exhibit greater large-scale order compared with runs that adopt explicit stellar feedback and runs with cooling and star formation but no feedback. The discrepancies mostly lie in gas denser than the galactic average, which requires cooling and explicit fragmentation to capture. Independent of the baryonic physics included, the magnetic field strength scales with gas density as B ∝ n2/3, suggesting isotropic flux freezing or equipartition between the magnetic and gravitational energies during the field amplification. We conclude that accurate treatments of cooling, star formation and stellar feedback are crucial for obtaining the correct magnetic field strength and morphology in dense gas, which, in turn, is essential for properly modelling other physical processes that depend on the magnetic field, such as cosmic ray feedback.

Computer program for calculation of ideal gas thermodynamic data

NASA Technical Reports Server (NTRS)

Gordon, S.; Mc Bride, B. J.

1968-01-01

Computer program calculates ideal gas thermodynamic properties for any species for which molecular constant data is available. Partial functions and derivatives from formulas based on statistical mechanics are provided by the program which is written in FORTRAN 4 and MAP.

Condensation and critical exponents of an ideal non-Abelian gas

NASA Astrophysics Data System (ADS)

Talaei, Zahra; Mirza, Behrouz; Mohammadzadeh, Hosein

2017-11-01

We investigate an ideal gas obeying non-Abelian statistics and derive the expressions for some thermodynamic quantities. It is found that thermodynamic quantities are finite at the condensation point where their derivatives diverge and, near this point, they behave as \\vert T-Tc\\vert^{-ρ} in which Tc denotes the condensation temperature and ρ is a critical exponent. The critical exponents related to the heat capacity and compressibility are obtained by fitting numerical results and others are obtained using the scaling law hypothesis for a three-dimensional non-Abelian ideal gas. This set of critical exponents introduces a new universality class.

Comment on “Equilibrium constants and rate constants for adsorbates: Two-dimensional (2D) ideal gas, 2D ideal lattice gas, and ideal hindered translator models”

DOE Office of Scientific and Technical Information (OSTI.GOV)

Savara, Aditya

The paper by Campbell et al. was recently brought to my attention. This comment is written to provide greater clarity to the community to prevent misconceptions regarding the entropies being discussed in that work and to clarify the differences between the adsorbate standard states suggested by Campbell and by Savara.

Comment on “Equilibrium constants and rate constants for adsorbates: Two-dimensional (2D) ideal gas, 2D ideal lattice gas, and ideal hindered translator models”

DOE PAGES

Savara, Aditya

2016-08-15

The paper by Campbell et al. was recently brought to my attention. This comment is written to provide greater clarity to the community to prevent misconceptions regarding the entropies being discussed in that work and to clarify the differences between the adsorbate standard states suggested by Campbell and by Savara.

Experimental investigation of nozzle/plume aerodynamics at hypersonic speeds

NASA Technical Reports Server (NTRS)

Bogdanoff, David W.; Cambier, Jean-Luc; Papadopoulos, Perikles

1994-01-01

Much of the work involved the Ames 16-Inch Shock Tunnel facility. The facility was reactivated and upgraded, a data acquisition system was configured and upgraded several times, several facility calibrations were performed and test entries with a wedge model with hydrogen injection and a full scramjet combustor model, with hydrogen injection, were performed. Extensive CFD modeling of the flow in the facility was done. This includes modeling of the unsteady flow in the driver and driven tubes and steady flow modeling of the nozzle flow. Other modeling efforts include simulations of non-equilibrium flows and turbulence, plasmas, light gas guns and the use of non-ideal gas equations of state. New experimental techniques to improve the performance of gas guns, shock tubes and tunnels and scramjet combustors were conceived and studied computationally. Ways to improve scramjet engine performance using steady and pulsed detonation waves were also studied computationally. A number of studies were performed on the operation of the ram accelerator, including investigations of in-tube gasdynamic heating and the use of high explosives to raise the velocity capability of the device.

On the Goertler instability in hypersonic flows: Sutherland law fluids and real gas effects

NASA Technical Reports Server (NTRS)

Fu, Yibin B.; Hall, Philip; Blackaby, Nicholas D.

1990-01-01

The Goertler vortex instability mechanism in a hypersonic boundary layer on a curved wall is investigated. The precise roles of the effects of boundary layer growth, wall cooling, and gas dissociation is clarified in the determination of stability properties. It is first assumed that the fluid is an ideal gas with viscosity given by Sutherland's law. It is shown that when the free stream Mach number M is large, the boundary layer divides into two sublayers: a wall layer of O(M sup 3/2) thickness over which the basic state temperature is O(M squared) and a temperature adjustment layer of O(1) thickness over which the basic state temperature decreases monotonically to its free stream value. Goertler vortices which have wavelengths comparable with the boundary layer thickness are referred to as wall modes. It is shown that their downstream evolution is governed by a set of parabolic partial differential equations and that they have the usual features of Goertler vortices in incompressible boundary layers. As the local wavenumber increases, the neutral Goertler number decreases and the center of vortex activity moves towards the temperature adjustment layer. Goertler vortices with wavenumbers of order one or larger must necessarily be trapped in the temperature adjustment layer and it is this mode which is most dangerous. For this mode, it was found that the leading order term in the Goertler number expansion is independent of the wavenumber and is due to the curvature of the basic state. This term is also the asymptotic limit of the neutral Goertler numbers of the wall mode. To determine the higher order corrections terms in the Goertler number expansion, two wall curvature cases are distinguished. Real gas effects were investigated by assuming that the fluid is an ideal dissociating gas. It was found that both gas dissociation and wall cooling are destabilizing for the mode trapped in the temperature adjustment layer, but for the wall mode trapped near the wall the effect of gas dissociation can be either destabilizing or stabilizing.

Shock Initiation and Equation of State of Ammonium Nitrate

NASA Astrophysics Data System (ADS)

Robbins, David; Sheffield, Steve; Dattelbaum, Dana; Chellappa, Raja; Velisavljevic, Nenad

2013-06-01

Ammonium nitrate (AN) is a widely used fertilizer and mining explosive commonly found in ammonium nitrate-fuel oil. Neat AN is a non-ideal explosive with measured detonation velocities approaching 4 km/s. Previously, we reported a thermodynamically-complete equation of state for AN based on its maximum density, and showed that near-full density AN did not initiate when subjected to shock input conditions up to 22 GPa. In this work, we extend these initial results, by presenting new Hugoniot data for intermediate density neat AN obtained from gas gun-driven plate impact experiments. AN at densities from 1.8 to 1.5 g/cm3 were impacted into LiF windows using a two-stage light gas gun. Dual VISARs were used to measure the interfacial particle velocity wave profile as a function of time following impact. The new Hugoniot data, in addition to updates to thermodynamic parameters derived from structural analysis and vibrational spectroscopy measurements in high pressure diamond anvil cell experiments, are used to refine the unreacted EOS for AN. Furthermore, shock initiation of neat AN was observed as the initial porosity increased (density decreased). Insights into the relationship(s) between initial density and shock initiation sensitivity are also presented, from evidence of shock initiation in the particle velocity profiles obtained for the lower density AN samples.

Fluctuation theorem for the effusion of an ideal gas.

PubMed

Cleuren, B; Van den Broeck, C; Kawai, R

2006-08-01

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.

General chemical kinetics computer program for static and flow reactions, with application to combustion and shock-tube kinetics

NASA Technical Reports Server (NTRS)

Bittker, D. A.; Scullin, V. J.

1972-01-01

A general chemical kinetics program is described for complex, homogeneous ideal-gas reactions in any chemical system. Its main features are flexibility and convenience in treating many different reaction conditions. The program solves numerically the differential equations describing complex reaction in either a static system or one-dimensional inviscid flow. Applications include ignition and combustion, shock wave reactions, and general reactions in a flowing or static system. An implicit numerical solution method is used which works efficiently for the extreme conditions of a very slow or a very fast reaction. The theory is described, and the computer program and users' manual are included.

Computer program for calculating and fitting thermodynamic functions

NASA Technical Reports Server (NTRS)

Mcbride, Bonnie J.; Gordon, Sanford

1992-01-01

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Numerical modelling of physical processes in a ballistic laboratory setup with a tapered adapter and plastic piston used for obtaining high muzzle velocities

NASA Astrophysics Data System (ADS)

Bykov, N. V.

2014-12-01

Numerical modelling of a ballistic setup with a tapered adapter and plastic piston is considered. The processes in the firing chamber are described within the framework of quasi- one-dimensional gas dynamics and a geometrical law of propellant burn by means of Lagrangian mass coordinates. The deformable piston is considered to be an ideal liquid with specific equations of state. The numerical solution is obtained by means of a modified explicit von Neumann scheme. The calculation results given show that the ballistic setup with a tapered adapter and plastic piston produces increased shell muzzle velocities by a factor of more than 1.5-2.

Evaluation of hydrogen as a cryogenic wind tunnel test gas

NASA Technical Reports Server (NTRS)

Haut, R. C.

1977-01-01

The nondimensional ratios used to describe various flow situations in hydrogen were determined and compared with the corresponding ideal diatomic gas ratios. The results were used to examine different inviscid flow configurations. The relatively high value of the characteristic rotational temperature causes the behavior of hydrogen, under cryogenic conditions, to deviate substantially from the behavior of an ideal diatomic gas in the compressible flow regime. Therefore, if an idea diatomic gas is to be modeled, cryogenic hydrogen is unacceptable as a wind tunnel test gas in a compressible flow situation.

A New Model for Gas Transfer and Storage in a Permeable Volcanic Edifice

NASA Astrophysics Data System (ADS)

Collinson, A. D.; Neuberg, J.

2011-12-01

There is a marked contrast between the behaviour of a volcano in an open system compared to one which is closed. It is therefore essential to understand degassing, to appreciate how much gas is lost and where. Previous studies by a variety of scientists have led to the accumulation of data via field evidence from both active and fossil volcanoes (Stasiuk et al., 1996), laboratory experiments (Moore et al., 1994) and conceptual modelling, in which Darcy's law has become increasingly applicable (Eichelberger et al., 1986; Edmonds et al., 2003). Of particular interest for this study, is the effect different permeabilities have on the degree and pattern of the gas flux. A new method has been devised to investigate gas transport and storage in a permeable volcanic edifice. The continuity equation and Darcy's law are amalgamated to derive a partial differential equation which is solved using a finite element method to obtain the gas pressure. The associated pressure gradient is then used within Darcy's law to calculate the gas flux. The properties of the gas are described by the ideal gas law. The strength of this method is that it allows the modelling of two and three dimensional structures both in stationary equilibrium and as a time dependent progression. A geometry is created and the pressure and permeabilites incorporated into the model as boundary and domain conditions respectively. The aim of the model is to investigate how variable permeability and pressure gradients influence the gas flux, for example highly permeable cracks in the dome, or impermeable layers within the volcanic structure. We also use this gas model to complement the model of Neuberg et al. (2006) in which brittle failure of the conduit-wall boundary is used as a trigger mechanism of low-frequency earthquakes. The associated behaviour of the gas in response to the brittle failure is simulated in our model by increasing the permeability through a narrow zone at the boundary between the conduit and country rock. In addition, we investigate how the presence of gas and variations in permeability influence the rate and degree of deformation seen in the volcanic edifice. Our model is highly versatile and has the potential to be integral to the understanding of gas transport and storage within a permeable volcanic edifice.

A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banks, J W; Schwendeman, D W; Kapila, A K

2006-02-13

A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on amore » uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.« less

A Demonstration of Ideal Gas Principles Using a Football.

ERIC Educational Resources Information Center

Bare, William D.; Andrews, Lester

1999-01-01

Uses a true-to-life story of accusations made against a college football team to illustrate ideal gas laws. Students are asked to decide whether helium-filled footballs would increase punt distances and how to determine whether a football contained air or helium. (WRM)

Fluctuation theorem for entropy production during effusion of a relativistic ideal gas.

PubMed

Cleuren, B; Willaert, K; Engel, A; Van den Broeck, C

2008-02-01

The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and antiparticle pair production and annihilation. In both cases, the fluctuation theorem is verified.

Computational flow predictions for hypersonic drag devices

NASA Technical Reports Server (NTRS)

Tokarcik, Susan A.; Venkatapathy, Ethiraj

1993-01-01

The effectiveness of two types of hypersonic decelerators is examined: mechanically deployable flares and inflatable ballutes. Computational fluid dynamics (CFD) is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The results from the ideal gas solver are compared to computational results from a thermochemical nonequilibrium solver. The surface pressure coefficient, the drag, and the extend of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.

A thermodynamic study of pyrite and pyrrhotite

USGS Publications Warehouse

Toulmin, P.; Barton, P.B.

1964-01-01

Through the use of the electrum-tarnish method the following equation has been found to interrelate the composition of pyrrhotite, fugacity of sulfur, and temperature: In this equation fs2 is the fugacity of sulfur relative to the ideal diatomic gas at 1 atm, N is the mol fraction of FeS in pyrrhotite (in the system FeS-S2), and T the absolute temperature. The experimental uncertainty in the equation is 0-003 in N. The activity of FeS (aFeS) in pyrrhotite relative to the pure substance at the temperature of consideration follows from the above equation by virtue of the Gibbs-Duhem relation; it is given by:. The electrum-tarnish method has permitted us to determine the fs2 vs. T curve for the univariant assemblage pyrrhotite-pyrite-vapor from 743 to 325??C. Our determinations of the composition of pyrrhotite are in excellent agreement with the results of Arnold. The activity of FeS in pyrite-saturated pyrrhotite is very different from unity, a fact that greatly influences the interpretation of some other phase equilibrium studies involving pyrrhotite and their application to sulfide mineral assemblages, but has little effect on the more general calculations of composition of hydrothermal or magmatic fluids. Pressure effects calculated from available volumetric data on the phases are small. ?? 1964.

How Is the Ideal Gas Law Explanatory?

ERIC Educational Resources Information Center

Woody, Andrea I.

2013-01-01

Using the ideal gas law as a comparative example, this essay reviews contemporary research in philosophy of science concerning scientific explanation. It outlines the inferential, causal, unification, and erotetic conceptions of explanation and discusses an alternative project, the functional perspective. In each case, the aim is to highlight…

Ram-pressure scaling and non-uniformity characterization of a spherically imploding liner formed by hypervelocity plasma jets

NASA Astrophysics Data System (ADS)

Cassibry, Jason; Dougherty, Jesse; Thompson, Seth; Hsu, Scott; Witherspoon, F. D.; University of AL in Huntsville Team; Los Alamos National Laboratory Team; HyperV Technologies Corp. Team

2014-10-01

Three-dimensional modeling of plasma liner formation and implosion is performed using the Smoothed Particle Hydrodynamics Code (SPHC) with radiation, thermal transport, and tabular equations of state (EOS), accounting for ionization, in support of a proposed 60-gun plasma liner formation experiment for plasma-jet driven magneto-inertial fusion (PJMIF). Previous SPHC modeling showed that ideal gas law scaling of peak stagnation pressure increased linearly with density and number of jets, quadratically with jet radius and velocity, and inversely with the initial jet length, while results with tabular EOS, thermal transport, and radiation have greater sensitivity to the initial jet distribution. A series of simulations are conducted to study the effects of initial jet conditions on peak ram pressure and liner non-uniformity during plasma liner implosion. The growth rate of large-amplitude density perturbations introduced by the discrete jets are computed and compared with predictions by the Bell-Plesset equation.

Ideal solar cell equation in the presence of photon recycling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lan, Dongchen, E-mail: d.lan@unsw.edu.au; Green, Martin A., E-mail: m.green@unsw.edu.au

Previous derivations of the ideal solar cell equation based on Shockley's p-n junction diode theory implicitly assume negligible effects of photon recycling. This paper derives the equation in the presence of photon recycling that modifies the values of dark saturation and light-generated currents, using an approach applicable to arbitrary three-dimensional geometries with arbitrary doping profile and variable band gap. The work also corrects an error in previous work and proves the validity of the reciprocity theorem for charge collection in such a more general case with the previously neglected junction depletion region included.

Investigation of the on-axis atom number density in the supersonic gas jet under high gas backing pressure by simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guanglong; Xu, Yi; Cao, Yunjiu

The supersonic gas jets from conical nozzles are simulated using 2D model. The on-axis atom number density in gas jet is investigated in detail by comparing the simulated densities with the idealized densities of straight streamline model in scaling laws. It is found that the density is generally lower than the idealized one and the deviation between them is mainly dependent on the opening angle of conical nozzle, the nozzle length and the gas backing pressure. The density deviation is then used to discuss the deviation of the equivalent diameter of a conical nozzle from the idealized d{sub eq} inmore » scaling laws. The investigation on the lateral expansion of gas jet indicates the lateral expansion could be responsible for the behavior of the density deviation. These results could be useful for the estimation of cluster size and the understanding of experimental results in laser-cluster interaction experiments.« less

Dipole-dipole interactions in a hot atomic vapor and in an ultracold gas of Rydberg atoms

NASA Astrophysics Data System (ADS)

Sautenkov, V. A.; Saakyan, S. A.; Bronin, S. Ya; Klyarfeld, A. B.; Zelener, B. B.; Zelener, B. V.

2018-01-01

In our paper ideal and non-ideal gas media of neutral atoms are analyzed. The first we discuss a dipole broadening of atomic transitions in excited dilute and dense metal vapors. Then the theoretical studies of the dipole-dipole interactions in dense ultracold gas of Rydberg atoms are considered. Possible future experiments on a base of our experimental arrangement are suggested.

Theoretical test of Jarzynski's equality for reversible volume-switching processes of an ideal gas system.

PubMed

Sung, Jaeyoung

2007-07-01

We present an exact theoretical test of Jarzynski's equality (JE) for reversible volume-switching processes of an ideal gas system. The exact analysis shows that the prediction of JE for the free energy difference is the same as the work done on the gas system during the reversible process that is dependent on the shape of path of the reversible volume-switching process.

Methods to produce calibration mixtures for anesthetic gas monitors and how to perform volumetric calculations on anesthetic gases.

PubMed

Christensen, P L; Nielsen, J; Kann, T

1992-10-01

A simple procedure for making calibration mixtures of oxygen and the anesthetic gases isoflurane, enflurane, and halothane is described. One to ten grams of the anesthetic substance is evaporated in a closed, 11,361-cc glass bottle filled with oxygen gas at atmospheric pressure. The carefully mixed gas is used to calibrate anesthetic gas monitors. By comparison of calculated and measured volumetric results it is shown that at atmospheric conditions the volumetric behavior of anesthetic gas mixtures can be described with reasonable accuracy using the ideal gas law. A procedure is described for calculating the deviation from ideal gas behavior in cases in which this is needed.

Teaching Classical Statistical Mechanics: A Simulation Approach.

ERIC Educational Resources Information Center

Sauer, G.

1981-01-01

Describes a one-dimensional model for an ideal gas to study development of disordered motion in Newtonian mechanics. A Monte Carlo procedure for simulation of the statistical ensemble of an ideal gas with fixed total energy is developed. Compares both approaches for a pseudoexperimental foundation of statistical mechanics. (Author/JN)

Joseph Boussinesq et son approximation : un aperçu actuel

NASA Astrophysics Data System (ADS)

Zeytounian, Radyadour Kh.

2003-08-01

A hundred years ago, in his 1903 volume II of the monograph devoted to 'Théorie Analytique de la Chaleur', Joseph Valentin Boussinesq observes that: "The v ariations of density can be ignored except were they are multiplied by the acceleration of gravity in equation of motion for the vertical component of the velocity vector." A spectacular consequence of this Boussinesq observation (called, in 1916, by Rayleigh, the 'Boussinesq approximation') is the possibility to work with a quasi-incompressible system of coupled dynamic, (Navier) and thermal (Fourier) equations where buoyancy is the main driving force. After a few words on the life of Boussinesq and on his observation, the applicability of this approximation is briefly discussed for various thermal, geophysical, astrophysical and magnetohydrodynamic problems in the framework of 'Boussinesquian fluid dynamics'. An important part of our contemporary view is devoted to a logical (100 years later) justification of this Boussinesq approximation for a perfect gas and an ideal liquid in the framework of an asymptotic modelling of the full fluid dynamics (Euler and Navier-Stokes-Fourier) equations with especially careful attention given to the validity of this approximation. To cite this article: R.Kh. Zeytounian, C. R. Mecanique 331 (2003).

Dynamic response of a collidant impacting a low pressure airbag

NASA Astrophysics Data System (ADS)

Dreher, Peter A.

There are many uses of low pressure airbags, both military and commercial. Many of these applications have been hampered by inadequate and inaccurate modeling tools. This dissertation contains the derivation of a four degree-of-freedom system of differential equations from physical laws of mass and energy conservation, force equilibrium, and the Ideal Gas Law. Kinematic equations were derived to model a cylindrical airbag as a single control volume impacted by a parallelepiped collidant. An efficient numerical procedure was devised to solve the simplified system of equations in a manner amenable to discovering design trends. The largest public airbag experiment, both in scale and scope, was designed and built to collect data on low-pressure airbag responses, otherwise unavailable in the literature. The experimental results were compared to computational simulations to validate the simplified numerical model. Experimental response trends are presented that will aid airbag designers. The two objectives of using a low pressure airbag to demonstrate the feasibility to (1) accelerate a munition to 15 feet per second velocity from a bomb bay, and (2) decelerate humans hitting trucks below the human tolerance level of 50 G's, were both met.

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Kailiang; Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn

The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with themore » aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.« less

Dust transportation in bounday layers on complex areas

NASA Astrophysics Data System (ADS)

Karelsky, Kirill; Petrosyan, Arakel

2017-04-01

This presentation is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or nonstationary boundaries. The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere with as small as one likes coefficient of molecular viscosity, the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. It is unconditionally in this case Prandtle hypothesis must be observed: for rather wide range of conditions in the surface neighboring layers energy dissipation of atmosphere flows is comparable by magnitude with manifestation of inertia forces. That is why according to Prandtle hypothesis in atmosphere movement characterizing by a high Reynolds number the boundary layer is forming near a planet surface, within which the required transition from zero velocities at the surface to magnitudes at the external boundary of the layer that are quite close to ones in ideal atmosphere flow. In that layer fast velocity gradients cause viscous effects to be comparable in magnitude with inertia forces influence. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by nonslip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of high wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations. We deal with describing high field gradients with the aid of scheme viscosity of numerical algorithm used to model near-surface phenomena. This idea is implemented in the model of ideal gas equations with variable equation of state describing particulates transportation within boundary layer with obstacles.

Diffusive Imaging of Hydraulically Induced and Natural Fracture Systems

NASA Astrophysics Data System (ADS)

Eftekhari, B.; Marder, M. P.; Patzek, T. W.

2017-12-01

Hydraulic fracturing of tight shales continues to provide the US with a major source of energy. Efficiency of gas recovery in shales depends upon the geometry of the resulting network of fractures, the details of which are not yet fully understood. The present research explores how much of the underlying geometry can be deduced from the time dependence of the flow of gas out of the reservoir. We consider both ideal and real gas. In the case of real gas, we calculate production rate for parallel planar hydrofractures embedded in an infinite reservoir. Transport is governed by a nonlinear diffusion equation, which we solve exactly with a scaling curve. The scaling curve production rate declines initially as 1 over square root time, then as an exponential, and finally as 1 over square root of time again at late time. We show that for a given hydraulically fractured well, the onsets of transition between different decline regimes provides a direct estimate of a characteristic spacing of the underlying fracture network. We show that the scaling solution accurately fits the production history of more than 15,000 wells in the Barnett Shale. Almost all of the wells either have not yet transitioned into the late time decline or have been refractured while in exponential decline. However, there are 36 wells which show the late time transition. These allow us to calculate the characteristic spacing, which turns out to have a mode at about 10 m, a minimum at 1.6 m and a maximum at 13.3 m. We estimate that over 30 years these wells will produce on average about 45% more gas because of diffusion from the infinite external reservoir than they would if this contribution is neglected. Finally, we compute the rate at which ideal gas diffuses within an infinite region of rock into a specific absorbing fractal fracture network, which we model using geological constraints and percolation theory. Our solution employs a Brownian walk and the first passage kinetic Monte Carlo algorithm that is robust and efficient. A striking feature of this solution is the presence of a power law decline.

Equations of motion for a flexible spacecraft-lumped parameter idealization

NASA Technical Reports Server (NTRS)

Storch, Joel; Gates, Stephen

1982-01-01

The equations of motion for a flexible vehicle capable of arbitrary translational and rotational motions in inertial space accompanied by small elastic deformations are derived in an unabridged form. The vehicle is idealized as consisting of a single rigid body with an ensemble of mass particles interconnected by massless elastic structure. The internal elastic restoring forces are quantified in terms of a stiffness matrix. A transformation and truncation of elastic degrees of freedom is made in the interest of numerical integration efficiency. Deformation dependent terms are partitioned into a hierarchy of significance. The final set of motion equations are brought to a fully assembled first order form suitable for direct digital implementation. A FORTRAN program implementing the equations is given and its salient features described.

Ideal thermodynamic processes of oscillatory-flow regenerative engines will go to ideal stirling cycle?

NASA Astrophysics Data System (ADS)

Luo, Ercang

2012-06-01

This paper analyzes the thermodynamic cycle of oscillating-flow regenerative machines. Unlike the classical analysis of thermodynamic textbooks, the assumptions for pistons' movement limitations are not needed and only ideal flowing and heat transfer should be maintained in our present analysis. Under such simple assumptions, the meso-scale thermodynamic cycles of each gas parcel in typical locations of a regenerator are analyzed. It is observed that the gas parcels in the regenerator undergo Lorentz cycle in different temperature levels, whereas the locus of all gas parcels inside the regenerator is the Ericson-like thermodynamic cycle. Based on this new finding, the author argued that ideal oscillating-flow machines without heat transfer and flowing losses is not the Stirling cycle. However, this new thermodynamic cycle can still achieve the same efficiency of the Carnot heat engine and can be considered a new reversible thermodynamic cycle under two constant-temperature heat sinks.

Heat Diffusion in Gases, Including Effects of Chemical Reaction

NASA Technical Reports Server (NTRS)

Hansen, C. Frederick

1960-01-01

The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

Evaluation of indoor air composition time variation in air-tight occupied spaces during night periods

NASA Astrophysics Data System (ADS)

Markov, Detelin

2012-11-01

This paper presents an easy-to-understand procedure for prediction of indoor air composition time variation in air-tight occupied spaces during the night periods. The mathematical model is based on the assumptions for homogeneity and perfect mixing of the indoor air, the ideal gas model for non-reacting gas mixtures, mass conservation equations for the entire system and for each species, a model for prediction of basal metabolic rate of humans as well as a model for prediction of O2 consumption rate and both CO2 and H2O generation rates by breathing. Time variation of indoor air composition is predicted at constant indoor air temperature for three scenarios based on the analytical solution of the mathematical model. The results achieved reveal both the most probable scenario for indoor air time variation in air-tight occupied spaces as well as the cause for morning tiredness after having a sleep in a modern energy efficient space.

Probing free jet expansions of supercritical fluids

NASA Astrophysics Data System (ADS)

Christen, W.; Rademann, K.

2009-10-01

Attempting to improve the comprehension of supersonic molecular beams at elevated pressures we present a comparative study of thermodynamic descriptions of the terminal flow velocity in free jet expansions. As model system we choose carbon dioxide due to its widespread utilization in supercritical fluid technology. Numerical results for the thermodynamic quantities are obtained using a high accuracy equation of state explicit in the Helmholtz free energy. The influence of pressure and temperature on the beam velocity is investigated for a broad range of stagnation conditions. A consistent physical picture is obtained for calculations employing the initial and final molar enthalpies, while enormous discrepancies are found for descriptions based on the molar isobaric heat capacity or the heat capacity ratio. The deviations are particularly pronounced at the gas-liquid phase transition and in the vicinity of the critical point and can be related to the diverse assumptions of ideal gas behavior. It is shown that computations using real fluid enthalpies permit to assess the fraction of condensation in supersonic jets.

On controlling nonlinear dissipation in high order filter methods for ideal and non-ideal MHD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sjogreen, B.

2004-01-01

The newly developed adaptive numerical dissipation control in spatially high order filter schemes for the compressible Euler and Navier-Stokes equations has been recently extended to the ideal and non-ideal magnetohydrodynamics (MHD) equations. These filter schemes are applicable to complex unsteady MHD high-speed shock/shear/turbulence problems. They also provide a natural and efficient way for the minimization of Div(B) numerical error. The adaptive numerical dissipation mechanism consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free from numerical dissipation contamination. The numerical dissipation considered consists of high order linear dissipation for the suppression of high frequency oscillation and the nonlinear dissipative portion of high-resolution shock-capturing methods for discontinuity capturing. The applicable nonlinear dissipative portion of high-resolution shock-capturing methods is very general. The objective of this paper is to investigate the performance of three commonly used types of nonlinear numerical dissipation for both the ideal and non-ideal MHD.

How Incorrect Is the Classical Partition Function for the Ideal Gas?

ERIC Educational Resources Information Center

Kroemer, Herbert

1980-01-01

Discussed is the classical partition function for the ideal gas and how it differs from the exact value for bosons or fermions in the classical regime. The differences in the two values are negligible hence the classical treatment leads in the end to correct answers for all observables. (Author/DS)

Experimental Verification of Boyle's Law and the Ideal Gas Law

ERIC Educational Resources Information Center

Ivanov, Dragia Trifonov

2007-01-01

Two new experiments are offered concerning the experimental verification of Boyle's law and the ideal gas law. To carry out the experiments, glass tubes, water, a syringe and a metal manometer are used. The pressure of the saturated water vapour is taken into consideration. For educational purposes, the experiments are characterized by their…

Spectral Decomposition and Other Seismic Attributes for Gas Hydrate Prospecting

DOE Office of Scientific and Technical Information (OSTI.GOV)

McConnell, Dan

Studying the sediments at the base of gas hydrate stability is ideal for determining the seismic response to gas hydrate saturation. First, assuming gas migration to the shallow section, this area is more likely to have concentrated gas hydrate because it encompasses the zone in which upward moving buoyant gas transitions to form immobile gas hydrate deposits. Second, this zone is interesting because these areas have the potential to show a hydrate filled zone and a gas filled zone within the same sediments. Third, the fundamental measurement within seismic data is impedance contrasts between velocity*density layers. High saturation gas hydratesmore » and free gas inhabit opposite ends of these measurements making the study of this zone ideal for investigating the seismic characteristics of gas hydrate and, hence, the investigation of other seismic attributes that may indicate gas hydrate fill.« less

Hydrodynamics of Normal Atomic Gases with Spin-orbit Coupling

PubMed Central

Hou, Yan-Hua; Yu, Zhenhua

2015-01-01

Successful realization of spin-orbit coupling in atomic gases by the NIST scheme opens the prospect of studying the effects of spin-orbit coupling on many-body physics in an unprecedentedly controllable way. Here we derive the linearized hydrodynamic equations for the normal atomic gases of the spin-orbit coupling by the NIST scheme with zero detuning. We show that the hydrodynamics of the system crucially depends on the momentum susceptibilities which can be modified by the spin-orbit coupling. We reveal the effects of the spin-orbit coupling on the sound velocities and the dipole mode frequency of the gases by applying our formalism to the ideal Fermi gas. We also discuss the generalization of our results to other situations. PMID:26483090

Hydrodynamics of Normal Atomic Gases with Spin-orbit Coupling.

PubMed

Hou, Yan-Hua; Yu, Zhenhua

2015-10-20

Successful realization of spin-orbit coupling in atomic gases by the NIST scheme opens the prospect of studying the effects of spin-orbit coupling on many-body physics in an unprecedentedly controllable way. Here we derive the linearized hydrodynamic equations for the normal atomic gases of the spin-orbit coupling by the NIST scheme with zero detuning. We show that the hydrodynamics of the system crucially depends on the momentum susceptibilities which can be modified by the spin-orbit coupling. We reveal the effects of the spin-orbit coupling on the sound velocities and the dipole mode frequency of the gases by applying our formalism to the ideal Fermi gas. We also discuss the generalization of our results to other situations.

Indirect Measurement Of Nitrogen In A Multi-Component Gas By Measuring The Speed Of Sound At Two States Of The Gas.

DOEpatents

Morrow, Thomas B.; Behring, II, Kendricks A.

2004-10-12

A methods of indirectly measuring the nitrogen concentration in a gas mixture. The molecular weight of the gas is modeled as a function of the speed of sound in the gas, the diluent concentrations in the gas, and constant values, resulting in a model equation. Regression analysis is used to calculate the constant values, which can then be substituted into the model equation. If the speed of sound in the gas is measured at two states and diluent concentrations other than nitrogen (typically carbon dioxide) are known, two equations for molecular weight can be equated and solved for the nitrogen concentration in the gas mixture.

Remarks on the derivation of the governing equations for the dynamics of a nonlinear beam to a non ideal shaft coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fenili, André; Lopes Rebello da Fonseca Brasil, Reyolando Manoel; Balthazar, José M., E-mail: jmbaltha@gmail.com

We derive nonlinear governing equations without assuming that the beam is inextensible. The derivation couples the equations that govern a weak electric motor, which is used to rotate the base of the beam, to those that govern the motion of the beam. The system is considered non-ideal in the sense that the response of the motor to an applied voltage and the motion of the beam must be obtained interactively. The moment that the motor exerts on the base of the beam cannot be determined without solving for the motion of the beam.

Modeling of heavy-gas effects on airfoil flows

NASA Technical Reports Server (NTRS)

Drela, Mark

1992-01-01

Thermodynamic models were constructed for a calorically imperfect gas and for a non-ideal gas. These were incorporated into a quasi one dimensional flow solver to develop an understanding of the differences in flow behavior between the new models and the perfect gas model. The models were also incorporated into a two dimensional flow solver to investigate their effects on transonic airfoil flows. Specifically, the calculations simulated airfoil testing in a proposed high Reynolds number heavy gas test facility. The results indicate that the non-idealities caused significant differences in the flow field, but that matching of an appropriate non-dimensional parameter led to flows similar to those in air.

Interchange mode excited by trapped energetic ions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nishimura, Seiya, E-mail: n-seiya@kobe-kosen.ac.jp

2015-07-15

The kinetic energy principle describing the interaction between ideal magnetohydrodynamic (MHD) modes with trapped energetic ions is revised. A model is proposed on the basis of the reduced ideal MHD equations for background plasmas and the bounce-averaged drift-kinetic equation for trapped energetic ions. The model is applicable to large-aspect-ratio toroidal devices. Specifically, the effect of trapped energetic ions on the interchange mode in helical systems is analyzed. Results show that the interchange mode is excited by trapped energetic ions, even if the equilibrium states are stable to the ideal interchange mode. The energetic-ion-induced branch of the interchange mode might bemore » associated with the fishbone mode in helical systems.« less

Quantized vortices in the ideal bose gas: a physical realization of random polynomials.

PubMed

Castin, Yvan; Hadzibabic, Zoran; Stock, Sabine; Dalibard, Jean; Stringari, Sandro

2006-02-03

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.

Similarity solutions for unsteady flow behind an exponential shock in a self-gravitating non-ideal gas with azimuthal magnetic field

NASA Astrophysics Data System (ADS)

Nath, G.; Pathak, R. P.; Dutta, Mrityunjoy

2018-01-01

Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law is obtained. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The effects of variation of ambient magnetic field, non-idealness of the gas, adiabatic exponent and gravitational parameter are worked out in detail. It is shown that the increase in the non-idealness of the gas or the adiabatic exponent of the gas or presence of magnetic field have decaying effect on the shock wave. Consideration of the isothermal flow and the self-gravitational field increase the shock strength. Also, the consideration of isothermal flow or the presence of magnetic field removes the singularity in the density distribution, which arises in the case of adiabatic flow. The result of our study may be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.

Kinetic Models for Adiabatic Reversible Expansion of a Monatomic Ideal Gas.

ERIC Educational Resources Information Center

Chang, On-Kok

1983-01-01

A fixed amount of an ideal gas is confined in an adiabatic cylinder and piston device. The relation between temperature and volume in initial/final phases can be derived from the first law of thermodynamics. However, the relation can also be derived based on kinetic models. Several of these models are discussed. (JN)

University Students Explaining Adiabatic Compression of an Ideal Gas--A New Phenomenon in Introductory Thermal Physics

ERIC Educational Resources Information Center

Leinonen, Risto; Asikainen, Mervi A.; Hirvonen, Pekka E.

2012-01-01

This study focuses on second-year university students' explanations and reasoning related to adiabatic compression of an ideal gas. The phenomenon was new to the students, but it was one which they should have been capable of explaining using their previous upper secondary school knowledge. The students' explanations and reasoning were…

Cooking under Pressure: Applying the Ideal Gas Law in the Kitchen

ERIC Educational Resources Information Center

Chen, Ling; Anderson, Jennifer Y.; Wang, Diane R.

2010-01-01

This case study uses a daily cooking scenario to demonstrate how the boiling point of water is directly related to the external pressures in order to reinforce the concepts of boiling and boiling point, apply ideal gas law, and relate chemical reaction rates with temperatures. It also extends its teaching to autoclaves used to destroy…

Energy Fluctuation of Ideal Fermi Gas Trapped under Generic Power Law Potential U=\\sum_{i=1}^{d} c_i\\vert x_{i}/a_{i}\\vert^{n_{i} } in d Dimensions

NASA Astrophysics Data System (ADS)

Mir, Mehedi Faruk; Muktadir Rahman, Md.; Dwaipayan, Debnath; Sakhawat Hossain Himel, Md.

2016-04-01

Energy fluctuation of ideal Fermi gas trapped under generic power law potential U=\\sumi=1d ci \\vertxi/ai \\vert n_i has been calculated in arbitrary dimensions. Energy fluctuation is scrutinized further in the degenerate limit μ ≫ KBT with the help of Sommerfeld expansion. The dependence of energy fluctuation on dimensionality and power law potential is studied in detail. Most importantly our general result can not only exactly reproduce the recently published result regarding free and harmonically trapped ideal Fermi gas in d = 3 but also can describe the outcome for any power law potential in arbitrary dimension.

Stepwise Bose-Einstein Condensation in a Spinor Gas.

PubMed

Frapolli, C; Zibold, T; Invernizzi, A; Jiménez-García, K; Dalibard, J; Gerbier, F

2017-08-04

We observe multistep condensation of sodium atoms with spin F=1, where the different Zeeman components m_{F}=0,±1 condense sequentially as the temperature decreases. The precise sequence changes drastically depending on the magnetization m_{z} and on the quadratic Zeeman energy q (QZE) in an applied magnetic field. For large QZE, the overall structure of the phase diagram is the same as for an ideal spin-1 gas, although the precise locations of the phase boundaries are significantly shifted by interactions. For small QZE, antiferromagnetic interactions qualitatively change the phase diagram with respect to the ideal case, leading, for instance, to condensation in m_{F}=±1, a phenomenon that cannot occur for an ideal gas with q>0.

Determination of gas & liquid two-phase flow regime transitions in wellbore annulus by virtual mass force coefficient when gas cut

NASA Astrophysics Data System (ADS)

Qu, Junbo; Yan, Tie; Sun, Xiaofeng; Chen, Ye; Pan, Yi

2017-10-01

With the development of drilling technology to deeper stratum, overflowing especially gas cut occurs frequently, and then flow regime in wellbore annulus is from the original drilling fluid single-phase flow into gas & liquid two-phase flow. By using averaged two-fluid model equations and the basic principle of fluid mechanics to establish the continuity equations and momentum conservation equations of gas phase & liquid phase respectively. Relationship between pressure and density of gas & liquid was introduced to obtain hyperbolic equation, and get the expression of the dimensionless eigenvalue of the equation by using the characteristic line method, and analyze wellbore flow regime to get the critical gas content under different virtual mass force coefficients. Results show that the range of equation eigenvalues is getting smaller and smaller with the increase of gas content. When gas content reaches the critical point, the dimensionless eigenvalue of equation has no real solution, and the wellbore flow regime changed from bubble flow to bomb flow. When virtual mass force coefficients are 0.50, 0.60, 0.70 and 0.80 respectively, the critical gas contents are 0.32, 0.34, 0.37 and 0.39 respectively. The higher the coefficient of virtual mass force, the higher gas content in wellbore corresponding to the critical point of transition flow regime, which is in good agreement with previous experimental results. Therefore, it is possible to determine whether there is a real solution of the dimensionless eigenvalue of equation by virtual mass force coefficient and wellbore gas content, from which we can obtain the critical condition of wellbore flow regime transformation. It can provide theoretical support for the accurate judgment of the annular flow regime.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheviakov, Alexei F., E-mail: chevaikov@math.usask.ca

Partial differential equations of the form divN=0, N{sub t}+curl M=0 involving two vector functions in R{sup 3} depending on t, x, y, z appear in different physical contexts, including the vorticity formulation of fluid dynamics, magnetohydrodynamics (MHD) equations, and Maxwell's equations. It is shown that these equations possess an infinite family of local divergence-type conservation laws involving arbitrary functions of space and time. Moreover, it is demonstrated that the equations of interest have a rather special structure of a lower-degree (degree two) conservation law in R{sup 4}(t,x,y,z). The corresponding potential system has a clear physical meaning. For the Maxwell's equations,more » it gives rise to the scalar electric and the vector magnetic potentials; for the vorticity equations of fluid dynamics, the potentialization inverts the curl operator to yield the fluid dynamics equations in primitive variables; for MHD equations, the potential equations yield a generalization of the Galas-Bogoyavlenskij potential that describes magnetic surfaces of ideal MHD equilibria. The lower-degree conservation law is further shown to yield curl-type conservation laws and determined potential equations in certain lower-dimensional settings. Examples of new nonlocal conservation laws, including an infinite family of nonlocal material conservation laws of ideal time-dependent MHD equations in 2+1 dimensions, are presented.« less

Experiments with Helium-Filled Balloons

NASA Astrophysics Data System (ADS)

Zable, Anthony C.

2010-12-01

The concepts of Newtonian mechanics, fluids, and ideal gas law physics are often treated as separate and isolated topics in the typical introductory college-level physics course, especially in the laboratory setting. To bridge these subjects, a simple experiment was developed that utilizes computer-based data acquisition sensors and a digital gram scale to estimate the molar mass of the gas in an inflated balloon. In this experiment, the comparable density of an inflated balloon to that of atmospheric air introduces a significant role for buoyancy that must be accounted for. The ideal gas law approximation is assumed for both the isolated gas mixture within the balloon and the surrounding air, which defines the relationship between the gas pressure, volume, temperature, and molar quantity. Analysis of the forces associated with the inflated balloon with the incorporation of Archimedes' principle and the ideal gas law into Newton's second law results in an experimental method for the measurement of the molar mass and mole fraction of a gas that is easy to implement yet academically challenging for students. The following narrative describes the basic setup of this experiment, along with a sample set of data as acquired and analyzed by a typical physics student from one of my classes.

Droplet evaporation and combustion in a liquid-gas multiphase system

NASA Astrophysics Data System (ADS)

Muradoglu, Metin; Irfan, Muhammad

2017-11-01

Droplet evaporation and combustion in a liquid-gas multiphase system are studied computationally using a front-tracking method. One field formulation is used to solve the flow, energy and species equations with suitable jump conditions. Both phases are assumed to be incompressible; however, the divergence-free velocity field condition is modified to account for the phase change at the interface. Both temperature and species gradient driven phase change processes are simulated. Extensive validation studies are performed using the benchmark cases: The Stefan and the sucking interface problems, d2 law and wet bulb temperature comparison with the psychrometric chart values. The phase change solver is then extended to incorporate the burning process following the evaporation as a first step towards the development of a computational framework for spray combustion. We used detailed chemistry, variable transport properties and ideal gas behaviour for a n-heptane droplet combustion; the chemical kinetics being handled by the CHEMKIN. An operator-splitting approach is used to advance temperature and species mass fraction in time. The numerical results of the droplet burning rate, flame temperature and flame standoff ratio show good agreement with the experimental and previous numeric.

A Multi-Fidelity Surrogate Model for the Equation of State for Mixtures of Real Gases

NASA Astrophysics Data System (ADS)

Ouellet, Frederick; Park, Chanyoung; Koneru, Rahul; Balachandar, S.; Rollin, Bertrand

2017-11-01

The explosive dispersal of particles is a complex multiphase and multi-species fluid flow problem. In these flows, the products of detonated explosives must be treated as real gases while the ideal gas equation of state is used for the ambient air. As the products expand outward, they mix with the air and create a region where both state equations must be satisfied. One of the most accurate, yet expensive, methods to handle this problem is an algorithm that iterates between both state equations until both pressure and thermal equilibrium are achieved inside of each computational cell. This work creates a multi-fidelity surrogate model to replace this process. This is achieved by using a Kriging model to produce a curve fit which interpolates selected data from the iterative algorithm. The surrogate is optimized for computing speed and model accuracy by varying the number of sampling points chosen to construct the model. The performance of the surrogate with respect to the iterative method is tested in simulations using a finite volume code. The model's computational speed and accuracy are analyzed to show the benefits of this novel approach. This work was supported by the U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program, as a Cooperative Agreement under the Predictive Science Academic Alliance Program, under Contract No. DE-NA00023.

Electrochemistry of single nanobubbles. Estimating the critical size of bubble-forming nuclei for gas-evolving electrode reactions.

PubMed

German, Sean R; Edwards, Martin A; Chen, Qianjin; Liu, Yuwen; Luo, Long; White, Henry S

2016-12-12

In this article, we address the fundamental question: "What is the critical size of a single cluster of gas molecules that grows and becomes a stable (or continuously growing) gas bubble during gas evolving reactions?" Electrochemical reactions that produce dissolved gas molecules are ubiquitous in electrochemical technologies, e.g., water electrolysis, photoelectrochemistry, chlorine production, corrosion, and often lead to the formation of gaseous bubbles. Herein, we demonstrate that electrochemical measurements of the dissolved gas concentration, at the instant prior to nucleation of an individual nanobubble of H 2 , N 2 , or O 2 at a Pt nanodisk electrode, can be analyzed using classical thermodynamic relationships (Henry's law and the Young-Laplace equation - including non-ideal corrections) to provide an estimate of the size of the gas bubble nucleus that grows into a stable bubble. We further demonstrate that this critical nucleus size is independent of the radius of the Pt nanodisk employed (<100 nm radius), and weakly dependent on the nature of the gas. For example, the measured critical surface concentration of H 2 of ∼0.23 M at the instant of bubble formation corresponds to a critical H 2 nucleus that has a radius of ∼3.6 nm, an internal pressure of ∼350 atm, and contains ∼1700 H 2 molecules. The data are consistent with stochastic fluctuations in the density of dissolved gas, at or near the Pt/solution interface, controlling the rate of bubble nucleation. We discuss the growth of the nucleus as a diffusion-limited process and how that process is affected by proximity to an electrode producing ∼10 11 gas molecules per second. Our study demonstrates the advantages of studying a single-entity, i.e., an individual nanobubble, in understanding and quantifying complex physicochemical phenomena.

Numerical modeling of the interaction of liquid drops and jets with shock waves and gas jets

NASA Astrophysics Data System (ADS)

Surov, V. S.

1993-02-01

The motion of a liquid drop (jet) and of the ambient gas is described, in the general case, by Navier-Stokes equations. An approximate solution to the interaction of a plane shock wave with a single liquid drop is presented. Based on the analysis, the general system of Navier-Stokes equations is reduced to two groups of equations, Euler equations for gas and Navier-Stokes equations for liquid; solutions to these equations are presented. The discussion also covers the modeling of the interaction of a shock wave with a drop screen, interaction of a liquid jet with a counterpropagating supersonic gas flow, and modeling of processes in a shock layer during the impact of a drop against an obstacle in gas flow.

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

DOE PAGES

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

2018-03-26

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

From Free Expansion to Abrupt Compression of an Ideal Gas

ERIC Educational Resources Information Center

Anacleto, Joaquim; Pereira, Mario G.

2009-01-01

Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 [less than or equal] r [less than or equal] 1 for expansions and r [greater than or equal] 1 for compressions.…

Shock wave structure in an ideal dissociating gas

NASA Technical Reports Server (NTRS)

Liu, K. H.

1975-01-01

Composition changes within the shock layer due to chemical reactions are considered. The Lighthill ideal dissociating gas model was used in an effort to describe the oxygen type molecule. First, the two limiting cases, when the chemical reaction rates are very slow and very fast in comparison to local convective rates, are investigated. Then, the problem is solved for arbitrary chemical reaction rates.

Condensation of an ideal gas obeying non-Abelian statistics.

PubMed

Mirza, Behrouz; Mohammadzadeh, Hosein

2011-09-01

We consider the thermodynamic geometry of an ideal non-Abelian gas. We show that, for a certain value of the fractional parameter and at the relevant maximum value of fugacity, the thermodynamic curvature has a singular point. This indicates a condensation such as Bose-Einstein condensation for non-Abelian statistics and we work out the phase transition temperature in various dimensions.

Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model.

PubMed

Baule, A; Evans, R M L; Olmsted, P D

2006-12-01

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena, Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime.

Fast and accurate calculation of dilute quantum gas using Uehling–Uhlenbeck model equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yano, Ryosuke, E-mail: ryosuke.yano@tokiorisk.co.jp

The Uehling–Uhlenbeck (U–U) model equation is studied for the fast and accurate calculation of a dilute quantum gas. In particular, the direct simulation Monte Carlo (DSMC) method is used to solve the U–U model equation. DSMC analysis based on the U–U model equation is expected to enable the thermalization to be accurately obtained using a small number of sample particles and the dilute quantum gas dynamics to be calculated in a practical time. Finally, the applicability of DSMC analysis based on the U–U model equation to the fast and accurate calculation of a dilute quantum gas is confirmed by calculatingmore » the viscosity coefficient of a Bose gas on the basis of the Green–Kubo expression and the shock layer of a dilute Bose gas around a cylinder.« less

Comet Gas and Dust Dynamics Modeling

NASA Technical Reports Server (NTRS)

Von Allmen, Paul A.; Lee, Seungwon

2010-01-01

This software models the gas and dust dynamics of comet coma (the head region of a comet) in order to support the Microwave Instrument for Rosetta Orbiter (MIRO) project. MIRO will study the evolution of the comet 67P/Churyumov-Gerasimenko's coma system. The instrument will measure surface temperature, gas-production rates and relative abundances, and velocity and excitation temperatures of each species along with their spatial temporal variability. This software will use these measurements to improve the understanding of coma dynamics. The modeling tool solves the equation of motion of a dust particle, the energy balance equation of the dust particle, the continuity equation for the dust and gas flow, and the dust and gas mixture energy equation. By solving these equations numerically, the software calculates the temperature and velocity of gas and dust as a function of time for a given initial gas and dust production rate, and a dust characteristic parameter that measures the ability of a dust particle to adjust its velocity to the local gas velocity. The software is written in a modular manner, thereby allowing the addition of more dynamics equations as needed. All of the numerical algorithms are added in-house and no third-party libraries are used.

Ballistic and diffusive dynamics in a two-dimensional ideal gas of macroscopic chaotic Faraday waves.

PubMed

Welch, Kyle J; Hastings-Hauss, Isaac; Parthasarathy, Raghuveer; Corwin, Eric I

2014-04-01

We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.

Infinitesimal Legendre symmetry in the Geometrothermodynamics programme

DOE Office of Scientific and Technical Information (OSTI.GOV)

García-Peláez, D., E-mail: dgarciap@up.edu.mx; Universidad Panamericana, Tecoyotitla 366. Col. Ex Hacienda Guadalupe Chimalistac, 01050 México D.F., México; López-Monsalvo, C. S., E-mail: cesar.slm@correo.nucleares.unam.mx

2014-08-15

The work within the Geometrothermodynamics programme rests upon the metric structure for the thermodynamic phase-space. Such structure exhibits discrete Legendre symmetry. In this work, we study the class of metrics which are invariant along the infinitesimal generators of Legendre transformations. We solve the Legendre-Killing equation for a K-contact general metric. We consider the case with two thermodynamic degrees of freedom, i.e., when the dimension of the thermodynamic phase-space is five. For the generic form of contact metrics, the solution of the Legendre-Killing system is unique, with the sole restriction that the only independent metric function – Ω – should bemore » dragged along the orbits of the Legendre generator. We revisit the ideal gas in the light of this class of metrics. Imposing the vanishing of the scalar curvature for this system results in a further differential equation for the metric function Ω which is not compatible with the Legendre invariance constraint. This result does not allow us to use Quevedo's interpretation of the curvature scalar as a measure of thermodynamic interaction for this particular class.« less

Modeling of the WSTF frictional heating apparatus in high pressure systems

NASA Technical Reports Server (NTRS)

Skowlund, Christopher T.

1992-01-01

In order to develop a computer program able to model the frictional heating of metals in high pressure oxygen or nitrogen a number of additions have been made to the frictional heating model originally developed for tests in low pressure helium. These additions include: (1) a physical property package for the gases to account for departures from the ideal gas state; (2) two methods for spatial discretization (finite differences with quadratic interpolation or orthogonal collocation on finite elements) which substantially reduce the computer time required to solve the transient heat balance; (3) more efficient programs for the integration of the ordinary differential equations resulting from the discretization of the partial differential equations; and (4) two methods for determining the best-fit parameters via minimization of the mean square error (either a direct search multivariable simplex method or a modified Levenburg-Marquardt algorithm). The resulting computer program has been shown to be accurate, efficient and robust for determining the heat flux or friction coefficient vs. time at the interface of the stationary and rotating samples.

Exact Theory of Compressible Fluid Turbulence

NASA Astrophysics Data System (ADS)

Drivas, Theodore; Eyink, Gregory

2017-11-01

We obtain exact results for compressible turbulence with any equation of state, using coarse-graining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scale-local energy cascade and ``pressure-work defect'', or pressure-work at viscous scales exceeding that in the inertial-range. Planar shocks in an ideal gas dissipate all kinetic energy by pressure-work defect, but the effect is omitted by standard LES modeling of pressure-dilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by large-scale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5th-type laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to sub-Kolmogorov values. Although precise exponents and detailed physics are Mach-dependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence.

Temperature scaling in a dense vibrofluidized granular material.

PubMed

Sunthar, P; Kumaran, V

1999-08-01

The leading order "temperature" of a dense two-dimensional granular material fluidized by external vibrations is determined. The grain interactions are characterized by inelastic collisions, but the coefficient of restitution is considered to be close to 1, so that the dissipation of energy during a collision is small compared to the average energy of a particle. An asymptotic solution is obtained where the particles are considered to be elastic in the leading approximation. The velocity distribution is a Maxwell-Boltzmann distribution in the leading approximation. The density profile is determined by solving the momentum balance equation in the vertical direction, where the relation between the pressure and density is provided by the virial equation of state. The temperature is determined by relating the source of energy due to the vibrating surface and the energy dissipation due to inelastic collisions. The predictions of the present analysis show good agreement with simulation results at higher densities where theories for a dilute vibrated granular material, with the pressure-density relation provided by the ideal gas law, are in error.

State-variable theories for nonelastic deformation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, C.Y.

The various concepts of mechanical equation of state for nonelastic deformation in crystalline solids, originally proposed for plastic deformation, have been recently extended to describe additional phenomena such as anelastic and microplastic deformation including the Bauschinger effect. It has been demonstrated that it is possible to predict, based on current state variables in a unified way, the mechanical response of a material under an arbitrary loading. Thus, if the evolution laws of the state variables are known, one can describe the behavior of a material for a thermal-mechanical path of interest, for example, during constant load (or stress) creep withoutmore » relying on specialized theories. Some of the existing theories of mechanical equation of state for nonelastic deformation are reviewed. The establishment of useful forms of mechanical equation of state has to depend on extensive experimentation in the same way as that involved in the development, for example, the ideal gas law. Recent experimental efforts are also reviewed. It has been possible to develop state-variable deformation models based on experimental findings and apply them to creep, cyclic deformation, and other time-dependent deformation. Attempts are being made to correlate the material parameters of the state-variable models with the microstructure of a material. 24 figures.« less

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

NASA Astrophysics Data System (ADS)

Eyink, Gregory L.; Drivas, Theodore D.

2018-02-01

We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and Péclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur via two mechanisms: an anomalous input of negative entropy (negentropy) by pressure work and a cascade of negentropy to small scales. We derive "4 /5 th-law"-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the "Big Power Law in the Sky" observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade or an inverse cascade of usual thermodynamic entropy.

Experimental study of the thermal-acoustic efficiency in a long turbulent diffusion-flame burner

NASA Technical Reports Server (NTRS)

Mahan, J. R.

1983-01-01

An acoustic source/propagation model is used to interpret measured noise spectra from a long turbulent burner. The acoustic model is based on the perturbation solution of the equations describing the unsteady one-dimensional flow of an inviscid ideal gas with a distributed heat source. The model assumes that the measured noise spectra are due uniquely to the unsteady component of combustion heat release. The model was applied to a long cylindrical hydrogen burner operating over a range of power levels between 4.5 kW and 22.3 kW. Acoustic impedances at the inlet to the burner and at the exit of the tube downstream of the burner were measured and are used as boundary conditions for the model. These measured impedances are also presented.

The thermal-vortex equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1987-01-01

The Boussinesq approximation is extended so as to explicitly account for the transfer of fluid energy through viscous action into thermal energy. Ideal and dissipative integral invariants are discussed, in addition to the general equations for thermal-fluid motion.

Measurement of optical Feshbach resonances in an ideal gas.

PubMed

Blatt, S; Nicholson, T L; Bloom, B J; Williams, J R; Thomsen, J W; Julienne, P S; Ye, J

2011-08-12

Using a narrow intercombination line in alkaline earth atoms to mitigate large inelastic losses, we explore the optical Feshbach resonance effect in an ultracold gas of bosonic (88)Sr. A systematic measurement of three resonances allows precise determinations of the optical Feshbach resonance strength and scaling law, in agreement with coupled-channel theory. Resonant enhancement of the complex scattering length leads to thermalization mediated by elastic and inelastic collisions in an otherwise ideal gas. Optical Feshbach resonance could be used to control atomic interactions with high spatial and temporal resolution.

The computation of thermo-chemical nonequilibrium hypersonic flows

NASA Technical Reports Server (NTRS)

Candler, Graham

1989-01-01

Several conceptual designs for vehicles that would fly in the atmosphere at hypersonic speeds have been developed recently. For the proposed flight conditions the air in the shock layer that envelops the body is at a sufficiently high temperature to cause chemical reaction, vibrational excitation, and ionization. However, these processes occur at finite rates which, when coupled with large convection speeds, cause the gas to be removed from thermo-chemical equilibrium. This non-ideal behavior affects the aerothermal loading on the vehicle and has ramifications in its design. A numerical method to solve the equations that describe these types of flows in 2-D was developed. The state of the gas is represented with seven chemical species, a separate vibrational temperature for each diatomic species, an electron translational temperature, and a mass-average translational-rotational temperature for the heavy particles. The equations for this gas model are solved numerically in a fully coupled fashion using an implicit finite volume time-marching technique. Gauss-Seidel line-relaxation is used to reduce the cost of the solution and flux-dependent differencing is employed to maintain stability. The numerical method was tested against several experiments. The calculated bow shock wave detachment on a sphere and two cones was compared to those measured in ground testing facilities. The computed peak electron number density on a sphere-cone was compared to that measured in a flight test. In each case the results from the numerical method were in excellent agreement with experiment. The technique was used to predict the aerothermal loads on an Aeroassisted Orbital Transfer Vehicle including radiative heating. These results indicate that the current physical model of high temperature air is appropriate and that the numerical algorithm is capable of treating this class of flows.

Group analysis of dynamics equations of self-gravitating polytropic gas

NASA Astrophysics Data System (ADS)

Klebanov, I.; Panov, A.; Ivanov, S.; Maslova, O.

2018-06-01

The Lie algebras admitted by the dynamics equations of self-gravitating gas for an arbitrary equation of state and a polytropic gas are calculated. A spherically symmetric submodel is constructed for the case of a polytropic gas. The Lie algebras and the optimal system of subalgebras for a spherically symmetric submodel are computed. An invariant solution describing the steady motion is obtained.

Indriect Measurement Of Nitrogen In A Mult-Component Natural Gas By Heating The Gas

DOEpatents

Morrow, Thomas B.; Behring, II, Kendricks A.

2004-06-22

Methods of indirectly measuring the nitrogen concentration in a natural gas by heating the gas. In two embodiments, the heating energy is correlated to the speed of sound in the gas, the diluent concentrations in the gas, and constant values, resulting in a model equation. Regression analysis is used to calculate the constant values, which can then be substituted into the model equation. If the diluent concentrations other than nitrogen (typically carbon dioxide) are known, the model equation can be solved for the nitrogen concentration.

Magnetogasdynamics shock waves in a rotational axisymmetric non-ideal gas with increasing energy and conductive and radiative heat-fluxes

NASA Astrophysics Data System (ADS)

Nath, Gorakh

2016-07-01

Self-similar solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamics cylindrical shock wave propagating in a rotational axisymmetric non ideal gas with increasing energy and conductive and radiative heat fluxes in presence of an azimuthal magnetic field. The fluid velocities and the azimuthal magnetic field in the ambient medium are assume to be varying and obeying power laws. In order to find the similarity solutions the angular velocity of the ambient medium is taken to be decreasing as the distance from the axis increases. The heat conduction is expressed in terms of Fourier's law and the radiation is considered to be the diffusion type for an optically thick grey gas model. The thermal conductivity and the absorption coefficient are assumed to vary with temperature and density. The effects of the presence of radiation and conduction, the non-idealness of the gas and the magnetic field on the shock propagation and the flow behind the shock are investigated.

Use, misuse and extensions of "ideal gas" models of animal encounter.

PubMed

Hutchinson, John M C; Waser, Peter M

2007-08-01

Biologists have repeatedly rediscovered classical models from physics predicting collision rates in an ideal gas. These models, and their two-dimensional analogues, have been used to predict rates and durations of encounters among animals or social groups that move randomly and independently, given population density, velocity, and distance at which an encounter occurs. They have helped to separate cases of mixed-species association based on behavioural attraction from those that simply reflect high population densities, and to detect cases of attraction or avoidance among conspecifics. They have been used to estimate the impact of population density, speeds of movement and size on rates of encounter between members of the opposite sex, between gametes, between predators and prey, and between observers and the individuals that they are counting. One limitation of published models has been that they predict rates of encounter, but give no means of determining whether observations differ significantly from predictions. Another uncertainty is the robustness of the predictions when animal movements deviate from the model's assumptions in specific, biologically relevant ways. Here, we review applications of the ideal gas model, derive extensions of the model to cover some more realistic movement patterns, correct several errors that have arisen in the literature, and show how to generate confidence limits for expected rates of encounter among independently moving individuals. We illustrate these results using data from mangabey monkeys originally used along with the ideal gas model to argue that groups avoid each other. Although agent-based simulations provide a more flexible alternative approach, the ideal gas model remains both a valuable null model and a useful, less onerous, approximation to biological reality.

Thermodynamics Fundamental Equation of a "Non-Ideal" Rubber Band from Experiments

ERIC Educational Resources Information Center

Ritacco, Herna´n A.; Fortunatti, Juan C.; Devoto, Walter; Ferna´ndez-Miconi, Eugenio; Dominguez, Claudia; Sanchez, Miguel D.

2014-01-01

In this paper, we describe laboratory and classroom exercises designed to obtain the "fundamental" equation of a rubber band by combining experiments and theory. The procedure shows students how classical thermodynamics formalism can help to obtain empirical equations of state by constraining and guiding in the construction of the…

Structural arrest in an ideal gas.

PubMed

van Ketel, Willem; Das, Chinmay; Frenkel, Daan

2005-04-08

We report a molecular dynamics study of a simple model system that has the static properties of an ideal gas, yet exhibits nontrivial "glassy" dynamics behavior at high densities. The constituent molecules of this system are constructs of three infinitely thin hard rods of length L, rigidly joined at their midpoints. The crosses have random but fixed orientation. The static properties of this system are those of an ideal gas, and its collision frequency can be computed analytically. For number densities NL(3)/V>1, the single-particle diffusivity goes to zero. As the system is completely structureless, standard mode-coupling theory cannot describe the observed structural arrest. Nevertheless, the system exhibits many dynamical features that appear to be mode-coupling-like. All high-density incoherent intermediate scattering functions collapse onto master curves that depend only on the wave vector.

Critical behavior of the ideal-gas Bose-Einstein condensation in the Apollonian network.

PubMed

de Oliveira, I N; dos Santos, T B; de Moura, F A B F; Lyra, M L; Serva, M

2013-08-01

We show that the ideal Boson gas displays a finite-temperature Bose-Einstein condensation transition in the complex Apollonian network exhibiting scale-free, small-world, and hierarchical properties. The single-particle tight-binding Hamiltonian with properly rescaled hopping amplitudes has a fractal-like energy spectrum. The energy spectrum is analytically demonstrated to be generated by a nonlinear mapping transformation. A finite-size scaling analysis over several orders of magnitudes of network sizes is shown to provide precise estimates for the exponents characterizing the condensed fraction, correlation size, and specific heat. The critical exponents, as well as the power-law behavior of the density of states at the bottom of the band, are similar to those of the ideal Boson gas in lattices with spectral dimension d(s)=2ln(3)/ln(9/5)~/=3.74.

Self-determined shapes and velocities of giant near-zero drag gas cavities

PubMed Central

Vakarelski, Ivan U.; Klaseboer, Evert; Jetly, Aditya; Mansoor, Mohammad M.; Aguirre-Pablo, Andres A.; Chan, Derek Y. C.; Thoroddsen, Sigurdur T.

2017-01-01

Minimizing the retarding force on a solid moving in liquid is the canonical problem in the quest for energy saving by friction and drag reduction. For an ideal object that cannot sustain any shear stress on its surface, theory predicts that drag force will fall to zero as its speed becomes large. However, experimental verification of this prediction has been challenging. We report the construction of a class of self-determined streamlined structures with this free-slip surface, made up of a teardrop-shaped giant gas cavity that completely encloses a metal sphere. This stable gas cavity is formed around the sphere as it plunges at a sufficiently high speed into the liquid in a deep tank, provided that the sphere is either heated initially to above the Leidenfrost temperature of the liquid or rendered superhydrophobic in water at room temperature. These sphere-in-cavity structures have residual drag coefficients that are typically less than 110 those of solid objects of the same dimensions, which indicates that they experienced very small drag forces. The self-determined shapes of the gas cavities are shown to be consistent with the Bernoulli equation of potential flow applied on the cavity surface. The cavity fall velocity is not arbitrary but is uniquely predicted by the sphere density and cavity volume, so larger cavities have higher characteristic velocities. PMID:28913434

Pore-Scale Determination of Gas Relative Permeability in Hydrate-Bearing Sediments Using X-Ray Computed Micro-Tomography and Lattice Boltzmann Method

NASA Astrophysics Data System (ADS)

Chen, Xiongyu; Verma, Rahul; Espinoza, D. Nicolas; Prodanović, Maša.

2018-01-01

This work uses X-ray computed micro-tomography (μCT) to monitor xenon hydrate growth in a sandpack under the excess gas condition. The μCT images give pore-scale hydrate distribution and pore habit in space and time. We use the lattice Boltzmann method to calculate gas relative permeability (krg) as a function of hydrate saturation (Shyd) in the pore structure of the experimental hydrate-bearing sand retrieved from μCT data. The results suggest the krg - Shyd data fit well a new model krg = (1-Shyd)·exp(-4.95·Shyd) rather than the simple Corey model. In addition, we calculate krg-Shyd curves using digital models of hydrate-bearing sand based on idealized grain-attaching, coarse pore-filling, and dispersed pore-filling hydrate habits. Our pore-scale measurements and modeling show that the krg-Shyd curves are similar regardless of whether hydrate crystals develop grain-attaching or coarse pore-filling habits. The dispersed pore filling habit exhibits much lower gas relative permeability than the other two, but it is not observed in the experiment and not compatible with Ostwald ripening mechanisms. We find that a single grain-shape factor can be used in the Carman-Kozeny equation to calculate krg-Shyd data with known porosity and average grain diameter, suggesting it is a useful model for hydrate-bearing sand.

Sociocultural pressures, thin-ideal internalization, self-objectification, and body dissatisfaction: could feminist beliefs be a moderating factor?

PubMed

Myers, Taryn A; Crowther, Janis H

2007-09-01

Theory and research suggest that sociocultural pressures, thin-ideal internalization, and self-objectification are associated with body dissatisfaction, while feminist beliefs may serve a protective function. This research examined thin-ideal internalization and self-objectification as mediators and feminist beliefs as a moderator in the relationship between sociocultural pressures to meet the thin-ideal and body dissatisfaction. Female undergraduate volunteers (N=195) completed self-report measures assessing sociocultural influences, feminist beliefs, thin-ideal internalization, self-objectification, and body dissatisfaction. Multisample structural equation modeling showed that feminist beliefs moderate the relationship between media awareness and thin-ideal internalization, but not the relationship between social influence and thin-ideal internalization. Research and clinical implications of these findings are discussed.

Dynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD

NASA Astrophysics Data System (ADS)

Kuznetsov, E. A.; Ruban, V. P.

Vortex line and magnetic line representations are introduced for description of flows in ideal hydrodynamics and MHD, respectively. For incompressible fluids it is shown that the equations of motion for vorticity φ and magnetic field with the help of this transformation follow from the variational principle. By means of this representation it is possible to integrate the system of hydrodynamic type with the Hamiltonian H=|φ|dr. It is also demonstrated that these representations allow to remove from the noncanonical Poisson brackets, defined on the space of divergence-free vector fields, degeneracy connected with the vorticity frozenness for the Euler equation and with magnetic field frozenness for ideal MHD. For MHD a new Weber type transformation is found. It is shown how this transformation can be obtained from the two-fluid model when electrons and ions can be considered as two independent fluids. The Weber type transformation for ideal MHD gives the whole Lagrangian vector invariant. When this invariant is absent this transformation coincides with the Clebsch representation analog introduced in [1].

Exploring the Ideal Gas Law through a Quantitative Gasometric Analysis of Nitrogen Produced by the Reaction of Sodium Nitrite with Sulfamic Acid

ERIC Educational Resources Information Center

Yu, Anne

2010-01-01

The gasometric analysis of nitrogen produced in a reaction between sodium nitrite, NaNO[superscript 2], and sulfamic acid, H(NH[superscript 2])SO[superscript 3], provides an alternative to more common general chemistry experiments used to study the ideal gas law, such as the experiment in which magnesium is reacted with hydrochloric acid. This…

Concepts of Ideal and Nonideal Explosives.

DTIC Science & Technology

1981-12-01

Akst and J. Hershkowitz, "Explosive Performance Modification by Cosolidifaction of Ammonium Nitrate with Fuels ," Technical Report 4987, Picatinny...explosives Equations of state Diameter effect Ammonium nitrate 20. ASSrRACr (ca’mes r w re t N netwezy ad identity by block number) The purpose of...this report is to stimulate discussion on the nonideality of ammonium nitrate and its composite explosives. The concept of ideal and non- ideal

SPH modelling of energy partitioning during impacts on Venus

NASA Technical Reports Server (NTRS)

Takata, T.; Ahrens, T. J.

1993-01-01

Impact cratering of the Venusian planetary surface by meteorites was investigated numerically using the Smoothed Particle Hydrodynamics (SPH) method. Venus presently has a dense atmosphere. Vigorous transfer of energy between impacting meteorites, the planetary surface, and the atmosphere is expected during impact events. The investigation concentrated on the effects of the atmosphere on energy partitioning and the flow of ejecta and gas. The SPH method is particularly suitable for studying complex motion, especially because of its ability to be extended to three dimensions. In our simulations, particles representing impactors and targets are initially set to a uniform density, and those of atmosphere are set to be in hydrostatic equilibrium. Target, impactor, and atmosphere are represented by 9800, 80, and 4200 particles, respectively. A Tillotson equation of state for granite is assumed for the target and impactor, and an ideal gas with constant specific heat ratio is used for the atmosphere. Two dimensional axisymmetric geometry was assumed and normal impacts of 10km diameter projectiles with velocities of 5, 10, 20, and 40 km/s, both with and without an atmosphere present were modeled.

Numerical modeling of the fetal blood flow in the placental circulatory system

NASA Astrophysics Data System (ADS)

Shannon, Alexander; Gallucci, Sergio; Mirbod, Parisa

2015-11-01

The placenta is a unique organ of exchange between the growing fetus and the mother. It incorporates almost all functions of the adult body, acting as the fetal lung, digestive and immune systems, to mention a few. The exchange of oxygen and nutrients takes place at the surface of the villous tree. Using an idealized geometry of the fetal villous trees in the mouse placenta, in this study we performed 3D computational analysis of the unsteady fetal blood flow, gas, and nutrient transport over the chorionic plate. The fetal blood was treated as an incompressible Newtonian fluid, and the oxygen and nutrient were treated as a passive scalar dissolved in blood plasma. The flow was laminar, and a commercial CFD code (COMSOL Multiphysics) has been used for the simulation. COMSOL has been selected because it is multi-physics FEM software that allows for the seamless coupling of different physics represented by partial differential equations. The results clearly illustrate that the specific branching pattern and the in-plane curvature of the fetal villous trees affect the delivery of blood, gas and nutrient transport to the whole placenta.

Proton Beam Driven Isochoric Heating to Warm Dense Matter Conditions on Texas Petawatt

NASA Astrophysics Data System (ADS)

Roycroft, R.; Dyer, G. M.; McCary, E.; Jiao, X.; Bowers, B.; Bernstein, A.; Ditmire, T.; Montgomery, M.; Winget, D.; Hegelich, B. M.

2017-10-01

Isochoric heating of solids and gases to warm dense matter conditions is relevant to the study of equation of state as well as laboratory astrophysics, specifically heating of hydrogen gas ( 1017-1019 cm3) to 0.5-3eV for the study of white dwarf atmospheres. In a series of experiments on Texas Petawatt, we have built a platform using the petawatt laser focused softly to a large focal spot (60-70um) to generate large numbers of intermediate energy protons via TNSA, ideal for isochoric heating. We have previously used the proton beam to isochorically heat 10um aluminum foils to 20eV. This poster presents results of experiments in which low Z materials such as methane gas, carbon foams, and hydrogen are heated using this platform. We are measuring the surface brightness temperature and heating with a streaked optical pyrometer, and XUV emissions using an XUV spectrometer. Supported by NNSA cooperative agreement DE-NA0002008, the DARPA PULSE program (12-63-PULSE-FP014), and the Air Force Office of Scientific Research (FA9550-14-1-0045).

Analysis and simulation of the I C engine Otto cycle using the second law of thermodynamics

NASA Astrophysics Data System (ADS)

Abdel-Rahim, Y. M.

The present investigation is an application of the second law of thermodynamics to the spark ignition engine cycle. A comprehensive thermodynamic analysis of the air standard cycle is conducted using the first and second laws of thermodynamics, the ideal gas equation of state and the perfect gas properties for air. The study investigates the effect of the cycle parameters on the cycle performance reflected by the first and second law efficiencies, the heat added, the work done, the available energy added as well as the history of the internal, available and unavailable energies along the cycle. The study shows that the second law efficiency is a function of the compression ratio, the initial temperature, the maximum temperature as well as the dead state temperature. A non-dimensional comprehensive thermodynamic simulation model for the actual Otto cycle is developed to study the effects of the design and operating parameters of the cycle on the cycle performance. The analysis takes into account engine geometry, mixture strength, heat transfer, piston motion, engine speed, mechanical friction, spark advance and combustion duration.

Numerical simulation of gas distribution in goaf under Y ventilation mode

NASA Astrophysics Data System (ADS)

Li, Shengzhou; Liu, Jun

2018-04-01

Taking the Y type ventilation of the working face as the research object, diffusion equation is introduced to simulate the diffusion characteristics of gas, using Navier-Stokes equation and Brinkman equation to simulate the gas flow in working face and goaf, the physical model of gas flow in coal mining face was established. With numerical simulation software COMSOL multiphysics methods, gas distribution in goaf under Y ventilation mode is simulated and gas distribution of the working face, the upper corner and goaf is analysised. The results show that the Y type ventilation system can effectively improve the corner gas accumulation and overrun problem.

Ultimate Temperature of Pulse Tube Cryocoolers

NASA Technical Reports Server (NTRS)

Kittel, Peter

2009-01-01

An ideal pulse tube cryocooler using an ideal gas can operate at any temperature. This is not true for real gases. The enthalpy flow resulting from the real gas effects of He-3, He-4, and their mixtures in ideal pulse tube cryocoolers puts limits on the operating temperature of pulse tube cryocoolers. The discussion of these effects follows a previous description of the real gas effects in ideal pulse tube cryocoolers and makes use of models of the thermophysical properties of He-3 and He-4. Published data is used to extend the analysis to mixtures of He-3 and He-4. The analysis was done for pressures below 2 MPa and temperatures below 2.5 K. Both gases and their mixtures show low temperature limits for pulse tube cryocoolers. These limits are in the 0.5-2.2 K range and depend on pressure and mixture. In some circumstances, even lower temperatures may be possible. Pulse tube cryocoolers using the two-fluid properties of dilute 3He in superfluid He-4 appear to have no limit.

Ultimate Temperature of Pulse Tube Cryocoolers

NASA Technical Reports Server (NTRS)

Kittel, Peter

2009-01-01

An ideal pulse tube cryocooler using an ideal gas can operate at any temperature. This is not true for real gases. The enthalpy flow resulting from the real gas effects of 3He, 4He, and their mixtures in ideal pulse tube cryocoolers puts limits on the operating temperature of pulse tube cryocoolers. The discussion of these effects follows a previous description of the real gas effects in ideal pulse tube cryocoolers and makes use of models of the thermophysical properties of 3He and 4He. Published data is used to extend the analysis to mixtures of 3He and 4He. The analysis was done for pressures below 2 MPa and temperatures below 2.5 K. Both gases and their mixtures show low temperature limits for pulse tube cryocoolers. These limits are in the 0.5-2.2 K range and depend on pressure and mixture. In some circumstances, even lower temperatures may be possible. Pulse tube cryocoolers using the ha-fluid properties of dilute 3He in superfluid 4He appear to have no limit.

Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas.

PubMed

Chevallier, Maguelonne; Krauth, Werner

2007-11-01

We discuss the relationship between the cycle probabilities in the path-integral representation of the ideal Bose gas, off-diagonal long-range order, and Bose-Einstein condensation. Starting from the Landsberg recursion relation for the canonic partition function, we use elementary considerations to show that in a box of size L3 the sum of the cycle probabilities of length k>L2 equals the off-diagonal long-range order parameter in the thermodynamic limit. For arbitrary systems of ideal bosons, the integer derivative of the cycle probabilities is related to the probability of condensing k bosons. We use this relation to derive the precise form of the pik in the thermodynamic limit. We also determine the function pik for arbitrary systems. Furthermore, we use the cycle probabilities to compute the probability distribution of the maximum-length cycles both at T=0, where the ideal Bose gas reduces to the study of random permutations, and at finite temperature. We close with comments on the cycle probabilities in interacting Bose gases.

ZMOTTO- MODELING THE INTERNAL COMBUSTION ENGINE

NASA Technical Reports Server (NTRS)

Zeleznik, F. J.

1994-01-01

The ZMOTTO program was developed to model mathematically a spark-ignited internal combustion engine. ZMOTTO is a large, general purpose program whose calculations can be established at five levels of sophistication. These five models range from an ideal cycle requiring only thermodynamic properties, to a very complex representation demanding full combustion kinetics, transport properties, and poppet valve flow characteristics. ZMOTTO is a flexible and computationally economical program based on a system of ordinary differential equations for cylinder-averaged properties. The calculations assume that heat transfer is expressed in terms of a heat transfer coefficient and that the cylinder average of kinetic plus potential energies remains constant. During combustion, the pressures of burned and unburned gases are assumed equal and their heat transfer areas are assumed proportional to their respective mass fractions. Even the simplest ZMOTTO model provides for residual gas effects, spark advance, exhaust gas recirculation, supercharging, and throttling. In the more complex models, 1) finite rate chemistry replaces equilibrium chemistry in descriptions of both the flame and the burned gases, 2) poppet valve formulas represent fluid flow instead of a zero pressure drop flow, and 3) flame propagation is modeled by mass burning equations instead of as an instantaneous process. Input to ZMOTTO is determined by the model chosen. Thermodynamic data is required for all models. Transport properties and chemical kinetics data are required only as the model complexity grows. Other input includes engine geometry, working fluid composition, operating characteristics, and intake/exhaust data. ZMOTTO accommodates a broad spectrum of reactants. The program will calculate many Otto cycle performance parameters for a number of consecutive cycles (a cycle being an interval of 720 crankangle degrees). A typical case will have a number of initial ideal cycles and progress through levels of nonideal cycles. ZMOTTO has restart capabilities and permits multicycle calculations with parameters varying from cycle to cycle. ZMOTTO is written in FORTRAN IV (IBM Level H) but has also been compiled with IBM VSFORTRAN (1977 standard). It was developed on an IBM 3033 under the TSS operating system and has also been implemented under MVS. Approximately 412K of 8 bit bytes of central memory are required in a nonpaging environment. ZMOTTO was developed in 1985.

An improved lattice Boltzmann scheme for multiphase fluid with multi-range interactions

NASA Astrophysics Data System (ADS)

Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles; Rousselle, François; Renaud, Christophe

2014-10-01

Modeling of fluids with liquid to gas phase transition has become important for understanding many environmental or industrial processes. Such simulations need new techniques, because traditional solvers are often limited. The Lattice Boltzmann Model (LBM) allows simulate complex fluids, because its mesoscopic nature gives possibility to incorporate additional physics in comparison to usual methods. In this work, an improved lattice Boltzmann model for phase transition flow will be introduced. First, the state of art for Shan & Chen [1] [2] (SC) type of LBM will be reminded. Then, link to real thermodynamics will be established with Maxwell equal areas construction. Convergence to isothermal liquid vapor equilibrium will be shown and discussed. Inclusion of an equation of state for real fluid and better incorporation of force term is presented [4] [5]. Multi-range interactions have been used for SC model [8], but it hasn't been yet applied to real fluid with non-ideal equation of state. In this work, we evaluate this model when it is applied to real liquid-vapor equilibrium. We show that important differences are found for evaluation of gas density. In order to recover thermodynamic consistency, we use a new scheme for calculation of force term, which is a combination of multi range model and numerical weighting used by Gong & Cheng [6] [7]. We show the superiority of our new model by studying convergence to equilibrium values over a large temperature range. We prove that spurious velocities remaining at equilibrium are decreased.

An improved lattice Boltzmann scheme for multiphase fluid with multi-range interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maquignon, Nicolas; Duchateau, Julien; Roussel, Gilles

2014-10-06

Modeling of fluids with liquid to gas phase transition has become important for understanding many environmental or industrial processes. Such simulations need new techniques, because traditional solvers are often limited. The Lattice Boltzmann Model (LBM) allows simulate complex fluids, because its mesoscopic nature gives possibility to incorporate additional physics in comparison to usual methods. In this work, an improved lattice Boltzmann model for phase transition flow will be introduced. First, the state of art for Shan and Chen (SC) type of LBM will be reminded. Then, link to real thermodynamics will be established with Maxwell equal areas construction. Convergence tomore » isothermal liquid vapor equilibrium will be shown and discussed. Inclusion of an equation of state for real fluid and better incorporation of force term is presented. Multi-range interactions have been used for SC model, but it hasn't been yet applied to real fluid with non-ideal equation of state. In this work, we evaluate this model when it is applied to real liquid-vapor equilibrium. We show that important differences are found for evaluation of gas density. In order to recover thermodynamic consistency, we use a new scheme for calculation of force term, which is a combination of multi range model and numerical weighting used by Gong and Cheng. We show the superiority of our new model by studying convergence to equilibrium values over a large temperature range. We prove that spurious velocities remaining at equilibrium are decreased.« less

A New Ferroelectric Varactor from Water Based Inorganic Precursors

DTIC Science & Technology

2003-04-03

See Equation 2). 0 0 4 OH +-)4T H13< Equation 2. Idealized Reaction of Titanium Isopropoxide with 2-ethylhexanoic acid. Inconsistent results with the...Equation 3). Equation 3. Reaction of 2-ethylhexanoic anhydride with Titanium Isopropoxide We have made over one hundred batches of both BST and SBTN MOD...aliphatic acids used in the more common MOD precursors. Equation 4 shows a comparison of the decomposition products of Titanium MOD precursors made from 2

General relativistic calculations for white dwarfs

NASA Astrophysics Data System (ADS)

Mathew, Arun; Nandy, Malay K.

2017-05-01

The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of 1.4562{M}⊙ is modified to 1.4166{M}⊙ in the general relativistic case for {}_2^4{{He}} (and {}_612{{C}}) white dwarfs. Using the same general relativistic treatment, the critical mass for {}2656{{Fe}} white dwarfs is obtained as 1.2230{M}⊙ . In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter’s EoS along with the TOV equation, yielding slightly lower values for the critical masses, namely 1.4081{M}⊙ for {}_2^4{{He}}, 1.3916{M}⊙ for {}_612{{C}} and 1.1565{M}⊙ for {}2656{{Fe}} white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that {}_2^4{{He}} and {}_612{{C}} white dwarfs are stable against neutronization with the critical values of 1.4081{M}⊙ and 1.3916{M}⊙ , respectively. However, the critical masses for {}_816{{O}}, {}1020{{Ne}}, {}1224{{Mg}}, {}1428{{Si}}, {}1632{{S}} and {}2656{{Fe}} white dwarfs are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.

Bose-Einstein condensation on a manifold with non-negative Ricci curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akant, Levent, E-mail: levent.akant@boun.edu.tr; Ertuğrul, Emine, E-mail: emine.ertugrul@boun.edu.tr; Tapramaz, Ferzan, E-mail: waskhez@gmail.com

The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with non-negative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas, Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite sizemore » effects on the ground state energy are proposed. The justification of the c-number substitution on a manifold is given.« less

Fundamental equations of a mixture of gas and small spherical solid particles from simple kinetic theory.

NASA Technical Reports Server (NTRS)

Pai, S. I.

1973-01-01

The fundamental equations of a mixture of a gas and pseudofluid of small spherical solid particles are derived from the Boltzmann equation of two-fluid theory. The distribution function of the gas molecules is defined in the same manner as in the ordinary kinetic theory of gases, but the distribution function for the solid particles is different from that of the gas molecules, because it is necessary to take into account the different size and physical properties of solid particles. In the proposed simple kinetic theory, two additional parameters are introduced: one is the radius of the spheres and the other is the instantaneous temperature of the solid particles in the distribution of the solid particles. The Boltzmann equation for each species of the mixture is formally written, and the transfer equations of these Boltzmann equations are derived and compared to the well-known fundamental equations of the mixture of a gas and small solid particles from continuum theory. The equations obtained reveal some insight into various terms in the fundamental equations. For instance, the partial pressure of the pseudofluid of solid particles is not negligible if the volume fraction of solid particles is not negligible as in the case of lunar ash flow.

Computations of ideal and real gas high altitude plume flows

NASA Technical Reports Server (NTRS)

Feiereisen, William J.; Venkatapathy, Ethiraj

1988-01-01

In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.

Green's function solution to heat transfer of a transparent gas through a tube

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1989-01-01

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

Kinetic Modeling of Slow Energy Release in Non-Ideal Carbon Rich Explosives

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vitello, P; Fried, L; Glaesemann, K

2006-06-20

We present here the first self-consistent kinetic based model for long time-scale energy release in detonation waves in the non-ideal explosive LX-17. Non-ideal, insensitive carbon rich explosives, such as those based on TATB, are believed to have significant late-time slow release in energy. One proposed source of this energy is diffusion-limited growth of carbon clusters. In this paper we consider the late-time energy release problem in detonation waves using the thermochemical code CHEETAH linked to a multidimensional ALE hydrodynamics model. The linked CHEETAH-ALE model dimensional treats slowly reacting chemical species using kinetic rate laws, with chemical equilibrium assumed for speciesmore » coupled via fast time-scale reactions. In the model presented here we include separate rate equations for the transformation of the un-reacted explosive to product gases and for the growth of a small particulate form of condensed graphite to a large particulate form. The small particulate graphite is assumed to be in chemical equilibrium with the gaseous species allowing for coupling between the instantaneous thermodynamic state and the production of graphite clusters. For the explosive burn rate a pressure dependent rate law was used. Low pressure freezing of the gas species mass fractions was also included to account for regions where the kinetic coupling rates become longer than the hydrodynamic time-scales. The model rate parameters were calibrated using cylinder and rate-stick experimental data. Excellent long time agreement and size effect results were achieved.« less

A Gas-Kinetic Scheme for Reactive Flows

NASA Technical Reports Server (NTRS)

Lian,Youg-Sheng; Xu, Kun

1998-01-01

In this paper, the gas-kinetic BGK scheme for the compressible flow equations is extended to chemical reactive flow. The mass fraction of the unburnt gas is implemented into the gas kinetic equation by assigning a new internal degree of freedom to the particle distribution function. The new variable can be also used to describe fluid trajectory for the nonreactive flows. Due to the gas-kinetic BGK model, the current scheme basically solves the Navier-Stokes chemical reactive flow equations. Numerical tests validate the accuracy and robustness of the current kinetic method.

An efficient direct solver for rarefied gas flows with arbitrary statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diaz, Manuel A., E-mail: f99543083@ntu.edu.tw; Yang, Jaw-Yen, E-mail: yangjy@iam.ntu.edu.tw; Center of Advanced Study in Theoretical Science, National Taiwan University, Taipei 10167, Taiwan

2016-01-15

A new numerical methodology associated with a unified treatment is presented to solve the Boltzmann–BGK equation of gas dynamics for the classical and quantum gases described by the Bose–Einstein and Fermi–Dirac statistics. Utilizing a class of globally-stiffly-accurate implicit–explicit Runge–Kutta scheme for the temporal evolution, associated with the discrete ordinate method for the quadratures in the momentum space and the weighted essentially non-oscillatory method for the spatial discretization, the proposed scheme is asymptotic-preserving and imposes no non-linear solver or requires the knowledge of fugacity and temperature to capture the flow structures in the hydrodynamic (Euler) limit. The proposed treatment overcomes themore » limitations found in the work by Yang and Muljadi (2011) [33] due to the non-linear nature of quantum relations, and can be applied in studying the dynamics of a gas with internal degrees of freedom with correct values of the ratio of specific heat for the flow regimes for all Knudsen numbers and energy wave lengths. The present methodology is numerically validated with the unified treatment by the one-dimensional shock tube problem and the two-dimensional Riemann problems for gases of arbitrary statistics. Descriptions of ideal quantum gases including rotational degrees of freedom have been successfully achieved under the proposed methodology.« less

Estimation of perimortal percent carboxy-heme in nonstandard postmortem specimens using analysis of carbon monoxide by GC/MS and iron by flame atomic absorption spectrophotometry.

PubMed

Middleberg, R A; Easterling, D E; Zelonis, S F; Rieders, F; Rieders, M F

1993-01-01

In decomposed, formalin-fixed, embalmed, exhumed, and some fire-dried cases in which normal blood is unavailable, the usual methods for determination of carboxyhemoglobin saturation frequently fail. To address these specimens, a method utilizing both gas chromatography/mass spectrometric (GC/MS) determination of carbon monoxide (CO) and flame atomic absorption spectrophotometry (FAAS) determination of iron (Fe), in the same specimen, was developed. The method is reported here, along with its application to seven pertinent forsensic death investigations. The CO analytical methodology involves acid liberation of the gas from the specimen aliquot in a headspace vial. After heating and equilibrating, a sample of the headspace vapor is injected into the GC/MS system with a gastight syringe. Quantitation is achieved by standard addition comparison utilizing the ideal gas law equation. Iron is quantified by FAAS analysis of the same aliquot used for the CO determination, following nitric acid digestion. The concentration is determined by comparison to a standard curve. A formula for determining the minimum percent carboxy-heme saturation was derived by using the ratio of the amount of CO to the amount of Fe in the aliquot analyzed. Tissue types analyzed include spleen, liver, muscle, dried blood, and unspecified decomposed tissue.

Differential molar heat capacities to test ideal solubility estimations.

PubMed

Neau, S H; Bhandarkar, S V; Hellmuth, E W

1997-05-01

Calculation of the ideal solubility of a crystalline solute in a liquid solvent requires knowledge of the difference in the molar heat capacity at constant pressure of the solid and the supercooled liquid forms of the solute, delta Cp. Since this parameter is not usually known, two assumptions have been used to simplify the expression. The first is that delta Cp can be considered equal to zero; the alternate assumption is that the molar entropy of fusion, delta Sf, is an estimate of delta Cp. Reports claiming the superiority of one assumption over the other, on the basis of calculations done using experimentally determined parameters, have appeared in the literature. The validity of the assumptions in predicting the ideal solubility of five structurally unrelated compounds of pharmaceutical interest, with melting points in the range 420 to 470 K, was evaluated in this study. Solid and liquid heat capacities of each compound near its melting point were determined using differential scanning calorimetry. Linear equations describing the heat capacities were extrapolated to the melting point to generate the differential molar heat capacity. Linear data were obtained for both crystal and liquid heat capacities of sample and test compounds. For each sample, ideal solubility at 298 K was calculated and compared to the two estimates generated using literature equations based on the differential molar heat capacity assumptions. For the compounds studied, delta Cp was not negligible and was closer to delta Sf than to zero. However, neither of the two assumptions was valid for accurately estimating the ideal solubility as given by the full equation.

Bose-Einstein condensation in the relativistic ideal Bose gas.

PubMed

Grether, M; de Llano, M; Baker, George A

2007-11-16

The Bose-Einstein condensation (BEC) critical temperature in a relativistic ideal Bose gas of identical bosons, with and without the antibosons expected to be pair-produced abundantly at sufficiently hot temperatures, is exactly calculated for all boson number densities, all boson point rest masses, and all temperatures. The Helmholtz free energy at the critical BEC temperature is lower with antibosons, thus implying that omitting antibosons always leads to the computation of a metastable state.

Computational flow predictions for hypersonic drag devices

NASA Technical Reports Server (NTRS)

Tokarcik, Susan; Venkatapathy, Ethiraj; Candler, Graham; Palmer, Grant

1991-01-01

The effectiveness of two types of hypersonic decelerators are computationally examined: mechanically deployable flares and inflatable ballutes. CFD is used to predict the flowfield around a solid rocket motor (SRM) with a deployed decelerator. The computations are performed with an ideal gas solver using an effective specific heat ratio of 1.15. The surface pressure coefficients, the drag, and the extent of the compression corner separation zone predicted by the ideal gas solver compare well with those predicted by the nonequilibrium solver. The ideal gas solver is computationally inexpensive and is shown to be well suited for preliminary design studies. The computed solutions are used to determine the size and shape of the decelerator that are required to achieve a drag coefficient of 5 in order to assure that the SRM will splash down in the Pacific Ocean. Heat transfer rates to the SRM and the decelerators are predicted to estimate the amount of thermal protection required.

Finite grid radius and thickness effects on retarding potential analyzer measured suprathermal electron density and temperature

NASA Technical Reports Server (NTRS)

Knudsen, William C.

1992-01-01

The effect of finite grid radius and thickness on the electron current measured by planar retarding potential analyzers (RPAs) is analyzed numerically. Depending on the plasma environment, the current is significantly reduced below that which is calculated using a theoretical equation derived for an idealized RPA having grids with infinite radius and vanishingly small thickness. A correction factor to the idealized theoretical equation is derived for the Pioneer Venus (PV) orbiter RPA (ORPA) for electron gasses consisting of one or more components obeying Maxwell statistics. The error in density and temperature of Maxwellian electron distributions previously derived from ORPA data using the theoretical expression for the idealized ORPA is evaluated by comparing the densities and temperatures derived from a sample of PV ORPA data using the theoretical expression with and without the correction factor.

SORPTION AND DESORPTION BY IDEAL TWO-COMPARTMENT SYSTEMS: UNUSUAL BEHAVIOR AND DATA INTERPRETATION PROBLEMS

EPA Science Inventory

This paper presents an evaluation of the results of fitting curves to isotherm and kinetic data for idealized two-compartment systems of soil or sediment. Data were produced by numerically solving sets of Freundlich isotherm and first-order kinetics equations for mixtures of up ...

Complex double-mass dynamic model of rotor on thrust foil gas dynamic bearings

NASA Astrophysics Data System (ADS)

Sytin, A.; Babin, A.; Vasin, S.

2017-08-01

The present paper considers simulation of a rotor’s dynamics behaviour on thrust foil gas dynamic bearings based on simultaneous solution of gas dynamics differential equations, equations of theory of elasticity, motion equations and some additional equations. A double-mass dynamic system was considered during the rotor’s motion simulation which allows not only evaluation of rotor’s dynamic behaviour, but also to evaluate the influence of operational and load parameters on the dynamics of the rotor-bearing system.

Shock Equation of State of Multi-Phase Epoxy-Based Composite (Al-MnO2-Epoxy)

DTIC Science & Technology

2010-10-01

single stage light gas gun , two...using three different loading techniques— single stage light gas gun , two stage light gas gun , and explosive loading—with multiple diagnostic...wave speed. B. Single stage gas gun loading experiments Four gas gun -driven equation of state experiments were conducted at NSWC-Indian Head using

Using explanatory crop models to develop simple tools for Advanced Life Support system studies

NASA Technical Reports Server (NTRS)

Cavazzoni, J.

2004-01-01

System-level analyses for Advanced Life Support require mathematical models for various processes, such as for biomass production and waste management, which would ideally be integrated into overall system models. Explanatory models (also referred to as mechanistic or process models) would provide the basis for a more robust system model, as these would be based on an understanding of specific processes. However, implementing such models at the system level may not always be practicable because of their complexity. For the area of biomass production, explanatory models were used to generate parameters and multivariable polynomial equations for basic models that are suitable for estimating the direction and magnitude of daily changes in canopy gas-exchange, harvest index, and production scheduling for both nominal and off-nominal growing conditions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Molecular Dynamics Simulations of an Idealized Shock Tube: N2 in Ar Bath Driven by He

NASA Astrophysics Data System (ADS)

Piskulich, Ezekiel Ashe; Sewell, Thomas D.; Thompson, Donald L.

2015-06-01

The dynamics of 10% N2 in Ar initially at 298 K in an idealized shock tube driven by He was studied using molecular dynamics. The simulations were performed using the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. Nitrogen was modeled as a Morse oscillator and non-covalent interactions were approximated by the Buckingham exponential-6 pair potential. The initial pressures in the He driver gas and the driven N2/Ar gas were 1000 atm and 20 atm, respectively. Microcanonical trajectories were followed for 2 ns following release of the driver gas. Results for excitation and subsequent relaxation of the N2, as well as properties of the gas during the simulations, will be reported.

DIPPR Project 871 For 1995 - Thermodynamic Properties and Ideal-Gas Enthalpies of Formation for Methyl Benzoate, Ethyl Benzoate, (R)-(+)-Limonene, Tert-Amyl Methyl Ether, Trans-Crotonaldehyde, and

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steele, W.V.

2002-07-01

Ideal-gas enthalpies of formation of methyl benzoate, ethyl benzoate, (R)-(+)-limonene, tert-amyl methyl ether, trans-crotonaldehyde, and diethylene glycol are reported. The standard energy of combustion and hence standard enthalpy of formation of each compound in the liquid phase has been measured using an oxygen rotating-bomb calorimeter without rotation. Vapor pressures were measured to a pressure limit of 270 kPa or the lower decomposition point for each of the six compounds using a twin ebulliometric apparatus. Liquid-phase densities along the saturation line were measured for each compound over a range of temperature (ambient to a maximum of 548 K). A differential scanningmore » calorimeter was used to measure two-phase (liquid + vapor) heat capacities for each compound in the temperature region ambient to the critical temperature or lower decomposition point. For methyl benzoate and tert-amyl methyl ether, critical temperatures and critical densities were determined from the DSC results and corresponding critical pressures derived from the fitting procedures. Fitting procedures were used to derive critical temperatures, critical pressures, and critical densities for each of the remaining compounds. The results of the measurements were combined to derive a series of thermophysical properties including critical temperature, critical density, critical pressure, acentric factor, enthalpies of vaporization (restricted to within {+-}50 K of the temperature region of the experimentally determined vapor pressures), and heat capacities along the saturation line. Wagner-type vapor-pressure equations were derived for each compound. All measured and derived values were compared with those obtained in a search of the literature. Recommended critical parameters are listed for each of the compounds studied. Group-additivity parameters, useful in the application of the Benson gas-phase group-contribution correlations, were derived.« less

Perfect gas effects in compressible rapid distortion theory

NASA Technical Reports Server (NTRS)

Kerschen, E. J.; Myers, M. R.

1987-01-01

The governing equations presented for small amplitude unsteady disturbances imposed on steady, compressible mean flows that are two-dimensional and nearly uniform have their basis in the perfect gas equations of state, and therefore generalize previous results based on tangent gas theory. While these equations are more complex, this complexity is required for adequate treatment of high frequency disturbances, especially when the base flow Mach number is large; under such circumstances, the simplifying assumptions of tangent gas theory are not applicable.

Mathematical modelling of a human external respiratory system

NASA Technical Reports Server (NTRS)

1977-01-01

A closed system of algebraic and common differential equations solved by computer is investigated. It includes equations which describe the activity pattern of the respiratory center, the phrenic nerve, the thrust produced by the diaphragm as a function of the lung volume and discharge frequency of the phrenic nerve, as well as certain relations of the lung stretch receptors and chemoreceptors on various lung and blood characteristics, equations for lung biomechanics, pulmonary blood flow, alveolar gas exchange and capillary blood composition equations to determine various air and blood flow and gas exchange parameters, and various gas mixing and arterial and venous blood composition equations, to determine other blood, air and gas mixing characteristics. Data are presented by means of graphs and tables, and some advantages of this model over others are demonstrated by test results.

Distortion of liquid film discharging from twin-fluid atomizer

NASA Astrophysics Data System (ADS)

Mehring, C.; Sirignano, W. A.

2001-11-01

The nonlinear distortion and disintegration of a thin liquid film exiting from a two-dimensional twin-fluid atomizer is analyzed numerically. Pulsed gas jets impacting on both sides of the discharging liquid film at the atomizer exit generate dilational and/or sinuous deformations of the film. Both liquid phase and gas phase are inviscid and incompressible. For the liquid phase the so-called long-wavelength approximation is employed yielding a system of unsteady one-dimensional equations for the planar film. Solution of Laplace's equation for the velocity potential yields the gas-phase velocity field on both sides of the liquid stream. Coupling between both phases is described through kinematic and dynamic boundary conditions at the phase interfaces, and includes the solution of the unsteady Bernoulli equation to determine the gas-phase pressure along the interfaces. Both gas- and liquid-phase equations are solved simultaneously. Solution of Laplace's equation for the gas streams is obtained by means of a boundary-element method. Numerical solutions for the liquid phase use the Lax-Wendroff method with Richtmyer splitting. Sheet distortion resulting from the stagnation pressure of the impacting gas jets and subsequent disturbance amplification due to Kelvin-Helmholtz effects are studied for various combinations of gas-pulse timing, gas-jet impact angles, gas-to-liquid-density ratio, liquid-phase Weber number and gas-jet-to-liquid-jet-momentum ratio. Dilational and sinuous oscillations of the liquid are examined and film pinch-off is predicted.

Gas occurrence property in shales of Tuha basin northwest china

NASA Astrophysics Data System (ADS)

Chen, Jinlong; Huang, Zhilong

2017-04-01

Pore of rock under formation condition must be fulfilled by gas, oil, or water, so the volume of water and gas is equation to porous volume in shale gas. The occurrences states of gas are free gas, solution gas, and absorbed gas. Field analysis is used to obtain total gas content by improved lost gas recover method. Free gas content acquired by pore proportion of gas, which use measured pore volume minus water and oil saturation, convert gas content of standard condition by state equation. Water saturation obtain from core water content, oil saturation obtain from extract carbohydrate. Solution gas need gas solubility in oil and water to calculate solution gas content in standard condition. Absorbed gas, introduce Absorbed Gas Saturation ɛ, which acquire from isothermal adsorption volume vs field analysis gas content in many basins of published paper, need isothermal adsorption and Absorbed Gas Saturation to obtain absorbed gas content. All of the data build connect with logging value by regression equation. The gas content is 0.92-1.53 m3/t from field analysis, evaluate gas content is 1.33 m3/t average, free gas proportion is about 47%, absorbed gas counter for 49%, and solution gas is average 4%.

An advanced kinetic theory for morphing continuum with inner structures

NASA Astrophysics Data System (ADS)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Real-gas effects associated with one-dimensional transonic flow of cryogenic nitrogen

NASA Technical Reports Server (NTRS)

Adcock, J. B.

1976-01-01

Real gas solutions for one-dimensional isentropic and normal-shock flows of nitrogen were obtained for a wide range of temperatures and pressures. These calculations are compared to ideal gas solutions and are presented in tables. For temperatures (300 K and below) and pressures (1 to 10 atm) that cover those anticipated for transonic cryogenic tunnels, the solutions are analyzed to obtain indications of the magnitude of inviscid flow simulation errors. For these ranges, the maximum deviation of the various isentropic and normal shock parameters from the ideal values is about 1 percent or less, and for most wind tunnel investigations this deviation would be insignificant.

Idiosyncratic Deals: Testing Propositions on Timing, Content, and the Employment Relationship

ERIC Educational Resources Information Center

Rousseau, Denise M.; Hornung, Severin; Kim, Tai Gyu

2009-01-01

This study tests propositions regarding idiosyncratic deals (i-deals) in a sample of N = 265 hospital employees using structural equation modeling. Timing and content of idiosyncratic employment arrangements are postulated to have differential consequences for the nature of the employment relationship. Results confirm that i-deals made after hire…

A new shock-capturing numerical scheme for ideal hydrodynamics

NASA Astrophysics Data System (ADS)

Fecková, Z.; Tomášik, B.

2015-05-01

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

Ideal flow theory for the double - shearing model as a basis for metal forming design

NASA Astrophysics Data System (ADS)

Alexandrov, S.; Trung, N. T.

2018-02-01

In the case of Tresca’ solids (i.e. solids obeying the Tresca yield criterion and its associated flow rule) ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal stress (and strain rate) is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is often advantageous for metal forming processes. Therefore, the ideal flow theory is used as the basis of a procedure for the preliminary design of such processes. The present paper extends the theory of stationary planar ideal flow to pressure dependent materials obeying the double shearing model and the double slip and rotation model. It is shown that the original problem of plasticity reduces to a purely geometric problem. The corresponding system of equations is hyperbolic. The characteristic relations are integrated in elementary functions. In regions where one family of characteristics is straight, mapping between the principal lines and Cartesian coordinates is determined by linear ordinary differential equations. An illustrative example is provided.

Use of Dimples to Suppress Boundary Layer Separation on a Low Pressure Turbine Blade

DTIC Science & Technology

2002-12-01

Brayton cycle for an ideal gas turbine engine.............................................. 11 Figure 5. T-S diagram for a non-ideal turbine stage...engine efficiency is well illustrated with a T-S diagram, where T is temperature and S is entropy. The ideal jet engine is represented with the Brayton ...the Brayton cycle represents an ideal engine, no losses are present, and entropy is not produced. Between station 3 and 4, fuel (energy) is added

Self-Consistency of the Theory of Elementary Stage Rates of Reversible Processes and the Equilibrium Distribution of Reaction Mixture Components

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-06-01

An analysis is presented of one of the key concepts of physical chemistry of condensed phases: the theory self-consistency in describing the rates of elementary stages of reversible processes and the equilibrium distribution of components in a reaction mixture. It posits that by equating the rates of forward and backward reactions, we must obtain the same equation for the equilibrium distribution of reaction mixture components, which follows directly from deducing the equation in equilibrium theory. Ideal reaction systems always have this property, since the theory is of a one-particle character. Problems arise in considering interparticle interactions responsible for the nonideal behavior of real systems. The Eyring and Temkin approaches to describing nonideal reaction systems are compared. Conditions for the self-consistency of the theory for mono- and bimolecular processes in different types of interparticle potentials, the degree of deviation from the equilibrium state, allowing for the internal motions of molecules in condensed phases, and the electronic polarization of the reagent environment are considered within the lattice gas model. The inapplicability of the concept of an activated complex coefficient for reaching self-consistency is demonstrated. It is also shown that one-particle approximations for considering intermolecular interactions do not provide a theory of self-consistency for condensed phases. We must at a minimum consider short-range order correlations.

The Statistical Mechanics of Ideal Homogeneous Turbulence

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2002-01-01

Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.

The Marriage of Gas and Dust

NASA Astrophysics Data System (ADS)

Price, D. J.; Laibe, G.

2015-10-01

Dust-gas mixtures are the simplest example of a two fluid mixture. We show that when simulating such mixtures with particles or with particles coupled to grids a problem arises due to the need to resolve a very small length scale when the coupling is strong. Since this is occurs in the limit when the fluids are well coupled, we show how the dust-gas equations can be reformulated to describe a single fluid mixture. The equations are similar to the usual fluid equations supplemented by a diffusion equation for the dust-to-gas ratio or alternatively the dust fraction. This solves a number of numerical problems as well as making the physics clear.

Motions, efforts and actuations in constrained dynamic systems: a multi-link open-chain example

NASA Astrophysics Data System (ADS)

Duke Perreira, N.

1999-08-01

The effort-motion method, which describes the dynamics of open- and closed-chain topologies of rigid bodies interconnected with revolute and prismatic pairs, is interpreted geometrically. Systems are identified for which the simultaneous control of forces and velocities is desirable, and a representative open-chain system is selected for use in the ensuing analysis. Gauge invariant transformations are used to recast the commonly used kinetic and kinematic equations into a dimensional gauge invariant form. Constraint elimination techniques based on singular value decompositions then recast the invariant equations into orthogonal and reciprocal sets of motion and effort equations written in state variable form. The ideal actuation is found that simultaneously achieves the obtainable portions of the desired constraining efforts and motions. The performance is then evaluated of using the actuation closest to the ideal actuation.

On the various forms of the energy equation for a dilute, monatomic mixture of nonreacting gases

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.

1994-01-01

In the case of gas mixtures, the governing equations become rather formidable and a complete listing of the equations in their various forms and methods to evaluate the transport coefficients is difficult to find. This paper seeks to compile common, as well as less well known, results in a single document. Various relationships between equations describing conservation of energy for a dilute, monatomic, nonreacting gas in local equilibrium are provided. The gas is treated as nonrelativistic, not subject to magnetic or electric fields, or radiative effects.

A minimum entropy principle in the gas dynamics equations

NASA Technical Reports Server (NTRS)

Tadmor, E.

1986-01-01

Let u(x bar,t) be a weak solution of the Euler equations, governing the inviscid polytropic gas dynamics; in addition, u(x bar, t) is assumed to respect the usual entropy conditions connected with the conservative Euler equations. We show that such entropy solutions of the gas dynamics equations satisfy a minimum entropy principle, namely, that the spatial minimum of their specific entropy, (Ess inf s(u(x,t)))/x, is an increasing function of time. This principle equally applies to discrete approximations of the Euler equations such as the Godunov-type and Lax-Friedrichs schemes. Our derivation of this minimum principle makes use of the fact that there is a family of generalized entrophy functions connected with the conservative Euler equations.

Inflow performance relationship for perforated wells producing from solution gas drive reservoir

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sukarno, P.; Tobing, E.L.

1995-10-01

The IPR curve equations, which are available today, are developed for open hole wells. In the application of Nodal System Analysis in perforated wells, an accurate calculation of pressure loss in the perforation is very important. Nowadays, the equation which is widely used is Blount, Jones and Glaze equation, to estimate pressure loss across perforation. This equation is derived for single phase flow, either oil or gas, therefore it is not suitable for two-phase production wells. In this paper, an IPR curve equation for perforated wells, producing from solution gas drive reservoir, is introduced. The equation has been developed usingmore » two phase single well simulator combine to two phase flow in perforation equation, derived by Perez and Kelkar. A wide range of reservoir rock and fluid properties and perforation geometry are used to develop the equation statistically.« less

Wide-range ideal 2D Rashba electron gas with large spin splitting in Bi2Se3/MoTe2 heterostructure

NASA Astrophysics Data System (ADS)

Wang, Te-Hsien; Jeng, Horng-Tay

2017-02-01

An application-expected ideal two-dimensional Rashba electron gas, i.e., nearly all the conduction electrons occupy the Rashba bands, is crucial for semiconductor spintronic applications. We demonstrate that such an ideal two-dimensional Rashba electron gas with a large Rashba splitting can be realized in a topological insulator Bi2Se3 ultrathin film grown on a transition metal dichalcogenides MoTe2 substrate through first-principle calculations. Our results show the Rashba bands exclusively over a very large energy interval of about 0.6 eV around the Fermi level within the MoTe2 semiconducting gap. Such a wide-range ideal two-dimensional Rashba electron gas with a large spin splitting, which is desirable for real devices utilizing the Rashba effect, has never been found before. Due to the strong spin-orbit coupling, the strength of the Rashba splitting is comparable with that of the heavy-metal surfaces such as Au and Bi surfaces, giving rise to a spin precession length as small as 10 nm. The maximum in-plane spin polarization of the inner (outer) Rashba band near the Γ point is about 70% (60%). The room-temperature coherence length is at least several times longer than the spin precession length, providing good coherency through the spin processing devices. The wide energy window for ideal Rashba bands, small spin precession length, as well as long spin coherence length in this two-dimensional topological insulator/transition metal dichalcogenides heterostructure pave the way for realizing an ultrathin nano-scale spintronic device such as the Datta-Das spin transistor at room-temperature.

Dynamo Effects in Magnetized Ideal Plasma Cosmologies

NASA Astrophysics Data System (ADS)

Kleidis, Kostas; Kuiroukidis, Apostolos; Papadopoulos, Demetrios; Vlahos, Loukas

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what is most important, is that, at late times, the magnetic-induction contrast (δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

Prolongation structures of nonlinear evolution equations. II

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1976-01-01

The prolongation structure of a closed ideal of exterior differential forms is further discussed, and its use illustrated by application to an ideal (in six dimensions) representing the cubically nonlinear Schroedinger equation. The prolongation structure in this case is explicitly given, and recurrence relations derived which support the conjecture that the structure is open - i.e., does not terminate as a set of structure relations of a finite-dimensional Lie group. We introduce the use of multiple pseudopotentials to generate multiple Baecklund transformation, and derive the double Baecklund transformation. This symmetric transformation concisely expresses the (usually conjectured) theorem of permutability, which must consequently apply to all solutions irrespective of asymptotic constraints.

An exact solution for ideal dam-break floods on steep slopes

USGS Publications Warehouse

Ancey, C.; Iverson, R.M.; Rentschler, M.; Denlinger, R.P.

2008-01-01

The shallow-water equations are used to model the flow resulting from the sudden release of a finite volume of frictionless, incompressible fluid down a uniform slope of arbitrary inclination. The hodograph transformation and Riemann's method make it possible to transform the governing equations into a linear system and then deduce an exact analytical solution expressed in terms of readily evaluated integrals. Although the solution treats an idealized case never strictly realized in nature, it is uniquely well-suited for testing the robustness and accuracy of numerical models used to model shallow-water flows on steep slopes. Copyright 2008 by the American Geophysical Union.

Application of the Flory-Huggins theory to the solubility of solids in glyceryl trioleate

USGS Publications Warehouse

Chiou, Cary T.; Manes, Milton

1986-01-01

The conventional thermodynamic deviation for ideal solid–liquid solubilities is modified by substituting the Flory–Huggins model for Raoult's law. A comparison of published data for eleven solides in glyceryl trioleate with the predictions of the conventional and modified equations shows that the significantly higher athermal solubilities from the modified equation are in much better agreement with the experimental data. This suggests that discrepancies between the data and the predictions of the conventional model for ideal systems result from the inappropriate use of Raoult's law for systems with significant solute–solvent size disparity rather than from specific interactions.

Alexander Dalgarno

NASA Astrophysics Data System (ADS)

Fox, Jane L.

Alex Dalgarno saved my career. I entered the Graduate School at Harvard in the Chemistry Department in September of 1973 from the University of Michigan, where I had (unfortunately) majored in Chemistry. Chemistry is considered a "laboratory science" but I had no talent in the laboratory. I had merely fallen in love with the ideal gas law in high school, and I had stubbornly allowed this to determine my course of studies, most of which had nothing to do with the ideal gas law, and much of which was focused on laboratory studies...

Microeconomics of the ideal gas like market models

NASA Astrophysics Data System (ADS)

Chakrabarti, Anindya S.; Chakrabarti, Bikas K.

2009-10-01

We develop a framework based on microeconomic theory from which the ideal gas like market models can be addressed. A kinetic exchange model based on that framework is proposed and its distributional features have been studied by considering its moments. Next, we derive the moments of the CC model (Eur. Phys. J. B 17 (2000) 167) as well. Some precise solutions are obtained which conform with the solutions obtained earlier. Finally, an output market is introduced with global price determination in the model with some necessary modifications.

Numerical study of the flow in a three-dimensional thermally driven cavity

NASA Astrophysics Data System (ADS)

Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart

2008-06-01

Solutions for the fully compressible Navier-Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied. Results are computed using a finite volume method on a structured, collocated grid. An explicit third-order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used. To stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced. The discrete equations are solved using a time-marching method with restrictions on the timestep corresponding to the explicit parts of the solver. Multigrid is used as acceleration technique.

Second-order small-disturbance solutions for hypersonic flow over power-law bodies

NASA Technical Reports Server (NTRS)

Townsend, J. C.

1975-01-01

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.

Part 1 of a Computational Study of a Drop-Laden Mixing Layer

NASA Technical Reports Server (NTRS)

Okong'o, Nora A.; Bellan, Josette

2004-01-01

This first of three reports on a computational study of a drop-laden temporal mixing layer presents the results of direct numerical simulations (DNS) of well-resolved flow fields and the derivation of the large-eddy simulation (LES) equations that would govern the larger scales of a turbulent flow field. The mixing layer consisted of two counterflowing gas streams, one of which was initially laden with evaporating liquid drops. The gas phase was composed of two perfect gas species, the carrier gas and the vapor emanating from the drops, and was computed in an Eulerian reference frame, whereas each drop was tracked individually in a Lagrangian manner. The flow perturbations that were initially imposed on the layer caused mixing and eventual transition to turbulence. The DNS database obtained included transitional states for layers with various liquid mass loadings. For the DNS, the gas-phase equations were the compressible Navier-Stokes equations for conservation of momentum and additional conservation equations for total energy and species mass. These equations included source terms representing the effect of the drops on the mass, momentum, and energy of the gas phase. From the DNS equations, the expression for the irreversible entropy production (dissipation) was derived and used to determine the dissipation due to the source terms. The LES equations were derived by spatially filtering the DNS set and the magnitudes of the terms were computed at transitional states, leading to a hierarchy of terms to guide simplification of the LES equations. It was concluded that effort should be devoted to the accurate modeling of both the subgridscale fluxes and the filtered source terms, which were the dominant unclosed terms appearing in the LES equations.

Determination of gas volume trapped in a closed fluid system

NASA Technical Reports Server (NTRS)

Hunter, W. F.; Jolley, J. E.

1971-01-01

Technique involves extracting known volume of fluid and measuring system before and after extraction, volume of entrapped gas is then computed. Formula derived from ideal gas laws is basis of this method. Technique is applicable to thermodynamic cycles and hydraulic systems.

A method for calculating a real-gas two-dimensional nozzle contour including the effects of gamma

NASA Technical Reports Server (NTRS)

Johnson, C. B.; Boney, L. R.

1975-01-01

A method for calculating two-dimensional inviscid nozzle contours for a real gas or an ideal gas by the method of characteristics is described. The method consists of a modification of an existing nozzle computer program. The ideal-gas nozzle contour can be calculated for any constant value of gamma. Two methods of calculating the center-line boundary values of the Mach number in the throat region are also presented. The use of these three methods of calculating the center-line Mach number distribution in the throat region can change the distance from the throat to the inflection point by a factor of 2.5. A user's guide is presented for input to the computer program for both the two-dimensional and axisymmetric nozzle contours.

Correlation between CO2 storage at the last minute of gas insufflation and area of retroperitoneal lacuna during retroperitoneal laparoscopic radical nephrectomy.

PubMed

Hu, Jian-Jun; Liu, Ya-Hua; Yu, Chan-Juan; Jialielihan, Nuerbolati

2016-07-22

Adequate operation interspace is the premise of laparoscopy, and carbon dioxide (CO2) was an ideal gas for forming lacuna. A retroperitoneal space is used to form operation interspace in retroperitoneal laparoscopic radical nephrectomy by making ballooning, and the retroperitoneal space has no relative complete and airtight serous membrane, therefore CO2 absorption may be greater in retroperitoneal than transperitoneal laparoscopic radical nephrectomy. Excess CO2 absorption may induce hypercapnemia and further cause physiopathological change of respiratory and circulatory system. Therefore, exact evaluation of amount of CO2 which is eliminated from body via minute ventilation is important during retroperitoneal laparoscopic radical nephrectomy. The aim of the paper is to study the correlation between CO2 storage at the last minute of gas insufflation and area of retroperitoneal lacuna during retroperitoneal laparoscopic radical nephrectomy. Forty ASA I/II patients undergoing retroperitoneal laparoscopic radical nephrectomy were enrolled. CO2 storage at the last minute of gas insufflation and area of a retroperitoneal lacuna were observed. Linear correlation and regression were performed to determine the correlation between them. There was positive correlation between CO2 storage at the last minute of gas insufflation and area of retroperitoneal lacuna (r = 0.880, P = 0.000), and the equation of linear regression was y = -83.097 + 0.925x (R(2) = 0.780, t = 11.610, P = 0.000). Amount of CO2 which is eliminated from body via mechanical ventilation could be calculated by measuring the area of retroperitoneal lacuna during retroperitoneal laparoscopic radical nephrectomy, and an anesthetist should be aware of the size of lacuna to predict high CO2 storage at the last minute of gas insufflation.

The ‘ideal selectivity’ vs ‘true selectivity’ for permeation of gas mixture in nanoporous membranes

NASA Astrophysics Data System (ADS)

He, Zhou; Wang, Kean

2018-03-01

In this study, we proposed and validated a novel and non-destructive experimental technology for measuring the permeation of binary gas mixture in nanoporous membranes. The traditional time lag rig was modified to examine the permeation characteristics of each gas component as well as that of the binary gas mixtures. The difference in boiling points of each species were explored. Binary gas mixtures of CO2/He were permeated through the nanoporous carbon molecular sieve membrane (CMSM). The results showed that, due to the strong interaction among different molecules and with the porous network of the membrane, the measured perm-selectivity or ‘true selectivity’ of a binary mixture can significantly deviate from the ‘ideal selectivity’ calculated form the permeation flux of each pure species, and this deviation is a complicated function of the molecular properties and operation conditions.

Converging shock flows for a Mie-Grüneisen equation of state

NASA Astrophysics Data System (ADS)

Ramsey, Scott D.; Schmidt, Emma M.; Boyd, Zachary M.; Lilieholm, Jennifer F.; Baty, Roy S.

2018-04-01

Previous work has shown that the one-dimensional (1D) inviscid compressible flow (Euler) equations admit a wide variety of scale-invariant solutions (including the famous Noh, Sedov, and Guderley shock solutions) when the included equation of state (EOS) closure model assumes a certain scale-invariant form. However, this scale-invariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of Mie-Grüneisen EOS. Intuitively, this incompatibility naturally arises from the presence of multiple dimensional scales in the Mie-Grüneisen EOS, which are otherwise absent from scale-invariant models that feature only dimensionless parameters (such as the adiabatic index in the ideal gas EOS). The current work extends previous efforts intended to rectify this inconsistency, by using a scale-invariant EOS model to approximate a Mie-Grüneisen EOS form. To this end, the adiabatic bulk modulus for the Mie-Grüneisen EOS is constructed, and its key features are used to motivate the selection of a scale-invariant approximation form. The remaining surrogate model parameters are selected through enforcement of the Rankine-Hugoniot jump conditions for an infinitely strong shock in a Mie-Grüneisen material. Finally, the approximate EOS is used in conjunction with the 1D inviscid Euler equations to calculate a semi-analytical Guderley-like imploding shock solution in a metal sphere and to determine if and when the solution may be valid for the underlying Mie-Grüneisen EOS.

Dissipative particle dynamics study of velocity autocorrelation function and self-diffusion coefficient in terms of interaction potential strength

NASA Astrophysics Data System (ADS)

Zohravi, Elnaz; Shirani, Ebrahim; Pishevar, Ahmadreza; Karimpour, Hossein

2018-07-01

This research focuses on numerically investigating the self-diffusion coefficient and velocity autocorrelation function (VACF) of a dissipative particle dynamics (DPD) fluid as a function of the conservative interaction strength. Analytic solutions to VACF and self-diffusion coefficients in DPD were obtained by many researchers in some restricted cases including ideal gases, without the account of conservative force. As departure from the ideal gas conditions are accentuated with increasing the relative proportion of conservative force, it is anticipated that the VACF should gradually deviate from its normally expected exponentially decay. This trend is confirmed through numerical simulations and an expression in terms of the conservative force parameter, density and temperature is proposed for the self-diffusion coefficient. As it concerned the VACF, the equivalent Langevin equation describing Brownian motion of particles with a harmonic potential is adapted to the problem and reveals an exponentially decaying oscillatory pattern influenced by the conservative force parameter, dissipative parameter and temperature. Although the proposed model for obtaining the self-diffusion coefficient with consideration of the conservative force could not be verified due to computational complexities, nonetheless the Arrhenius dependency of the self-diffusion coefficient to temperature and pressure permits to certify our model over a definite range of DPD parameters.

Teaching Thermodynamics of Ideal Solutions: An Entropy-Based Approach to Help Students Better Understand and Appreciate the Subtleties of Solution Models

ERIC Educational Resources Information Center

Tomba, J. Pablo

2015-01-01

The thermodynamic formalism of ideal solutions is developed in most of the textbooks postulating a form for the chemical potential of a generic component, which is adapted from the thermodynamics of ideal gas mixtures. From this basis, the rest of useful thermodynamic properties can be derived straightforwardly without further hypothesis. Although…

The Dependence of Water Permeability in Quartz Sand on Gas Hydrate Saturation in the Pore Space

NASA Astrophysics Data System (ADS)

Kossel, E.; Deusner, C.; Bigalke, N.; Haeckel, M.

2018-02-01

Transport of fluids in gas hydrate bearing sediments is largely defined by the reduction of the permeability due to gas hydrate crystals in the pore space. Although the exact knowledge of the permeability behavior as a function of gas hydrate saturation is of crucial importance, state-of-the-art simulation codes for gas production scenarios use theoretically derived permeability equations that are hardly backed by experimental data. The reason for the insufficient validation of the model equations is the difficulty to create gas hydrate bearing sediments that have undergone formation mechanisms equivalent to the natural process and that have well-defined gas hydrate saturations. We formed methane hydrates in quartz sand from a methane-saturated aqueous solution and used magnetic resonance imaging to obtain time-resolved, three-dimensional maps of the gas hydrate saturation distribution. These maps were fed into 3-D finite element method simulations of the water flow. In our simulations, we tested the five most well-known permeability equations. All of the suitable permeability equations include the term (1-SH)n, where SH is the gas hydrate saturation and n is a parameter that needs to be constrained. The most basic equation describing the permeability behavior of water flow through gas hydrate bearing sand is k = k0 (1-SH)n. In our experiments, n was determined to be 11.4 (±0.3). Results from this study can be directly applied to bulk flow analysis under the assumption of homogeneous gas hydrate saturation and can be further used to derive effective permeability models for heterogeneous gas hydrate distributions at different scales.

A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

NASA Astrophysics Data System (ADS)

Coquel, Frédéric; Hérard, Jean-Marc; Saleh, Khaled

2017-02-01

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Tokareva-Toro's HLLC scheme [44]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.

A positive and entropy-satisfying finite volume scheme for the Baer–Nunziato model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coquel, Frédéric, E-mail: frederic.coquel@cmap.polytechnique.fr; Hérard, Jean-Marc, E-mail: jean-marc.herard@edf.fr; Saleh, Khaled, E-mail: saleh@math.univ-lyon1.fr

We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer–Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in for the isentropic Baer–Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound aremore » also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer–Nunziato model, namely Schwendeman–Wahle–Kapila's Godunov-type scheme and Tokareva–Toro's HLLC scheme . The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions.« less

Local Equating Using the Rasch Model, the OPLM, and the 2PL IRT Model--or--What Is It Anyway if the Model Captures Everything There Is to Know about the Test Takers?

ERIC Educational Resources Information Center

von Davier, Matthias; González B., Jorge; von Davier, Alina A.

2013-01-01

Local equating (LE) is based on Lord's criterion of equity. It defines a family of true transformations that aim at the ideal of equitable equating. van der Linden (this issue) offers a detailed discussion of common issues in observed-score equating relative to this local approach. By assuming an underlying item response theory model, one of…

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

PubMed

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

Ideal Gas with a Varying (Negative Absolute) Temperature: an Alternative to Dark Energy?

NASA Astrophysics Data System (ADS)

Saha, Subhajit; Mondal, Anindita; Corda, Christian

2018-02-01

The present work is an attempt to investigate whether the evolutionary history of the Universe from the offset of inflation can be described by assuming the cosmic fluid to be an ideal gas with a specific gas constant but a varying negative absolute temperature (NAT). The motivation of this work is to search for an alternative to the "exotic" and "supernatural" dark energy (DE). In fact, the NAT works as an "effective quintessence" and there is need to deal neither with exotic matter like DE nor with modified gravity theories. For the sake of completeness, we release some clarifications on NATs in Section 3 of the paper.

A Generalized Fluid Formulation for Turbomachinery Computations

NASA Technical Reports Server (NTRS)

Merkle, Charles L.; Sankaran, Venkateswaran; Dorney, Daniel J.; Sondak, Douglas L.

2003-01-01

A generalized formulation of the equations of motion of an arbitrary fluid are developed for the purpose of defining a common iterative algorithm for computational procedures. The method makes use of the equations of motion in conservation form with separate pseudo-time derivatives used for defining the numerical flux for a Riemann solver and the convergence algorithm. The partial differential equations are complemented by an thermodynamic and caloric equations of state of a complexity necessary for describing the fluid. Representative solutions with a new code based on this general equation formulation are provided for three turbomachinery problems. The first uses air as a working fluid while the second uses gaseous oxygen in a regime in which real gas effects are of little importance. These nearly perfect gas computations provide a basis for comparing with existing perfect gas code computations. The third case is for the flow of liquid oxygen through a turbine where real gas effects are significant. Vortex shedding predictions with the LOX formulations reduce the discrepancy between perfect gas computations and experiment by approximately an order of magnitude, thereby verifying the real gas formulation as well as providing an effective case where its capabilities are necessary.

Susceptibility for thin ideal media and eating styles.

PubMed

Anschutz, Doeschka J; Engels, Rutger C M E; Van Strien, Tatjana

2008-03-01

This study examined the relations between susceptibility for thin ideal media and restrained, emotional and external eating, directly and indirectly through body dissatisfaction. Thin ideal media susceptibility, body dissatisfaction and eating styles were measured in a sample of 163 female students. Structural equation modelling was used for analyses, controlling for BMI. Higher susceptibility for thin ideal media was directly related to higher scores on all eating styles, and indirectly related to higher restrained and emotional eating through elevated levels of body dissatisfaction. So, thin ideal media susceptibility was not only related to restraint through body dissatisfaction, but also directly. Emotional eaters might be more vulnerable for negative affect, whereas external eaters might be more sensitive to external cues in general.

van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD.

PubMed

Vovchenko, Volodymyr; Gorenstein, Mark I; Stoecker, Horst

2017-05-05

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters a and b are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within the VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region T∼140-190  MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in the thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.

Fluctuations in non-ideal pion gas with dynamically fixed particle number

NASA Astrophysics Data System (ADS)

Kolomeitsev, E. E.; Voskresensky, D. N.

2018-05-01

We consider a non-ideal hot pion gas with the dynamically fixed number of particles in the model with the λϕ4 interaction. The effective Lagrangian for the description of such a system is obtained after dropping the terms responsible for the change of the total particle number. Reactions π+π- ↔π0π0, which determine the isospin balance of the medium, are permitted. Within the self-consistent Hartree approximation we compute the effective pion mass, thermodynamic characteristics of the system and the variance of the particle number at temperatures above the critical point of the induced Bose-Einstein condensation when the pion chemical potential reaches the value of the effective pion mass. We analyze conditions for the condensate formation in the process of thermalization of an initially non-equilibrium pion gas. The normalized variance of the particle number increases with a temperature decrease but remains finite in the critical point of the Bose-Einstein condensation. This is due to the non-perturbative account of the interaction and is in contrast to the ideal-gas case. In the kinetic regime of the condensate formation the variance is shown to stay finite also.

Spectral Analysis of Non-ideal MRI Modes: The Effect of Hall Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohandas, Gopakumar; Pessah, Martin E., E-mail: gopakumar@nbi.ku.dk, E-mail: mpessah@nbi.ku.dk

The effect of magnetic field diffusion on the stability of accretion disks is a problem that has attracted considerable interest of late. In particular, the Hall effect has the potential to bring about remarkable changes in the dynamical behavior of disks that are without parallel. In this paper, we conduct a systematic examination of the linear eigenmodes in a weakly magnetized differentially rotating gas with a special focus on Hall diffusion. We first develop a geometrical representation of the eigenmodes and provide a detailed quantitative description of the polarization properties of the oscillatory modes under the combined influence of themore » Coriolis and Hall effects. We also analyze the effects of magnetic diffusion on the structure of the unstable modes and derive analytical expressions for the kinetic and magnetic stresses and energy densities associated with the non-ideal magnetorotational instability (MRI). Our analysis explicitly demonstrates that, if the dissipative effects are relatively weak, the kinetic stresses and energies make up the dominant contribution to the total stress and energy density when the equilibrium angular momentum and magnetic field vectors are anti-parallel. This is in sharp contrast to what is observed in the case of the ideal or dissipative MRI. We conduct shearing box simulations and find very good agreement with the results derived from linear theory. Because the modes under consideration are also exact solutions of the nonlinear equations, the unconventional nature of the kinetic and magnetic stresses may have significant implications for the nonlinear evolution in some regions of protoplanetary disks.« less

Runaway electrons and ITER

NASA Astrophysics Data System (ADS)

Boozer, Allen H.

2017-05-01

The potential for damage, the magnitude of the extrapolation, and the importance of the atypical—incidents that occur once in a thousand shots—make theory and simulation essential for ensuring that relativistic runaway electrons will not prevent ITER from achieving its mission. Most of the theoretical literature on electron runaway assumes magnetic surfaces exist. ITER planning for the avoidance of halo and runaway currents is focused on massive-gas or shattered-pellet injection of impurities. In simulations of experiments, such injections lead to a rapid large-scale magnetic-surface breakup. Surface breakup, which is a magnetic reconnection, can occur on a quasi-ideal Alfvénic time scale when the resistance is sufficiently small. Nevertheless, the removal of the bulk of the poloidal flux, as in halo-current mitigation, is on a resistive time scale. The acceleration of electrons to relativistic energies requires the confinement of some tubes of magnetic flux within the plasma and a resistive time scale. The interpretation of experiments on existing tokamaks and their extrapolation to ITER should carefully distinguish confined versus unconfined magnetic field lines and quasi-ideal versus resistive evolution. The separation of quasi-ideal from resistive evolution is extremely challenging numerically, but is greatly simplified by constraints of Maxwell’s equations, and in particular those associated with magnetic helicity. The physics of electron runaway along confined magnetic field lines is clarified by relations among the poloidal flux change required for an e-fold in the number of electrons, the energy distribution of the relativistic electrons, and the number of relativistic electron strikes that can be expected in a single disruption event.

Runaway electrons and ITER

DOE PAGES

Boozer, Allen H.

2017-03-24

The potential for damage, the magnitude of the extrapolation, and the importance of the atypical—incidents that occur once in a thousand shots—make theory and simulation essential for ensuring that relativistic runaway electrons will not prevent ITER from achieving its mission. Most of the theoretical literature on electron runaway assumes magnetic surfaces exist. ITER planning for the avoidance of halo and runaway currents is focused on massive gas or shattered-pellet injection of impurities. In simulations of experiments, such injections lead to a rapid large-scale magnetic-surface breakup. Surface breakup, which is a magnetic reconnection, can occur on a quasi-ideal Alfvénic time scalemore » when the resistance is sufficiently small. Nevertheless, the removal of the bulk of the poloidal flux, as in halo-current mitigation, is on a resistive time scale. The acceleration of electrons to relativistic energies requires the confinement of some tubes of magnetic flux within the plasma and a resistive time scale. The interpretation of experiments on existing tokamaks and their extrapolation to ITER should carefully distinguish confined versus unconfined magnetic field lines and quasi-ideal versus resistive evolution. The separation of quasi-ideal from resistive evolution is extremely challenging numerically, but is greatly simplified by constraints of Maxwell’s equations, and in particular those associated with magnetic helicity. Thus, the physics of electron runaway along confined magnetic field lines is clarified by relations among the poloidal flux change required for an e-fold in the number of electrons, the energy distribution of the relativistic electrons, and the number of relativistic electron strikes that can be expected in a single disruption event.« less

Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

NASA Technical Reports Server (NTRS)

Deyoung, J.

1980-01-01

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.

Vortex rings in Bose gas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belyaev, S. T., E-mail: bst@kiae.ru

2016-06-15

We consider excitations that exist, in addition to phonons, in the ideal Bose gas at zero temperature. These excitations are vortex rings whose energy spectrum is similar to the roton one in liquid helium.

Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics.

PubMed

Holm, Darryl D.

2002-06-01

We begin by placing the generalized Lagrangian mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged Lagrangian. This is the Lagrangian averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a Lagrangian trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the Eulerian mean fluid quantities by the fluctuating displacements of the Lagrangian trajectories in terms of their Eulerian second moments. The derivation of the glm equations uses the linearized relations between Eulerian and Lagrangian fluctuations, in the tradition of Lagrangian stability analysis for fluids. The glm derivation also uses the method of averaged Lagrangians, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the Lagrangian statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for Lagrangian averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.

A van der Waals Equation of State for a Dilute Boson Gas

ERIC Educational Resources Information Center

Deeney, F. A.; O'Leary, J. P.

2012-01-01

An equation of state of a system is a relationship that connects the thermodynamic variables of the system such as pressure and temperature. Such equations are well known for classical gases but less so for quantum systems. In this paper we develop a van der Waals equation of state for a dilute boson gas that may be used to explain the occurrence…

Unsteady combustion of solid propellants

NASA Astrophysics Data System (ADS)

Chung, T. J.; Kim, P. K.

The oscillatory motions of all field variables (pressure, temperature, velocity, density, and fuel fractions) in the flame zone of solid propellant rocket motors are calculated using the finite element method. The Arrhenius law with a single step forward chemical reaction is used. Effects of radiative heat transfer, impressed arbitrary acoustic wave incidence, and idealized mean flow velocities are also investigated. Boundary conditions are derived at the solid-gas interfaces and at the flame edges which are implemented via Lagrange multipliers. Perturbation expansions of all governing conservation equations up to and including the second order are carried out so that nonlinear oscillations may be accommodated. All excited frequencies are calculated by means of eigenvalue analyses, and the combustion response functions corresponding to these frequencies are determined. It is shown that the use of isoparametric finite elements, Gaussian quadrature integration, and the Lagrange multiplier boundary matrix scheme offers a convenient approach to two-dimensional calculations.

Forced canonical thermalization in a hadronic transport approach at high density

NASA Astrophysics Data System (ADS)

Oliinychenko, Dmytro; Petersen, Hannah

2017-03-01

Hadronic transport approaches based on an effective solution of the relativistic Boltzmann equation are widely applied for the dynamical description of heavy ion reactions at low beam energies. At high densities, the assumption of binary interactions often used in hadronic transport approaches may not be applicable anymore. Therefore, we effectively simulate the high-density regime using the local forced canonical thermalization. This framework provides the opportunity to interpolate in a dynamical way between two different limits of kinetic theory: the dilute gas approximation and the ideal fluid case. This approach will be important for studies of the dynamical evolution of heavy ion collisions at low and intermediate energies as experimentally investigated at the beam energy scan program at RHIC, and in the future at FAIR and NICA. On the other hand, this new way of modeling hot and dense strongly interacting matter might be relevant for small systems at high energies (LHC and RHIC) as well.

Keyhole and weld shapes for plasma arc welding under normal and zero gravity

NASA Technical Reports Server (NTRS)

Keanini, R. G.; Rubinsky, B.

1990-01-01

A first order study of the interfacial (keyhole) shape between a penetrating argon plasma arc jet and a stationary liquid metal weld pool is presented. The interface is determined using the Young-Laplace equation by assuming that the plasma jet behaves as a one-dimensional ideal gas flow and by neglecting flow within the weld pool. The solution for the keyhole shape allows an approximate determination of the liquid-solid metal phase boundary location based on the assumption that the liquid melt is a stagnant thermal boundary layer. Parametric studies examine the effect of plasma mass flow rate, initial plasma enthalpy, liquid metal surface tension, and jet shear on weldment shape under both normal and zero gravity. Among the more important findings of this study is that keyhole and weld geometries are minimally affected by gravity, suggesting that data gathered under gravity can be used in planning in-space welding.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doebling, Scott William

This paper documents the escape of high explosive (HE) products problem. The problem, first presented by Fickett & Rivard, tests the implementation and numerical behavior of a high explosive detonation and energy release model and its interaction with an associated compressible hydrodynamics simulation code. The problem simulates the detonation of a finite-length, one-dimensional piece of HE that is driven by a piston from one end and adjacent to a void at the other end. The HE equation of state is modeled as a polytropic ideal gas. The HE detonation is assumed to be instantaneous with an infinitesimal reaction zone. Viamore » judicious selection of the material specific heat ratio, the problem has an exact solution with linear characteristics, enabling a straightforward calculation of the physical variables as a function of time and space. Lastly, implementation of the exact solution in the Python code ExactPack is discussed, as are verification cases for the exact solution code.« less

Structural characterization/correlation of calorimetric properties of coal fluids. First annual report, September 1, 1985-August 31, 1986

DOE Office of Scientific and Technical Information (OSTI.GOV)

Starling, K.E.; Mallinson, R.G.; Li, M.H.

The objective of this research is to examine the relationship between the calorimetric properties of coal liquids and their molecular functional group composition. Coal liquid samples which have had their calorimetric properties measured are characterized using proton NMR, ir and elemental analysis. These characterizations are then used in a chemical structural model to determine the composition of the coal liquid in terms of the important molecular functional groups. These functional groups are particularly important in determining the intramolecular based properties of a fluid, such as ideal gas heat capacities. Correlational frameworks for heat capacities will then be examined within anmore » existing equation of state methodology to determine an optimal correlation. Also, the optimal recipe for obtaining the characterization/chemical structure information and the sensitivity of the correlation to the characterization and structural model will be examined and determined. 7 refs.« less

Astrophysical Connections to Collapsing Radiative Shock Experiments

NASA Astrophysics Data System (ADS)

Reighard, A. B.; Hansen, J. F.; Bouquet, S.; Koenig, M.

2005-10-01

Radiative shocks occur in many high-energy density explosions, but prove difficult to create in laboratory experiments or to fully model with astrophysical codes. Low astrophysical densities combined with powerful explosions provide ideal conditions for producing radiative shocks. Here we describe an experiment significant to astrophysical shocks, which produces a driven, planar radiative shock in low density Xe gas. Including radiation effects precludes scaling experiments directly to astrophysical conditions via Euler equations, as can be done in purely hydrodynamic experiments. We use optical depth considerations to make comparisons between the driven shock in xenon and specific astrophysical phenomena. This planar shock may be subject to thin shell instabilities similar to those affecting the evolution of astrophysical shocks. This research was sponsored by the National Nuclear Security Administration under the Stewardship Science Academic Alliances program through DOE Research Grants DE-FG52-03NA00064, DE-FG53-2005-NA26014, and other grants and contracts.

Non-Ideal Compressible-Fluid Dynamics of Fast-Response Pressure Probes for Unsteady Flow Measurements in Turbomachinery

NASA Astrophysics Data System (ADS)

Gori, G.; Molesini, P.; Persico, G.; Guardone, A.

2017-03-01

The dynamic response of pressure probes for unsteady flow measurements in turbomachinery is investigated numerically for fluids operating in non-ideal thermodynamic conditions, which are relevant for e.g. Organic Rankine Cycles (ORC) and super-critical CO2 applications. The step response of a fast-response pressure probe is investigated numerically in order to assess the expected time response when operating in the non-ideal fluid regime. Numerical simulations are carried out exploiting the Non-Ideal Compressible Fluid-Dynamics (NICFD) solver embedded in the open-source fluid dynamics code SU2. The computational framework is assessed against available experimental data for air in dilute conditions. Then, polytropic ideal gas (PIG), i.e. constant specific heats, and Peng-Robinson Stryjek-Vera (PRSV) models are applied to simulate the flow field within the probe operating with siloxane fluid octamethyltrisiloxane (MDM). The step responses are found to depend mainly on the speed of sound of the working fluid, indicating that molecular complexity plays a major role in determining the promptness of the measurement devices. According to the PRSV model, non-ideal effects can increase the step response time with respect to the acoustic theory predictions. The fundamental derivative of gas-dynamic is confirmed to be the driving parameter for evaluating non-ideal thermodynamic effects related to the dynamic calibration of fast-response aerodynamic pressure probes.

Defining constants, equations, and abbreviated tables of the 1975 US Standard Atmosphere

NASA Technical Reports Server (NTRS)

Minzner, R. A.; Reber, C. A.; Jacchia, L. G.; Huang, F. T.; Cole, A. E.; Kantor, A. J.; Keneshea, T. J.; Zimmerman, S. P.; Forbes, J. M.

1976-01-01

The U.S. Standard Atmosphere, 1975 (COESA, 1975) is an idealized, steady-state representation of the earth's atmosphere from the surface of the earth to 1000-km altitude, as it is assumed to exist in a period of moderate solar activity. From 0 to 86 km, the atmospheric model is specified in terms of the hydrostatic equilibrium of a perfect gas, with that portion of the model from 0 to 51 geopotential kilometers being identical with that of the U.S. Standard Atmosphere, 1962 (COESA, 1962). Between 51 and 86 km, the defining temperature-height profile has been modified from that of the 1962 Standard to lower temperatures between 51 and 69.33 km, and to greater values between 69.33 and 86 km. Above 86 km, the model is defined in terms of quasi-dynamic considerations involving the vertical component of the flux of molecules of individual gas species. These conditions lead to the generation of independent number-density distributions of the major species, N2, O2, O, Ar, Ne, and H, consistent with observations. The detailed definitions of the model are presented along with graphs and abbreviated tables of the atmospheric properties of the 1975 Standard.

Recovery of burner acoustic source structure from far-field sound spectra

NASA Technical Reports Server (NTRS)

Mahan, J. R.; Jones, J. D.

1984-01-01

A method is presented that permits the thermal-acoustic efficiency spectrum in a long turbulent burner to be recovered from the corresponding far-field sound spectrum. An acoustic source/propagation model is used based on the perturbation solution of the equations describing the unsteady one-dimensional flow of an inviscid ideal gas with a distributed heat source. The technique is applied to a long cylindrical hydrogen-flame burner operating over power levels of 4.5-22.3 kW. The results show that the thermal-acoustic efficiency at a given frequency, defined as the fraction of the total burner power converted to acoustic energy at that frequency, is rather insensitive to burner power, having a maximum value on the order of 10 to the -4th at 150 Hz and rolling off steeply with increasing frequency. Evidence is presented that acoustic agitation of the flame at low frequencies enhances the mixing of the unburned fuel and air with the hot products of combustion. The paper establishes the potential of the technique as a useful tool for characterizing the acoustic source structure in any burner, such as a gas turbine combustor, for which a reasonable acoustic propagation model can be postulated.

Compression Shocks in Two-Dimensional Gas Flows

NASA Technical Reports Server (NTRS)

Busemann, A.

1949-01-01

The following are arguments on the compression shocks in gas flow start with a simplified representation of the results of the study made by Th. Meyer as published in the Forschungsheft 62 of the VDI, supplemented by several amplifications for the application.In the treatment of compression shocks, the equation of energy, the equation of continuity, the momentum equation, the equation of state of the particular gas, as well as the condition Of the second law of thermodynamics that no decrease of entropy is possible in an isolated system, must be taken into consideration. The result is that, in those cases where the sudden change of state according to the second law of thermodynamics is possible, there always occurs a compression of the gas which is uniquely determined by the other conditions.

[Effect of physical properties of respiratory gas on pneumotachographic measurement of ventilation in newborn infants].

PubMed

Foitzik, B; Schmalisch, G; Wauer, R R

1994-04-01

The measurement of ventilation in neonates has a number of specific characteristics; in contrast to lung function testing in adults, the inspiratory gas for neonates is often conditioned. In pneumotachographs (PNT) based on Hagen-Poiseuille's law, changes in physical characteristics of respiratory gas (temperature, humidity, pressure and oxygen fraction [FiO2]) produce a volume change as calculated with the ideal gas equation p*V/T = const; in addition, the viscosity of the gas is also changed, thus leading to measuring errors. In clinical practice, the effect of viscosity on volume measurement is often ignored. The accuracy of these empirical laws was investigated in a size 0 Fleisch-PNT using a flow-through technique and variously processed respiratory gas. Spontaneous breathing was simulated with the aid of a calibration syringe (20 ml) and a rate of 30 min-1. The largest change in viscosity (11.6% at 22 degrees C and dry gas) is found with an increase in FiO2 (21...100%). A rise in temperature from 24 to 35 degrees C (dry air) produced an increase in viscosity of 5.2%. An increase of humidity (0...90%, 35 degrees C) decreased the viscosity by 3%. A partial compensation of these viscosity errors is thus possible. Pressure change (0...50 mbar, under ambient conditions) caused no measurable viscosity error. With the exception of temperature, the measurements have shown good agreement between the measured volume measuring errors and those calculated from viscosity changes. If the respiratory gas differs from ambient air (e.g. elevated FiO2) or if the PNT is calibrated under BTPS conditions, changes in viscosity must not be neglected when performing accurate ventilation measurements. On the basis of the well-known physical laws of Dalton, Thiesen and Sutherland, a numerical correction of adequate accuracy is possible.

Biot-Gassmann theory for velocities of gas hydrate-bearing sediments

USGS Publications Warehouse

Lee, M.W.

2002-01-01

Elevated elastic velocities are a distinct physical property of gas hydrate-bearing sediments. A number of velocity models and equations (e.g., pore-filling model, cementation model, effective medium theories, weighted equations, and time-average equations) have been used to describe this effect. In particular, the weighted equation and effective medium theory predict reasonably well the elastic properties of unconsolidated gas hydrate-bearing sediments. A weakness of the weighted equation is its use of the empirical relationship of the time-average equation as one element of the equation. One drawback of the effective medium theory is its prediction of unreasonably higher shear-wave velocity at high porosities, so that the predicted velocity ratio does not agree well with the observed velocity ratio. To overcome these weaknesses, a method is proposed, based on Biot-Gassmann theories and assuming the formation velocity ratio (shear to compressional velocity) of an unconsolidated sediment is related to the velocity ratio of the matrix material of the formation and its porosity. Using the Biot coefficient calculated from either the weighted equation or from the effective medium theory, the proposed method accurately predicts the elastic properties of unconsolidated sediments with or without gas hydrate concentration. This method was applied to the observed velocities at the Mallik 2L-39 well, Mackenzie Delta, Canada.

On the hierarchy of partially invariant submodels of differential equations

NASA Astrophysics Data System (ADS)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

Variational principles for stochastic fluid dynamics

PubMed Central

Holm, Darryl D.

2015-01-01

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The paper proceeds by taking variations in the SVP to derive stochastic Stratonovich fluid equations; writing their Itô representation; and then investigating the properties of these stochastic fluid models in comparison with each other, and with the corresponding deterministic fluid models. The circulation properties of the stochastic Stratonovich fluid equations are found to closely mimic those of the deterministic ideal fluid models. As with deterministic ideal flows, motion along the stochastic Stratonovich paths also preserves the helicity of the vortex field lines in incompressible stochastic flows. However, these Stratonovich properties are not apparent in the equivalent Itô representation, because they are disguised by the quadratic covariation drift term arising in the Stratonovich to Itô transformation. This term is a geometric generalization of the quadratic covariation drift term already found for scalar densities in Stratonovich's famous 1966 paper. The paper also derives motion equations for two examples of stochastic geophysical fluid dynamics; namely, the Euler–Boussinesq and quasi-geostropic approximations. PMID:27547083

Detonation velocity in poorly mixed gas mixtures

NASA Astrophysics Data System (ADS)

Prokhorov, E. S.

2017-10-01

The technique for computation of the average velocity of plane detonation wave front in poorly mixed mixture of gaseous hydrocarbon fuel and oxygen is proposed. Here it is assumed that along the direction of detonation propagation the chemical composition of the mixture has periodic fluctuations caused, for example, by layered stratification of gas charge. The technique is based on the analysis of functional dependence of ideal (Chapman-Jouget) detonation velocity on mole fraction (with respect to molar concentration) of the fuel. It is shown that the average velocity of detonation can be significantly (by more than 10%) less than the velocity of ideal detonation. The dependence that permits to estimate the degree of mixing of gas mixture basing on the measurements of average detonation velocity is established.

Buoyancy instability of homologous implosions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, B. M.

2015-06-15

With this study, I consider the hydrodynamic stability of imploding ideal gases as an idealized model for inertial confinement fusion capsules, sonoluminescent bubbles and the gravitational collapse of astrophysical gases. For oblate modes (short-wavelength incompressive modes elongated in the direction of the mean flow), a second-order ordinary differential equation is derived that can be used to assess the stability of any time-dependent flow with planar, cylindrical or spherical symmetry. Upon further restricting the analysis to homologous flows, it is shown that a monatomic gas is governed by the Schwarzschild criterion for buoyant stability. Under buoyantly unstable conditions, both entropy andmore » vorticity fluctuations experience power-law growth in time, with a growth rate that depends upon mean flow gradients and, in the absence of dissipative effects, is independent of mode number. If the flow accelerates throughout the implosion, oblate modes amplify by a factor (2C) |N0|ti, where C is the convergence ratio of the implosion, N 0 is the initial buoyancy frequency and t i is the implosion time scale. If, instead, the implosion consists of a coasting phase followed by stagnation, oblate modes amplify by a factor exp(π|N 0|t s), where N 0 is the buoyancy frequency at stagnation and t s is the stagnation time scale. Even under stable conditions, vorticity fluctuations grow due to the conservation of angular momentum as the gas is compressed. For non-monatomic gases, this additional growth due to compression results in weak oscillatory growth under conditions that would otherwise be buoyantly stable; this over-stability is consistent with the conservation of wave action in the fluid frame. The above analytical results are verified by evolving the complete set of linear equations as an initial value problem, and it is demonstrated that oblate modes are the fastest-growing modes and that high mode numbers are required to reach this limit (Legendre mode ℓ ≳ 100 for spherical flows). Finally, comparisons are made with a Lagrangian hydrodynamics code, and it is found that a numerical resolution of ~30 zones per wavelength is required to capture these solutions accurately. This translates to an angular resolution of ~(12/ℓ)°, or ≲ 0.1° to resolve the fastest-growing modes.« less

The H-theorem and equation of state for kinetic model of imperfect gas

NASA Astrophysics Data System (ADS)

Bishaev, A. M.; Rikov, V. A.; Abgaryan, M. V.

2018-03-01

In the offered article, having used earlier constructed kinetic model for imperfect gas, the equation of state for such gas which takes place which is able in a thermodynamic equilibrium is received and also expression for critical temperature as functions is received from an interaction potential between molecules.

Non-ideal magnetohydrodynamics on a moving mesh

NASA Astrophysics Data System (ADS)

Marinacci, Federico; Vogelsberger, Mark; Kannan, Rahul; Mocz, Philip; Pakmor, Rüdiger; Springel, Volker

2018-05-01

In certain astrophysical systems, the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfvén waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.

Application of Stochastic and Deterministic Approaches to Modeling Interstellar Chemistry

NASA Astrophysics Data System (ADS)

Pei, Yezhe

This work is about simulations of interstellar chemistry using the deterministic rate equation (RE) method and the stochastic moment equation (ME) method. Primordial metal-poor interstellar medium (ISM) is of our interest and the socalled “Population-II” stars could have been formed in this environment during the “Epoch of Reionization” in the baby universe. We build a gas phase model using the RE scheme to describe the ionization-powered interstellar chemistry. We demonstrate that OH replaces CO as the most abundant metal-bearing molecule in such interstellar clouds of the early universe. Grain surface reactions play an important role in the studies of astrochemistry. But the lack of an accurate yet effective simulation method still presents a challenge, especially for large, practical gas-grain system. We develop a hybrid scheme of moment equations and rate equations (HMR) for large gas-grain network to model astrochemical reactions in the interstellar clouds. Specifically, we have used a large chemical gas-grain model, with stochastic moment equations to treat the surface chemistry and deterministic rate equations to treat the gas phase chemistry, to simulate astrochemical systems as of the ISM in the Milky Way, the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). We compare the results to those of pure rate equations and modified rate equations and present a discussion about how moment equations improve our theoretical modeling and how the abundances of the assorted species are changed by varied metallicity. We also model the observed composition of H2O, CO and CO2 ices toward Young Stellar Objects in the LMC and show that the HMR method gives a better match to the observation than the pure RE method.

Relaxation of the accelerating-gas boundary layer to the test-gas boundary layer on a flat plate in an expansion tube

NASA Technical Reports Server (NTRS)

Gupta, R. N.; Trimpi, R. L.

1973-01-01

An analytic investigation of the relaxation of the accelerating-gas boundary layer to the test-gas boundary layer over a flat plate mounted in an expansion tube has been conducted. In this treatment, nitrogen has been considered as the test gas and helium as the accelerating gas. The problem is analyzed in two conically similar limits: (1) when the time lag between the arrival of the shock and the interface at the leading edge of the plate is very large, and (2) when this time lag is negligible. The transient laminar boundary-layer equations of a perfect binary-gas mixture are taken as the flow governing equations. These coupled equations have been solved numerically by Gauss-Seidel line-relaxation method. The results predict the transient behavior as well as the time required for an all-helium accelerating-gas boundary layer to relax to an all-nitrogen boundary layer.

Time-dependent Processes in the Sheath Between the Heliospheric Termination Shock and the Heliopause

NASA Astrophysics Data System (ADS)

Pogorelov, N. V.; Borovikov, S. N.; Heerikhuisen, J.; Kim, T. K.; Zank, G. P.

2014-09-01

In this paper, we present the results of our numerical simulation of the solar wind (SW) interaction with the local interstellar medium (LISM). In particular, a solar cycle model based on Ulysses measurements allowed us to estimate the interrelationship between heliospheric asymmetries due to the action of the interstellar magnetic field and the decrease in the solar wind ram pressure. We evaluate the possibility to develop an improved approach to derive SW boundary conditions from interplanetary scintillation data. It is shown that solar cycle affects stability of the heliopause in a way favorable for the interpretation of Voyager 1 “early” penetration into the local interstellar medium. We also show that the heliotail is always a subject of violent Kelvin-Helmholtz instability, which ultimately should make the heliotail indistinguishable from the LISM. Numerical results are obtained with a Multi-Scale Fluid-Kinetic Simulation Suite (MS-FLUKSS), which is a package of numerical codes capable of performing adaptive mesh refinement simulations of complex plasma flows in the presence of discontinuities and charge exchange between ions and neutral atoms. The flow of the ionized component is described with the ideal MHD equations, while the transport of atoms is governed either by the Boltzmann equation or multiple Euler gas dynamics equations. We have enhanced the code with additional physical treatments for the transport of turbulence and acceleration of pickup ions in interplanetary space and at the termination shock.

Adiabatic Expansion of Electron Gas in a Magnetic Nozzle.

PubMed

Takahashi, Kazunori; Charles, Christine; Boswell, Rod; Ando, Akira

2018-01-26

A specially constructed experiment shows the near perfect adiabatic expansion of an ideal electron gas resulting in a polytropic index greater than 1.4, approaching the adiabatic value of 5/3, when removing electric fields from the system, while the polytropic index close to unity is observed when the electrons are trapped by the electric fields. The measurements were made on collisionless electrons in an argon plasma expanding in a magnetic nozzle. The collision lengths of all electron collision processes are greater than the scale length of the expansion, meaning the system cannot be in thermodynamic equilibrium, yet thermodynamic concepts can be used, with caution, in explaining the results. In particular, a Lorentz force, created by inhomogeneities in the radial plasma density, does work on the expanding magnetic field, reducing the internal energy of the electron gas that behaves as an adiabatically expanding ideal gas.

Adiabatic Expansion of Electron Gas in a Magnetic Nozzle

NASA Astrophysics Data System (ADS)

Takahashi, Kazunori; Charles, Christine; Boswell, Rod; Ando, Akira

2018-01-01

A specially constructed experiment shows the near perfect adiabatic expansion of an ideal electron gas resulting in a polytropic index greater than 1.4, approaching the adiabatic value of 5 /3 , when removing electric fields from the system, while the polytropic index close to unity is observed when the electrons are trapped by the electric fields. The measurements were made on collisionless electrons in an argon plasma expanding in a magnetic nozzle. The collision lengths of all electron collision processes are greater than the scale length of the expansion, meaning the system cannot be in thermodynamic equilibrium, yet thermodynamic concepts can be used, with caution, in explaining the results. In particular, a Lorentz force, created by inhomogeneities in the radial plasma density, does work on the expanding magnetic field, reducing the internal energy of the electron gas that behaves as an adiabatically expanding ideal gas.

78 FR 68161 - Greenhouse Gas Reporting Program: Final Amendments and Confidentiality Determinations for...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-13

... measurements corrected for temperature and non-ideal gas behavior). For gases with low volume consumption for... effect of that abatement system when using either the emission factors and calculation methods in 40 CFR...) basis. To develop the preliminary estimate, the reporter must use the gas consumption in the tools...

Articulated Multimedia Physics, Lesson 14, Gases, The Gas Laws, and Absolute Temperature.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

As the fourteenth lesson of the Articulated Multimedia Physics Course, instructional materials are presented in this study guide with relation to gases, gas laws, and absolute temperature. The topics are concerned with the kinetic theory of gases, thermometric scales, Charles' law, ideal gases, Boyle's law, absolute zero, and gas pressures. The…

An Ideal Molecular Sieve for Acetylene Removal from Ethylene with Record Selectivity and Productivity.

PubMed

Li, Bin; Cui, Xili; O'Nolan, Daniel; Wen, Hui-Min; Jiang, Mengdie; Krishna, Rajamani; Wu, Hui; Lin, Rui-Biao; Chen, Yu-Sheng; Yuan, Daqiang; Xing, Huabin; Zhou, Wei; Ren, Qilong; Qian, Guodong; Zaworotko, Michael J; Chen, Banglin

2017-12-01

Realization of ideal molecular sieves, in which the larger gas molecules are completely blocked without sacrificing high adsorption capacities of the preferred smaller gas molecules, can significantly reduce energy costs for gas separation and purification and thus facilitate a possible technological transformation from the traditional energy-intensive cryogenic distillation to the energy-efficient, adsorbent-based separation and purification in the future. Although extensive research endeavors are pursued to target ideal molecular sieves among diverse porous materials, over the past several decades, ideal molecular sieves for the separation and purification of light hydrocarbons are rarely realized. Herein, an ideal porous material, SIFSIX-14-Cu-i (also termed as UTSA-200), is reported with ultrafine tuning of pore size (3.4 Å) to effectively block ethylene (C 2 H 4 ) molecules but to take up a record-high amount of acetylene (C 2 H 2 , 58 cm 3 cm -3 under 0.01 bar and 298 K). The material therefore sets up new benchmarks for both the adsorption capacity and selectivity, and thus provides a record purification capacity for the removal of trace C 2 H 2 from C 2 H 4 with 1.18 mmol g -1 C 2 H 2 uptake capacity from a 1/99 C 2 H 2 /C 2 H 4 mixture to produce 99.9999% pure C 2 H 4 (much higher than the acceptable purity of 99.996% for polymer-grade C 2 H 4 ), as demonstrated by experimental breakthrough curves. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Rigorous investigation of the reduced density matrix for the ideal Bose gas in harmonic traps by a loop-gas-like approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beau, Mathieu, E-mail: mbeau@stp.dias.ie; Savoie, Baptiste, E-mail: baptiste.savoie@gmail.com

2014-05-15

In this paper, we rigorously investigate the reduced density matrix (RDM) associated to the ideal Bose gas in harmonic traps. We present a method based on a sum-decomposition of the RDM allowing to treat not only the isotropic trap, but also general anisotropic traps. When focusing on the isotropic trap, the method is analogous to the loop-gas approach developed by Mullin [“The loop-gas approach to Bose-Einstein condensation for trapped particles,” Am. J. Phys. 68(2), 120 (2000)]. Turning to the case of anisotropic traps, we examine the RDM for some anisotropic trap models corresponding to some quasi-1D and quasi-2D regimes. Formore » such models, we bring out an additional contribution in the local density of particles which arises from the mesoscopic loops. The close connection with the occurrence of generalized-Bose-Einstein condensation is discussed. Our loop-gas-like approach provides relevant information which can help guide numerical investigations on highly anisotropic systems based on the Path Integral Monte Carlo method.« less

Arterial blood gas reference values for sea level and an altitude of 1,400 meters.

PubMed

Crapo, R O; Jensen, R L; Hegewald, M; Tashkin, D P

1999-11-01

Blood gas measurements were collected on healthy lifetime nonsmokers at sea level (n = 96) and at an altitude of 1,400 meters (n = 243) to establish reference equations. At each study site, arterial blood samples were analyzed in duplicate on two separate blood gas analyzers and CO-oximeters. Arterial blood gas variables included Pa(O(2)), Pa(CO(2)), pH, and calculated alveolar-arterial PO(2) difference (AaPO(2)). CO-oximeter variables were Hb, COHb, MetHb, and Sa(O(2)). Subjects were 18 to 81 yr of age with 166 male and 173 female. Outlier data were excluded from multiple regression analysis, and reference equations were fitted to the data in two ways: (1) best fit using linear, squared, and cross-product terms; (2) simple equations, including only the variables that explained at least 3% of the variance. Two sets of equations were created: (1) using only the sea level data and (2) using the combined data with barometric pressure as an independent variable. Comparisons with earlier studies revealed small but significant differences; the decline in Pa(O(2)) with age at each altitude was consistent with most previous studies. At sea level, the equation that included barometric pressure predicted Pa(O(2)) slightly better than the sea level specific equation. The inclusion of barometric pressure in the equations allows better prediction of blood gas reference values at sea level and at altitudes as high as 1,400 meters.

Asymptotic research of transonic gas flows

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Tamarova, Yuliya A.

2017-12-01

The article is dedicated to the development asymptotic theory of gas flowing at speed next to sound velocity, particularly of gas transonic flows, i.e. the flows, containing both, subsonic and supersonic areas. The main issue, when styding such flows, are nonlinearity and combined type of equations, describing the transonic flow. Based on asymptotic nonlinear equation obtained in the article, the gas transonic flows is studied, considering transverse disturbance with respect to the main flow. The asymptotic conditions at shock-wave front and conditions on the streamlined surface are found. Moreover, the equation of sound surface and asymptotic formula defining the pressure are recorded. Several exact particular solutions of such equation are given, and their application to solve several tasks of transonic aerodynamics is indicated. Specifically, the polynomial form solution describing gas axisymmetric flows in Laval nozzles with constant acceleration in direction of the nozzle's axis and flow swirling is obtained. The solutions describing the unsteady flow along the channels between spinning surfaces are presented. The asymptotic equation is obtained, describing the flow, appearing during non-separated and separated flow past, closely approximated to cylindrical one. Specific solutions are given, based on which the examples of steady flow are formed.

Idealized cultural beliefs about gender: implications for mental health.

PubMed

Mahalingam, Ramaswami; Jackson, Benita

2007-12-01

In this paper, we examined the relationship between culture-specific ideals (chastity, masculinity, caste beliefs) and self-esteem, shame and depression using an idealized cultural model proposed by Mahalingam (2006, In: Mahalingam R (ed) Cultural psychology of immigrants. Lawrence Erlbaum, Mahwah, NJ, pp 1-14). Participants were from communities with a history of extreme male-biased sex ratios in Tamilnadu, India (N = 785). We hypothesized a dual-process model of self-appraisals suggesting that achieving idealized cultural identities would increase both self-esteem and shame, with the latter leading to depression, even after controlling for key covariates. We tested this using structural equation modeling. The proposed idealized cultural identities model had an excellent fit (CFI = 0.99); the effect of idealized identities on self-esteem, shame and depression differed by gender. Idealized beliefs about gender relate to psychological well-being in gender specific ways in extreme son preference communities. We discuss implications of these findings for future research and community-based interventions.

Numerical Simulations of Turbulent Molecular Clouds Regulated by Radiation Feedback Forces. II. Radiation-Gas Interactions and Outflows

NASA Astrophysics Data System (ADS)

Raskutti, Sudhir; Ostriker, Eve C.; Skinner, M. Aaron

2017-12-01

Momentum deposition by radiation pressure from young, massive stars may help to destroy molecular clouds and unbind stellar clusters by driving large-scale outflows. We extend our previous numerical radiation hydrodynamic study of turbulent star-forming clouds to analyze the detailed interaction between non-ionizing UV radiation and the cloud material. Our simulations trace the evolution of gas and star particles through self-gravitating collapse, star formation, and cloud destruction via radiation-driven outflows. These models are idealized in that we include only radiation feedback and adopt an isothermal equation of state. Turbulence creates a structure of dense filaments and large holes through which radiation escapes, such that only ˜50% of the radiation is (cumulatively) absorbed by the end of star formation. The surface density distribution of gas by mass as seen by the central cluster is roughly lognormal with {σ }{ln{{Σ }}}=1.3{--}1.7, similar to the externally projected surface density distribution. This allows low surface density regions to be driven outwards to nearly 10 times their initial escape speed {v}{esc}. Although the velocity distribution of outflows is broadened by the lognormal surface density distribution, the overall efficiency of momentum injection to the gas cloud is reduced because much of the radiation escapes. The mean outflow velocity is approximately twice the escape speed from the initial cloud radius. Our results are also informative for understanding galactic-scale wind driving by radiation, in particular, the relationship between velocity and surface density for individual outflow structures and the resulting velocity and mass distributions arising from turbulent sources.

Transport equations for low-energy solar particles in evolving interplanetary magnetic fields

NASA Technical Reports Server (NTRS)

Ng, C. K.

1988-01-01

Two new forms of a simplified Fokker-Planck equation are derived for the transport of low-energy solar energetic particles in an evolving interplanetary magnetic field, carried by a variable radial solar wind. An idealized solution suggests that the 'invariant' anisotropy direction reported by Allum et al. (1974) may be explained within the conventional theoretical framework. The equations may be used to relate studies of solar particle propagation to solar wind transients, and vice versa.

Thermal engineering research. [Runge-Kutta investigation of gas flow inside multilayer insulation system for rocket booster fuel tanks

NASA Technical Reports Server (NTRS)

Shih, C. C.

1973-01-01

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

Analytical treatment of gas flows through multilayer insulation, project 1

NASA Technical Reports Server (NTRS)

Lin, J. T.

1972-01-01

A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.

An analytical coarse-graining method which preserves the free energy, structural correlations, and thermodynamic state of polymer melts from the atomistic to the mesoscale.

PubMed

McCarty, J; Clark, A J; Copperman, J; Guenza, M G

2014-05-28

Structural and thermodynamic consistency of coarse-graining models across multiple length scales is essential for the predictive role of multi-scale modeling and molecular dynamic simulations that use mesoscale descriptions. Our approach is a coarse-grained model based on integral equation theory, which can represent polymer chains at variable levels of chemical details. The model is analytical and depends on molecular and thermodynamic parameters of the system under study, as well as on the direct correlation function in the k → 0 limit, c0. A numerical solution to the PRISM integral equations is used to determine c0, by adjusting the value of the effective hard sphere diameter, dHS, to agree with the predicted equation of state. This single quantity parameterizes the coarse-grained potential, which is used to perform mesoscale simulations that are directly compared with atomistic-level simulations of the same system. We test our coarse-graining formalism by comparing structural correlations, isothermal compressibility, equation of state, Helmholtz and Gibbs free energies, and potential energy and entropy using both united atom and coarse-grained descriptions. We find quantitative agreement between the analytical formalism for the thermodynamic properties, and the results of Molecular Dynamics simulations, independent of the chosen level of representation. In the mesoscale description, the potential energy of the soft-particle interaction becomes a free energy in the coarse-grained coordinates which preserves the excess free energy from an ideal gas across all levels of description. The structural consistency between the united-atom and mesoscale descriptions means the relative entropy between descriptions has been minimized without any variational optimization parameters. The approach is general and applicable to any polymeric system in different thermodynamic conditions.

Quantum-mechanical engines working with an ideal gas with a finite number of particles confined in a power-law trap

NASA Astrophysics Data System (ADS)

Wang, Jianhui; Ma, Yongli; He, Jizhou

2015-07-01

Based on quantum thermodynamic processes, we make a quantum-mechanical (QM) extension of the typical heat engine cycles, such as the Carnot, Brayton, Otto, Diesel cycles, etc., with no introduction of the concept of temperature. When these QM engine cycles are implemented by an ideal gas confined in an arbitrary power-law trap, a relation between the quantum adiabatic exponent and trap exponent is found. The differences and similarities between the efficiency of a given QM engine cycle and its classical counterpart are revealed and discussed.

Investigation of Bose Condensation in Ideal Bose Gas Trapped under Generic Power Law Potential in d Dimension

NASA Astrophysics Data System (ADS)

Mehedi Faruk, Mir; Sazzad Hossain, Md.; Muktadir Rahman, Md.

2016-02-01

The changes in characteristics of Bose condensation of ideal Bose gas due to an external generic power law potential U=\\sumi=1dci\\vert xi/ai\\vertni are studied carefully. Detailed calculation of Kim et al. (J. Phys. Condens. Matter 11 (1999) 10269) yielded the hierarchy of condensation transitions with changing fractional dimensionality. In this manuscript, some theorems regarding specific heat at constant volume CV are presented. Careful examination of these theorems reveal the existence of hidden hierarchy of the condensation transition in trapped systems as well.

A proof of the Biswas-Mitra-Bhattacharyya conjecture for the ideal quantum gas trapped under the generic power law potential U=\\sum\

NASA Astrophysics Data System (ADS)

Mehedi Faruk, Mir; Muktadir Rahman, Md

2016-03-01

The well known relation for ideal classical gas $\\Delta \\epsilon^2=kT^2 C_V$ which does not remain valid for quantum system is revisited. A new connection is established between energy fluctuation and specific heat for quantum gases, valid in the classical limit and the degenerate quantum regime as well. Most importantly the proposed Biswas-Mitra-Bhattacharyya (BMB) conjecture (Biswas $et.$ $al.$, J. Stat. Mech. P03013, 2015.) relating hump in energy fluctuation and discontinuity of specific heat is proved and precised in this manuscript.

Speed of sound and ideal-gas heat capacity of freon R-236ea

NASA Astrophysics Data System (ADS)

Komarov, S. G.; Gruzdev, V. A.; Stankus, S. V.

2008-09-01

Speed of sound in the gaseous freon R-236ea with the purity of 99.68 mol. % has been measured by the method of ultrasonic interferometer in the range from 263 to 423 K and at pressures from 17 kPA to 4.2 MPa. Errors of temperature, pressure, and speed of sound measurement were estimated to be within +/- 20 mK, ± 1.5 kPa, and ±(0.1+0.2) % respectively. Temperature dependence of ideal-gas heat capacity of R-236ea has been calculated on the basis of the obtained data.

Probability theory for 3-layer remote sensing in ideal gas law environment.

PubMed

Ben-David, Avishai; Davidson, Charles E

2013-08-26

We extend the probability model for 3-layer radiative transfer [Opt. Express 20, 10004 (2012)] to ideal gas conditions where a correlation exists between transmission and temperature of each of the 3 layers. The effect on the probability density function for the at-sensor radiances is surprisingly small, and thus the added complexity of addressing the correlation can be avoided. The small overall effect is due to (a) small perturbations by the correlation on variance population parameters and (b) cancellation of perturbation terms that appear with opposite signs in the model moment expressions.

Generalized hydrodynamic reductions of the kinetic equation for a soliton gas

NASA Astrophysics Data System (ADS)

Pavlov, M. V.; Taranov, V. B.; El, G. A.

2012-05-01

We derive generalized multiflow hydrodynamic reductions of the nonlocal kinetic equation for a soliton gas and investigate their structure. These reductions not only provide further insight into the properties of the new kinetic equation but also could prove to be representatives of a novel class of integrable systems of hydrodynamic type beyond the conventional semi-Hamiltonian framework.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

A Hybrid Method of Moment Equations and Rate Equations to Modeling Gas-Grain Chemistry

NASA Astrophysics Data System (ADS)

Pei, Y.; Herbst, E.

2011-05-01

Grain surfaces play a crucial role in catalyzing many important chemical reactions in the interstellar medium (ISM). The deterministic rate equation (RE) method has often been used to simulate the surface chemistry. But this method becomes inaccurate when the number of reacting particles per grain is typically less than one, which can occur in the ISM. In this condition, stochastic approaches such as the master equations are adopted. However, these methods have mostly been constrained to small chemical networks due to the large amounts of processor time and computer power required. In this study, we present a hybrid method consisting of the moment equation approximation to the stochastic master equation approach and deterministic rate equations to treat a gas-grain model of homogeneous cold cloud cores with time-independent physical conditions. In this model, we use the standard OSU gas phase network (version OSU2006V3) which involves 458 gas phase species and more than 4000 reactions, and treat it by deterministic rate equations. A medium-sized surface reaction network which consists of 21 species and 19 reactions accounts for the productions of stable molecules such as H_2O, CO, CO_2, H_2CO, CH_3OH, NH_3 and CH_4. These surface reactions are treated by a hybrid method of moment equations (Barzel & Biham 2007) and rate equations: when the abundance of a surface species is lower than a specific threshold, say one per grain, we use the ``stochastic" moment equations to simulate the evolution; when its abundance goes above this threshold, we use the rate equations. A continuity technique is utilized to secure a smooth transition between these two methods. We have run chemical simulations for a time up to 10^8 yr at three temperatures: 10 K, 15 K, and 20 K. The results will be compared with those generated from (1) a completely deterministic model that uses rate equations for both gas phase and grain surface chemistry, (2) the method of modified rate equations (Garrod 2008), which partially takes into account the stochastic effect for surface reactions, and (3) the master equation approach solved using a Monte Carlo technique. At 10 K and standard grain sizes, our model results agree well with the above three methods, while discrepancies appear at higher temperatures and smaller grain sizes.

Calculation of heat flux through a wall containing a cavity: Comparison of several models

NASA Astrophysics Data System (ADS)

Park, J. E.; Kirkpatrick, J. R.; Tunstall, J. N.; Childs, K. W.

1986-02-01

This paper describes the calculation of the heat transfer through the standard stud wall structure of a residential building. The wall cavity contains no insulation. Results from five test cases are presented. The first four represent progressively more complicated approximations to the heat transfer through and within a hollow wall structure. The fifth adds the model components necessary to severely inhibit the radiative energy transport across the empty cavity. Flow within the wall cavity is calculated from the Navier-Stokes equations and the energy conservation equation for an ideal gas using an improvement to the Implicit-Compressible Eulerian (ICE) algorithm of Harlow and Amsden. An algorithm is described to efficiently couple the fluid flow calculations to the radiation-conduction model for the solid portions of the system. Results indicate that conduction through still plates contributes less than 2% of the total heat transferred through a composite wall. All of the other elements (conduction through wall board, sheathing, and siding; convection from siding and wallboard to am bients; and radiation across the wall cavity) are required to accurately predict the heat transfer through a wall. Addition of a foil liner on one inner surface of the wall cavity reduces the total heat transferred by almost 50%.

Astrophysical fluid dynamics

NASA Astrophysics Data System (ADS)

Ogilvie, Gordon I.

2016-06-01

> These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is `frozen in' to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

Kinetic modeling of non-ideal explosives with CHEETAH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fried, L E; Howard, W M; Souers, P C

1998-08-06

We report an implementation of the Wood-Kirkwood kinetic detonation model based on multi-species equations of state and multiple reaction rate laws. Finite rate laws are used for the slowest chemical reactions. Other reactions are given infinite rates and are kept in constant thermodynamic equilibrium. We model a wide range of ideal and non-ideal composite energetic materials. We find that we can replicate experimental detonation velocities to within a few per cent, while obtaining good agreement with estimated reaction zone lengths. The detonation velocity as a function of charge radius is also correctly reproduced.

Ideal hydrodynamics and elliptic flow at CERN Super Proton Synchrotron (SPS) energies: Importance of the initial conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petersen, Hannah; Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main; Bleicher, Marcus

2009-05-15

The elliptic flow excitation function calculated in a full (3+1) dimensional hybrid Boltzmann approach with an intermediate hydrodynamic stage for heavy ion reactions from GSI Schwerionen Synchrotron to the highest CERN Super Proton Synchrotron (SPS) energies is discussed in the context of the experimental data. In this study, we employ a hadron gas equation of state to investigate the differences in the dynamics and viscosity effects. The specific event-by-event setup with initial conditions and freeze-out from a nonequilibrium transport model allows for a direct comparison between ideal fluid dynamics and transport simulations. At higher SPS energies, where the pure transportmore » calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. In contrast to previous studies within pure hydrodynamics, the more realistic initial conditions employed here and the inclusion of a sequential final state hadronic decoupling provides results that are in line with the experimental data almost over the whole energy range from E{sub lab}=2-160A GeV. Thus, this new approach leads to a substantially different shape of the v{sub 2}/{epsilon} scaling curve as a function of (1/SdN{sub ch}/dy) in line with the experimental data compared to previous ideal hydrodynamic calculations. This hints at a strong influence of the initial conditions for the hydrodynamic evolution on the finally observed v{sub 2} values, thus questioning the standard interpretation that the hydrodynamic limit is only reached at BNL Relativistic Heavy Ion Collider energies.« less

Reduced viscosity interpreted for fluid/gas mixtures

NASA Technical Reports Server (NTRS)

Lewis, D. H.

1981-01-01

Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.

Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

The fully implicit ablation and thermal response code simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid.This work describes new modeling capabilities that are added to a special version of code. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Two groups of parametric studies of the phenolic impregnated carbon ablator are performed. In the first group, an Orion flight environment for a proposed lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results indicate that the presence of chemical nonequilibrium pyrolysis gas flow does not significantly alter the in-depth thermal response performance predicted using the chemical equilibrium gas model.

Multiscale Numerical Methods for Non-Equilibrium Plasma

DTIC Science & Technology

2015-08-01

current paper reports on the implementation of a numerical solver on the Graphic Processing Units (GPUs) to model reactive gas mixtures with detailed...Governing equations The flow ismodeled as amixture of gas specieswhile neglecting viscous effects. The chemical reactions taken place between the gas ...components are to be modeled in great detail. The set of the Euler equations for a reactive gas mixture can be written as: ∂Q ∂t + ∇ · F̄ = Ω̇ (1) where Q

Numerical solution of Boltzmann tranport equation for TEA CO 2 laser having nitrogen-lean gas mixtures to predict laser characteristics and gas lifetime

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Khare, Jai; Nath, A. K.

2007-02-01

Selective laser isotope separation by TEA CO 2 laser often needs short tail-free pulses. Using laser mixtures having very little nitrogen almost tail free laser pulses can be generated. The laser pulse characteristics and its gas lifetime is an important issue for long-term laser operation. Boltzmann transport equation is therefore solved numerically for TEA CO 2 laser gas mixtures having very little nitrogen to predict electron energy distribution function (EEDF). The distribution function is used to calculate various excitation and dissociation rate of CO 2 to predict laser pulse characteristics and laser gas lifetime, respectively. Laser rate equations have been solved with the calculated excitation rates for numerically evaluated discharge current and voltage profiles to calculate laser pulse shape. The calculated laser pulse shape and duration are in good agreement with the measured laser characteristics. The gas lifetime is estimated by integrating the equation governing the dissociation of CO 2. An experimental study of gas lifetime was carried out using quadrapole mass analyzer for such mixtures to estimate the O 2 being produced due to dissociation of CO 2 in the pulse discharge. The theoretically calculated O 2 concentration in the laser gas mixture matches with experimentally observed value. In the present TEA CO 2 laser system, for stable discharge the O 2 concentration should be below 0.2%.

On the Equipartition of Kinetic Energy in an Ideal Gas Mixture

ERIC Educational Resources Information Center

Peliti, L.

2007-01-01

A refinement of an argument due to Maxwell for the equipartition of translational kinetic energy in a mixture of ideal gases with different masses is proposed. The argument is elementary, yet it may work as an illustration of the role of symmetry and independence postulates in kinetic theory. (Contains 1 figure.)

The Heat Capacity of Ideal Gases

ERIC Educational Resources Information Center

Scott, Robert L.

2006-01-01

The heat capacity of an ideal gas has been shown to be calculable directly by statistical mechanics if the energies of the quantum states are known. However, unless one makes careful calculations, it is not easy for a student to understand the qualitative results. Why there are maxima (and occasionally minima) in heat capacity-temperature curves…

The Role of Multiple Representations in the Understanding of Ideal Gas Problems

ERIC Educational Resources Information Center

Madden, Sean P.; Jones, Loretta L.; Rahm, Jrene

2011-01-01

This study examined the representational competence of students as they solved problems dealing with the temperature-pressure relationship for ideal gases. Seven students enrolled in a first-semester general chemistry course and two advanced undergraduate science majors participated in the study. The written work and transcripts from videotaped…

Solubility of 3-Caffeoylquinic Acid in Different Solvents at 291-340 K

NASA Astrophysics Data System (ADS)

Wang, Y. T.; Zhang, C. L.; Cheng, X. L.; Zhao, J. H.; Wang, L. C.

2017-12-01

Using a laser monitoring observation technique the solubilities of 3-caffeoylquinic acid in pure solvents, water, methanol, ethanol, 1-propanol, 1-butanol, and two mixed solvents, methanol + water, ethanol + water have been determined at temperature range from 291-340 K. The experimental data were correlated by the modified Apelblat equation, λ h equation, and ideal model. The calculated solubilities were turned out very consistent with the experimental results, and the modified Apelblat equation shows the best agreement.

Dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages. [equations of motion

NASA Technical Reports Server (NTRS)

Likins, P. W.

1974-01-01

Equations of motion are derived for use in simulating a spacecraft or other complex electromechanical system amenable to idealization as a set of hinge-connected rigid bodies of tree topology, with rigid axisymmetric rotors and nonrigid appendages attached to each rigid body in the set. In conjunction with a previously published report on finite-element appendage vibration equations, this report provides a complete minimum-dimension formulation suitable for generic programming for digital computer numerical integration.

Pseudo-critical point in anomalous phase diagrams of simple plasma models

NASA Astrophysics Data System (ADS)

Chigvintsev, A. Yu; Iosilevskiy, I. L.; Noginova, L. Yu

2016-11-01

Anomalous phase diagrams in subclass of simplified (“non-associative”) Coulomb models is under discussion. The common feature of this subclass is absence on definition of individual correlations for charges of opposite sign. It is e.g. modified OCP of ions on uniformly compressible background of ideal Fermi-gas of electrons OCP(∼), or a superposition of two non-ideal OCP(∼) models of ions and electrons etc. In contrast to the ordinary OCP model on non-compressible (“rigid”) background OCP(#) two new phase transitions with upper critical point, boiling and sublimation, appear in OCP(∼) phase diagram in addition to the well-known Wigner crystallization. The point is that the topology of phase diagram in OCP(∼) becomes anomalous at high enough value of ionic charge number Z. Namely, the only one unified crystal- fluid phase transition without critical point exists as continuous superposition of melting and sublimation in OCP(∼) at the interval (Z 1 < Z < Z 2). The most remarkable is appearance of pseudo-critical points at both boundary values Z = Z 1 ≈ 35.5 and Z = Z 2 ≈ 40.0. It should be stressed that critical isotherm is exactly cubic in both these pseudo-critical points. In this study we have improved our previous calculations and utilized more complicated model components equation of state provided by Chabrier and Potekhin (1998 Phys. Rev. E 58 4941).

Dissipative dark matter halos: The steady state solution. II.

NASA Astrophysics Data System (ADS)

Foot, R.

2018-05-01

Within the mirror dark matter model and dissipative dark matter models in general, halos around galaxies with active star formation (including spirals and gas-rich dwarfs) are dynamical: they expand and contract in response to heating and cooling processes. Ordinary type II supernovae (SNe) can provide the dominant heat source, which is possible if kinetic mixing interaction exists with strength ɛ ˜10-9- 10-10 . Dissipative dark matter halos can be modeled as a fluid governed by Euler's equations. Around sufficiently isolated and unperturbed galaxies the halo can relax to a steady state configuration, where heating and cooling rates locally balance and hydrostatic equilibrium prevails. These steady state conditions can be solved to derive the physical properties, including the halo density and temperature profiles, for model galaxies. Here, we consider idealized spherically symmetric galaxies within the mirror dark particle model, as in our earlier paper [Phys. Rev. D 97, 043012 (2018), 10.1103/PhysRevD.97.043012], but we assume that the local halo heating in the SN vicinity dominates over radiative sources. With this assumption, physically interesting steady state solutions arise which we compute for a representative range of model galaxies. The end result is a rather simple description of the dark matter halo around idealized spherically symmetric systems, characterized in principle by only one parameter, with physical properties that closely resemble the empirical properties of disk galaxies.

Modeling the release, spreading, and burning of LNG, LPG, and gasoline on water.

PubMed

Johnson, David W; Cornwell, John B

2007-02-20

Current interest in the shipment of liquefied natural gas (LNG) has renewed the debate about the safety of shipping large volumes of flammable fuels. The size of a spreading pool following a release of LNG from an LNG tank ship has been the subject of numerous papers and studies dating back to the mid-1970s. Several papers have presented idealized views of how the LNG would be released and spread across a quiescent water surface. There is a considerable amount of publicly available material describing these idealized releases, but little discussion of how other flammable fuels would behave if released from similar sized ships. The purpose of this paper is to determine whether the models currently available from the United States Federal Energy Regulatory Commission (FERC) can be used to simulate the release, spreading, vaporization, and pool fire impacts for materials other than LNG, and if so, identify which material-specific parameters are required. The review of the basic equations and principles in FERC's LNG release, spreading, and burning models did not reveal a critical fault that would prevent their use in evaluating the consequences of other flammable fluid releases. With the correct physical data, the models can be used with the same level of confidence for materials such as LPG and gasoline as they are for LNG.

Hydrodynamic flow of ions and atoms in partially ionized plasmas.

PubMed

Nemirovsky, R A; Fredkin, D R; Ron, A

2002-12-01

We have derived the hydrodynamic equations of motion for a partially ionized plasma, when the ionized component and the neutral components have different flow velocities and kinetic temperatures. Starting from the kinetic equations for a gas of ions and a gas of atoms we have considered various processes of encounters between the two species: self-collisions, interspecies collisions, ionization, recombination, and charge exchange. Our results were obtained by developing a general approach for the hydrodynamics of a gas in a binary mixture, in particular when the components drift with respect to each other. This was applied to a partially ionized plasma, when the neutral-species gas and the charged-species gas have separate velocities. We have further suggested a generalized version of the relaxation time approximation and obtained the contributions of the interspecies encounters to the transport equations.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Three-dimensional time-dependent computer modeling of the electrothermal atomizers for analytical spectrometry

NASA Astrophysics Data System (ADS)

Tsivilskiy, I. V.; Nagulin, K. Yu.; Gilmutdinov, A. Kh.

2016-02-01

A full three-dimensional nonstationary numerical model of graphite electrothermal atomizers of various types is developed. The model is based on solution of a heat equation within solid walls of the atomizer with a radiative heat transfer and numerical solution of a full set of Navier-Stokes equations with an energy equation for a gas. Governing equations for the behavior of a discrete phase, i.e., atomic particles suspended in a gas (including gas-phase processes of evaporation and condensation), are derived from the formal equations molecular kinetics by numerical solution of the Hertz-Langmuir equation. The following atomizers test the model: a Varian standard heated electrothermal vaporizer (ETV), a Perkin Elmer standard THGA transversely heated graphite tube with integrated platform (THGA), and the original double-stage tube-helix atomizer (DSTHA). The experimental verification of computer calculations is carried out by a method of shadow spectral visualization of the spatial distributions of atomic and molecular vapors in an analytical space of an atomizer.

The Role of Sign in Students' Modeling of Scalar Equations

ERIC Educational Resources Information Center

Hayes, Kate; Wittmann, Michael C.

2010-01-01

Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way…

On thermodynamical inconsistency of isotherm equations: Gibbs's thermodynamics.

PubMed

Tóth, József

2003-06-01

It has been proven that all isotherm equations which include the expression 1-Theta contradict the exact Gibbs thermodynamics. These contradictions have been discussed in detail in the case of the Langmuir (L) equation applied to gas/solid (G/S), solid/liquid (S/L), and gas/liquid (G/L) interfaces. In G/S adsorption the L equation can theoretically be applied only at low equilibrium pressures on condition that vg > vs . vg is the molar volume of the adsorbed amount in the gas phase and vs is the same in the Gibbs phase. In S/L and G/L adsorption the L equation is practically applicable only in the domain of very low concentrations. The cause of these contradictions (inconsistencies) is that Gibbs thermodynamics takes excess adsorbed amounts into account; however, the L and other isotherm equations calculate with the absolute adsorbed amount. The two amounts may be practically equal to each other when the limiting conditions mentioned above are fulfilled. It is also discussed how these inconsistent isotherm equations can be transformed into consistent ones.

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

PubMed

Gu, Xiao-Jun; Emerson, David R

2014-06-01

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

NASA Technical Reports Server (NTRS)

Xu, Kun

1999-01-01

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Inverse-dispersion technique for assessing lagoon gas emissions

USDA-ARS?s Scientific Manuscript database

Measuring gas emissions from treatment lagoons and storage ponds poses challenging conditions for existing micrometeorological techniques because of non-ideal wind conditions, such as those induced by trees and crops surrounding the lagoons, and lagoons with dimensions too small to establish equilib...

Accuracy of lagoon gas emissions using an inverse dispersion method

USDA-ARS?s Scientific Manuscript database

Measuring gas emissions from treatment lagoons and storage ponds poses challenging conditions for existing micrometeorological techniques because of non-ideal wind conditions. These include those induced by trees and crops surrounding the lagoons, and lagoons with dimensions too small to establish ...

Computer program determines gas flow rates in piping systems

NASA Technical Reports Server (NTRS)

Franke, R.

1966-01-01

Computer program calculates the steady state flow characteristics of an ideal compressible gas in a complex piping system. The program calculates the stagnation and total temperature, static and total pressure, loss factor, and forces on each element in the piping system.

Engineering Test Report Paint Waste Reduction Fluidized Bed Process Demonstration at Letterkenny Army Depot Chambersburg, Pennsylvania

DTIC Science & Technology

1991-07-01

predicted by equation using actual chart response obtained from each calibration gas response. (Concentration of cal. gas,l Calibration error, % span • ppm...Analyzer predicted by cali- Col. gas Chart divisions equation* bration Cylinder conc., error,** Drift,***INo. ppm or % Pretest Posttest Pretest Posttest...2m ~J * Correlation coef. * qgq’jq **Analyzer ca.error, % spn (Cal. gas conc. conc. predicted ) x 1003 cal spanSpan value Acceptable limit x ɚ% of

Isotope Separation in Concurrent Gas Centrifuges

NASA Astrophysics Data System (ADS)

Bogovalov, S. V.; Borman, V. D.

An analytical equation defining separative power of an optimized concurrent gas centrifuge is obtained for an arbitrary binary mixture of isotopes. In the case of the uranium isotopes the equation gives δU= 12.7(V/700 m/s)2(300 K/T)L, kg SWU/yr, where L and V are the length and linear velocity of the rotor of the gas centrifuge, T is the temperature. This formula well agrees with an empirical separative power of counter current gas centrifuges.

Theoretical study on some plasma parameters and thermophysical properties of various gas mixtures in gas-discharge lasers

NASA Astrophysics Data System (ADS)

Temelkov, K. A.; Slaveeva, S. I.; Fedchenko, Yu I.; Chernogorova, T. P.

2018-03-01

Using the well-known Wassiljewa equation and a new simple method, the thermal conductivities of various 2- and 3-component gas mixtures were calculated and compared under gas-discharge conditions optimal for two prospective lasers excited in a nanosecond pulsed longitudinal discharge. By solving the non-stationary heat-conduction equation for electrons, a 2D numerical model was also developed for determination of the radial and temporal dependences of the electron temperature Te (r, t).