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Appendix to: Methodology for Creating Thermodynamic Tables for Application to Computation of Speed of Sound by the Global Reference Atmospheric Model (GRAM) Suite: Validation Testing

The primary report to which this document appends provides the background, methodology, and outputs for the development of constituent-specific tables of specific heats as functions of temperature and pressure. These tables are used by the GRAM Suite to compute speed of sound by a process detailed in the primary report. The current document details verification and validation testing that was performed on the contents and implementation of the output tables.

Speed of Sound↗

Thermodynamics of clathrate hydrate at low and high pressures with application to the outer solar system

The thermodynamic stability of clathrate hydrate is calculated to predict the formation conditions corresponding to a range of solar system parameters. The calculations were performed using the statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data concerning clathrate hydrate and its components. Dissociation pressures and partition functions (Langmuir constants) are predicted at low pressure for CO clathrate (hydrate) using the properties of chemicals similar to CO. It is argued that nonsolar but well constrained noble gas abundances may be measurable by the Galileo spacecraft in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances of the Jovian satellite Titan are predicted, assuming that most of the methane in Titan is accreted as clathrate. It is suggested that under thermodynamically appropriate conditions, complete clathration of water ice could have occurred in high-pressure nebulas around giant planets, but probably not in the outer solar nebula. The stability of clathrate in other pressure ranges is also discussed.

Lunine, J. I.↗

Non-solar noble gas abundances in the atmosphere of Jupiter

The thermodynamic stability of clathrate hydrate is calculated to predict the formation conditions corresponding to a range of solar system parameters. The calculations were performed using the statistical mechanical theory developed by van der Waals and Platteeuw (1959) and existing experimental data concerning clathrate hydrate and its components. Dissociation pressures and partition functions (Langmuir constants) are predicted at low pressure for CO clathrate (hydrate) using the properties of chemicals similar to CO. It is argued that nonsolar but well constrained noble gas abundances may be measurable by the Galileo spacecraft in the Jovian atmosphere if the observed carbon enhancement is due to bombardment of the atmosphere by clathrate-bearing planetesimals sometime after planetary formation. The noble gas abundances of the Jovian satellite Titan are predicted, assuming that most of the methane in Titan is accreted as clathrate. It is suggested that under thermodynamically appropriate conditions, complete clathration of water ice could have occurred in high-pressure nebulas around giant planets, but probably not in the outer solar nebula. The stability of clathrate in other pressure ranges is also discussed.

Lunine, Jonathan I.↗

Some physical and thermodynamic properties of rocket exhaust clouds measured with infrared scanners

Measurements using infrared scanners were made of the radiation from exhaust clouds from liquid- and solid-propellant rocket boosters. Field measurements from four launches were discussed. These measurements were intended to explore the physical and thermodynamic properties of these exhaust clouds during their formation and subsequent dispersion. Information was obtained concerning the initial cloud's buoyancy, the stabilized cloud's shape and trajectory, the cloud volume as a function of time, and it's initial and stabilized temperatures. Differences in radiation intensities at various wavelengths from ambient and stabilized exhaust clouds were investigated as a method of distinguishing between the two types of clouds. The infrared remote sensing method used can be used at night when visible range cameras are inadequate. Infrared scanning techniques developed in this project can be applied directly to natural clouds, clouds containing certain radionuclides, or clouds of industrial pollution.

Gomberg, R. I.↗

[Two-phase Interfaces in Weak External Fields]

Our aim has been that of understanding from first principles the behavior of two-phase interfaces in the absence of gravitational constraints. This is fundamental to our ability to deal with the fluid structures that abound in the real biological, chemical, and physical world. A substantial effort was mounted to determine how familiar hydrodynamic concepts have to be modified and interpreted to make them appropriate to the multi-level structure alluded to above. This was primarily in the context of the microscopic symmetric pressure tensor, which was, for the first time, expressed in the invaluable density functional format, and the used to follow the predictions of popular microscopic models of the energetics of interfacial systems. In the course of these investigations, the previous murky relation between pressure tensor and thermodynamics was completely clarified. The process of extending thermodynamic information to interfacial dynamics was initiated along two paths. One was from the viewpoint of an inertialess lattice gas, resulting in the surprising conclusion that at this level, all transport is governed by precisely the thermodynamic free energy, albeit with a non-trivial effective particle mobility. The other aimed at understanding the fashion in which slow macroscopic motions, accounted for by a time-varying microscopic energy, generate effective hydrodynamic parameters. By examining a solvable model system, it was found that all current procedures for doing so are deficient, and suitable alleviation suggested. The major effect of this project was to set the stage for the analysis of the substantial dynamical regimes in which extensive equilibrium information provides the dominant background. This produces a smooth junction to the models of Araki and Munakata, Giacomin and Lebowitz, and Oxtoby. It is also crucial to our understanding of the complex interfacial equilibrium configurations required for intermediate stages of two-phase separation, for which the "phase-field" techniques we have been developing are uniquely effective. And it puts us within striking range of the physical experiments that can provide incisive tests of the theoretical framework.

Percus, J. K.↗

A Simplified Model for an Evolving Protoplanetary Nebula

The dynamical evolution of the protoplanetary nebula is investigated using analytical solutions of the surface density transport equations. Constant and beta viscosity turbulence models are compared with a functional analytical model and the well-known alpha viscosity formulation. The beta viscosity model, heretofore used for steady-state disks, is shown to be a viable tool for separating dynamic and thermodynamic properties of an evolving disk.

Davis, Sanford S.↗

GUI for Computational Simulation of a Propellant Mixer

Control Panel is a computer program that generates a graphical user interface (GUI) for computational simulation of a rocket-test-stand propellant mixer in which gaseous hydrogen (GH2) is injected into flowing liquid hydrogen (LH2) to obtain a combined flow having desired thermodynamic properties. The GUI is used in conjunction with software that models the mixer as a system having three inputs (the positions of the GH2 and LH2 inlet valves and an outlet valve) and three outputs (the pressure inside the mixer and the outlet flow temperature and flow rate). The user can specify valve characteristics and thermodynamic properties of the input fluids via userfriendly dialog boxes. The user can enter temporally varying input values or temporally varying desired output values. The GUI provides (1) a set-point calculator function for determining fixed valve positions that yield desired output values and (2) simulation functions that predict the response of the mixer to variations in the properties of the LH2 and GH2 and manual- or feedback-control variations in valve positions. The GUI enables scheduling of a sequence of operations that includes switching from manual to feedback control when a certain event occurs.

Figueroa, Fernando↗

Thermodynamic efficiency of present types of internal combustion engines for aircraft

Report presents requirements of internal combustion engines suitable for aircraft. Topics include: (1) service requirements for aeronautic engines - power versus weight, reliability, and adaptability factors, (2) general characteristics of present aero engines, (3) aero engine processes and functions of parts versus power-weight ratio, reliability, and adaptability factors, and (4) general arrangement, form, proportions, and materials of aero parts - power-weight ratio, reliability, and adaptability.

Lucke, Charles E↗

Fractionation in the solar nebula - Condensation of yttrium and the rare earth elements

The condensation of Y and the rare earth elements (REE) from the solar nebula may be controlled by thermodynamic equilibrium between gas and condensed solids. Highly fractionated REE patterns may result if condensates are removed from the gas before condensation is complete. It is found that the fractionation is not a smooth function of REE ionic radius but varies in an extremely irregular pattern. Both Yb and Eu are predicted to be extremely depleted in the early condensate without the requirement of condensation in the divalent state. The model is discussed with respect to a highly fractionated pattern observed by Tanaka and Masuda (1973), in a pink Ca-Al-rich inclusion from the Allende meteorite and can account for the abundances of each REE determined. According to the model this inclusion represents a condensate from a previously fractionated gas rather than from a gas of solar composition. Before the condensation of this inclusion, an earlier condensate was formed and was removed from equilibrium with the gas.

Boynton, W. V.↗

The evolution of an impact-generated atmosphere

The minimum impact velocities and pressures required to form a primary H2O atmosphere during planetary accretion from chondritelike planetessimals are determined by means of shock wave and thermodynamic data for rock-forming and volatile-bearing minerals. Attenuation of impact-induced shock pressure is modelled to the extent that the amount of released water can be estimated as a function of projectile radius, impact velocity, weight fraction of target water, target porosity, and dehydration efficiency. The two primary processes considered are the impact release of water bound in such hydrous minerals as serpentine, and the subsequent reincorporation of free water by hydration of forsterite and enstatite. These processes are described in terms of model calculations for the accretion of the earth. It is concluded that the concept of dehydration efficiency is of dominant importance in determining the degree to which an accreting planet acquires an atmosphere during its formation.

Lange, M. A.↗

An empirical polytrope law for solar wind thermal electrons between 0.45 and 4.76 AU - Voyager 2 and Mariner 10

In this paper empirical evidence is presented that between 0.4 and 5 AU the thermal portion (but not all) of the solar wind electron population obeys a polytrope relation. It is also shown that this functional relationship is a member of a broader class of possible laws required of a steady state, fully ionized plasma whose proper frame electric field is dominated by the polarization electric field. The empirically determined, thermodynamically interesting value of the polytrope index (1.175) is virtually that predicted (1.16) by the theoretical considerations of Scudder and Olbert (1979). Strong, direct, empirical evidence for the nearly isothermal behavior of solar wind electrons as has been indirectly argued in the literature for some time is provided.

Sittler, E. C., Jr.↗

Computational and Experimental Investigation of Li-doped Ionic Liquid Electrolytes: [pyr14][tfsi], [pyr13][fsi], and [EMIM][BF4]

We employ molecular dynamics (MD) simulation and experiment to investigate the structure, thermodynamics, and transport of N-methyl-N-butylpyrrolidinium bis(trifluoromethylsufonyl)imide ([pyr14][TFSI]), N -methyl-N-propylpyrrolidinium bis(fluorosufonyl)imide ([pyr13][FSI]), and 1-ethyl-3-methylimidazolium boron tetrafluoride ([EMIM][BF4]), as a function of Li-salt mole fraction (0.05 xLi+ 0.33) and temperature (298 K T 393 K). Structurally, Li+ is shown to be solvated by three anion neigh- bors in [pyr14][TFSI] and four anion neighbors in both [pyr13][FSI] and [EMIM][BF4], and at all levels of xLi+ we find the presence of lithium aggregates. Pulsed field gradient spin-echo NMR measurements of diffusion and electrochemical impedance spectroscopy measurements of ionic conductivity are made for the neat ionic liquids as well as 0.5 molal solutions of Li-salt in the ionic liquids. Bulk ionic liquid properties (density, diffusion, viscosity, and ionic conductivity) are obtained with MD and show excellent agreement with experiment. While the diffusion exhibits a systematic decrease with increasing xLi+, the contribution of Li+ to ionic conductivity increases until reach- ing a saturation doping level of xLi+ 0.10. Comparatively, the Li+ conductivity of [pyr14][TFSI] is an order of magnitude lower than that of the other liquids, which range between 0.1-0.3 mScm. Our transport results also demonstrate the necessity of long MD simulation runs ( 200 ns) required to converge transport properties at room T. The differences in Li+ transport are reflected in the residence times of Li+ with the anions (Li), which are revealed to be much larger for [pyr14][TFSI] (up to 100 ns at the highest doping levels) than in either [EMIM][BF4] or [pyr13][FSI]. Finally, to comment on the relative kinetics of Li+ transport in each liquid, we find that while the net motion of Li+ with its solvation shell (vehicular) significantly contributes to net diffusion in all liquids, the importance of transport through anion exchange (hopping) increases at high xLi+ and in liquids with large anions.

electrolytes↗

Thermodynamic properties and crystallization kinetics at high liquid undercooling

The heat capacities of liquid and crystalline Au-Pb-Sb alloys in the glass-forming composition range were measured with droplet emulsion and bulk samples. Based on the measured C(sub p) data, the entropy, enthalpy, and Gibbs free energy functions of the eutectic, solid mixture, and undercooled liquid were determined as a function of undercooling and compared with theoretical predictions. The results indicate an isentropic temperature at 313 + or - 5 K, which agrees well with experimental data for the glass transition. A kinetics analysis of the nucleation undercooling response suggests that the proper choice for the Gibbs free energy change during crystallization is most important in analyzing the nucleation kinetics. By classical nucleation theory, the prefactors obtained, based on a variety of theoretical predictions for the driving force, can differ by six orders of magnitude. If the nucleation rates are extrapolated to high undercooling, the extrapolations based on measured heat capacity data show agreement, whereas the predicted nucleation rates are inconsistent with results from drop tower experiments. The implications for microg experiments are discussed.

Fecht, Hans J.↗

Revised Perturbation Statistics for the Global Scale Atmospheric Model

Magnitudes and scales of atmospheric perturbations about the monthly mean for the thermodynamic variables and wind components are presented by month at various latitudes. These perturbation statistics are a revision of the random perturbation data required for the global scale atmospheric model program and are from meteorological rocket network statistical summaries in the 22 to 65 km height range and NASA grenade and pitot tube data summaries in the region up to 90 km. The observed perturbations in the thermodynamic variables were adjusted to make them consistent with constraints required by the perfect gas law and the hydrostatic equation. Vertical scales were evaluated by Buell's depth of pressure system equation and from vertical structure function analysis. Tables of magnitudes and vertical scales are presented for each month at latitude 10, 30, 50, 70, and 90 degrees.

Justus, C. G.↗

Modal content of noise generated by a coaxial jet in a pipe

Noise generated by air flow through a coaxial obstruction in a long, straight pipe was investigated with concentration on the modal characteristics of the noise field inside the pipe and downstream of the restriction. Two measurement techniques were developed for separation of the noise into the acoustic duct modes. The instantaneous mode separation technique uses four microphones, equally spaced in the circumferential direction, at the same axial location. The time-averaged mode separation technique uses three microphones mounted at the same axial location. A matrix operation on time-averaged data produces the modal pressure levels. This technique requires the restrictive assumption that the acoustic modes are uncorrelated with each other. The measured modal pressure spectra were converted to modal power spectra and integrated over the frequency range 200-6000 Hz. The acoustic efficiency levels (acoustic power normalized by jet kinetic energy flow), when plotted vs. jet Mach number, showed a strong dependence on the ratio of restriction diameter to pipe diameter. The acoustic energy flow analyses based on the thermodynamic energy equation and on the results of Mohring both resulted in orthogonality properties for the eigenfunctions of the radial mode shape equation. These orthogonality relationships involve the eigenvalues and derivatives of the radial mode shape functions.

Kerschen, E. J.↗

CFD Modeling of Helium Pressurant Effects on Cryogenic Tank Pressure Rise Rates in Normal Gravity

A recently developed computational fluid dynamics modeling capability for cryogenic tanks is used to simulate both self-pressurization from external heating and also depressurization from thermodynamic vent operation. Axisymmetric models using a modified version of the commercially available FLOW-3D software are used to simulate actual physical tests. The models assume an incompressible liquid phase with density that is a function of temperature only. A fully compressible formulation is used for the ullage gas mixture that contains both condensable vapor and a noncondensable gas component. The tests, conducted at the NASA Marshall Space Flight Center, include both liquid hydrogen and nitrogen in tanks with ullage gas mixtures of each liquid's vapor and helium. Pressure and temperature predictions from the model are compared to sensor measurements from the tests and a good agreement is achieved. This further establishes the accuracy of the developed FLOW-3D based modeling approach for cryogenic systems.

Grayson, Gary↗

Investigation of Structure and Transport in Li-Doped Ionic Liquid Electrolytes: [pyr14][TFSI], [pyr13][FSI] and [EMIM][BF4]

Ionic liquid electrolytes have been proposed as a means of improving the safety and cycling behavior of advanced lithium batteries; however, the properties of these electrolytes under high lithium doping are poorly understood. Here, we employ both polarizable molecular dynamics simulation and experiment to investigate the structure, thermodynamics and transport of three potential electrolytes, N-methyl-Nbutylpyrrolidinium bis(trifluoromethylsufonyl)imide ([pyr14][TFSI]), N- methyl-Npropylpyrrolidinium bis(fluorosufonyl)imide ([pyr13][FSI]), and 1-ethyl-3-- methylimidazolium boron tetrafluoride ([EMIM][BF4]), as a function of Li-salt concentration and temperature. Structurally, Li(+) is shown to be solvated by three anion neighbors in [pyr14][TFSI] and four anion neighbors in both [pyr13][FSI] and [EMIM][BF4], and at all levels of x(sub Li) we find the presence of lithium aggregates. Furthermore, the computed density, diffusion, viscosity, and ionic conductivity show excellent agreement with experimental data. While the diffusion and viscosity exhibit a systematic decrease and increase, respectively, with increasing x(sub Li), the contribution of Li(+) to ionic conductivity increases until reaching a saturation doping level of x(sub Li) is approximately 0.10. Comparatively, the Li(+) conductivity of [pyr14][TFSI] is an order of magnitude lower than that of the other liquids, which range between 0.1 - 0.3 mS/cm. The differences in Li(+) transport are reflected in the residence times of Li(+) with the anions, which are revealed to be much larger for [pyr14][TFSI] (up to 100 ns at the highest doping levels) than in either [EMIM][BF4] or [pyr13][FSI]. Finally, we comment on the relative kinetics of Li(+) transport in each liquid and we present strong evidence for transport through anion exchange (hopping) as opposed to the net motion of Li(+) with its solvation shell (vehicular).

lithium batteries↗