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Results for “adiabatic approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

A Physical Relationship Between Electron-Proton Temperature Equilibration and Mach Number in Fast Collisionless Shocks

The analysis of Balmer-dominated optical spectra from nonradiative (adiabatic) SNRs has shown that the ratio of the electron to proton temperature at the blast wave is close to unity at v(s) approximate or smaller than 400 km s(-1) but declines sharply down to the minimum value of m(e) /m(p) dictated by the jump conditions at shock speeds exceeding 2000 km s(-1). We propose a physical model for the heating of electrons and ions in non-cosmic-ray-dominated, strong shocks (v(s) 400 km s(-1)) wherein the electrons are heated by lower hybrid waves immediately ahead of the shock front. These waves arise naturally from the cosmic ray pressure gradient upstream from the shock. Our model predicts a nearly constant level of electron heating over a wide range of shock speeds, producing a relationship (T(e)/T(p))sub 0 proportional to v(-2/s) (proportional to M(-2)) that is fully consistent with the observations.

SNR(ONRADIATIVE SUPERNOVA REMNANTS)↗
NASA NTRS1974

Quasi-linear theory via the cumulant expansion approach

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

Jones, F. C.↗
NASA NTRS2017

Viscous Three-Dimensional Simulation of Flow in an Axial Low Pressure Compressor at Engine Icing Operating Points

Viscous three-dimensional simulations of the Honeywell ALF502R-5 low pressure compressor (sometimes called a booster) using the NASA Glenn code GlennHT have been carried out. A total of ten simulations were produced. Five operating points are investigated, with each point run with two different wall thermal conditions. These operating points are at, or near, points where engine icing has been determined to be likely. In the future, the results of this study will be used for further analysis such as predicting collection efficiency of ice particles and ice growth rates at various locations in the compressor. A mixing plane boundary condition is used between each blade row, resulting in convergence to steady state within each blade row. The k-omega turbulence model of Wilcox, combined with viscous grid spacing near the wall on the order of one, is used to resolve the turbulent boundary layers. For each of the operating points, heat transfer coefficients are generated on the blades and walls. The heat transfer coefficients are produced by running the operating point with two different wall thermal conditions and then solving simultaneously for the heat transfer coefficient and adiabatic wall temperature at each point. Average Nusselt numbers are calculated for the most relevant surfaces. The values are seen to scale with Reynolds number to approximately a power of 0.7. Additionally, images of surface distribution of Nusselt number are presented. Qualitative comparison between the five operating points show that there is relatively little change in the character of the distribution. The dominant observed effect is that of an overall scaling, which is expected due to Reynolds number differences. One interesting aspect about the Nusselt number distribution is observed on the casing (outer diameter) downstream of the exit guide vanes (EGVs). The Nusselt number is relatively high between the pairs of EGVs, with two lower troughs downstream of each EGV trailing edge. This is of particular interest since rather complex ice shapes have been observed in that region.

compressor↗
NASA NTRS1996

Experimental Constraints on the Origin of Lunar High-Ti Ultramafic Glasses

Phase equilibria and dissolution rate experiments are used to develop a petrogenetic model for the high-Ti lunar ultramafic glasses. Near-liquidus phase relations of the Apollo 14 black glass, the most Ti-rich lunar ultramafic glass, are determined to 2.2-GPa. The liquidus is saturated with Cr-spinel at 1-atm, olivine between approximately 0.5- and 1.5-GPa, and low-Ca pyroxene + Cr-spinel above 1.5-GPa. Ilmenite does not crystallize near the liquidus and implies that high-Ti ultramafic glasses are not produced by melting of an ilmenite-saturated source. We infer that high-Ti ultramafic magmas are derived from low-Ti ultramafic parent magmas by assimilation of ilmenite +/- clinopyroxene +/- urKREEP +/- pigeonite in the shallow lunar interior. Heat is provided by adiabatic ascent of the low-Ti ultramafic primary magmas from the deeper lunar interior and crystallization of olivine during assimilation. The assimilation reaction is modeled by mass balance and requires that ilmenite and high-Ca pyroxene are assimilated in a approximately 3:1 ratio, a much higher ratio than the proportion in which these minerals are thought to exist in the lunar interior. In an effort to understand the kinetic controls on this reaction, the dissolution of ilmenite is examined experimentally in both low- and high-Ti lunar magmas. We find that ilmenite dissolves incongruently to Cr-spinel and a high-Ti melt. The dissolution reaction proceeds by a diffusion-controlled mechanism. An assimilation model for the origin of high-Ti melts is developed that leaves the magma ocean cumulates in their initial stratigraphic positions and obviates source hybridization models that require lunar overturn.

Wagner, T. P.↗
NASA NTRS1993

A generalized version of the Rankine-Hugoniot relations including ionization, dissociation and related phenomena

For purposes of computing shocks in stellars atmospheres and winds we have developed a generalized version of the Rankine-Hugoniot relations including ionization, dissociation, radiation and related phenomena such as excitation, rotation and vibration of molecules. The new equations are given in analytical form. They are valid as long as the internal energy E, the total pressure P, and the first adiabatic coefficient gamma(sub 1) can be evaluated. However, we have not treated shock structures. In the case of non-LTE we have to employ an approximation for gamma(sub 1) because in that case no definition exists. Our new version of the Rankine-Hugoniot relations can easily be used for many purposes including ab-initio modeling. In our derivation we introduce a parameter gamma(sub H), which is definded as the ratio of the enthalpy H (sometimes called heat function w) to the internal energy E (sometimes called U). Using this parameter we solve the equations for changing mu and (d(natural log P)/d(natural log rho))(sub ad) identically equal to gamma(sub 1) on both sides of the shock. Both gamma(sub H) and gamma(sub 1), and also mu are functions of pressure P and temperature T. We present: (1) the derivation, (2) examples of gamma(sub 1) (P,T) and gamma(sub H) (P,T) which include/exclude ionization and radiation, and (3) as an example the differences in post-shock parameters as function of the pre-shock temperature for the case with ionization and without radiation.

Nieuwenhuijzen, H.↗
NASA NTRS1994

Modulating terrestrial impacts from Oort cloud comets by the adiabatically changing galactic tides

Time modulation of the flux of new Jupiter-dominated Oort cloud comets is the subject of interest here. The major perturbation of these comets during the present epoch is due to the tidal field of the relatively smooth distribution of matter in the galactic disk. A secondary source of the near-parabolic comet flux are stars penetrating the inner Oort cloud and providing impulses that create brief comet showers. Substantial stellar-induced showers occur approximately every 100 m.y. Less frequent (but stronger) impulses due to giant molecular clouds can also perturb comets from the inner cloud. These occur on timescales of approximately equal to 500 m.y. In contrast to these infrequent stochastic shower phenomena is the continuously varying tidal-induced flux due to the galaxy. As the Sun orbits the galactic center it undergoes quasiharmonic motion about the galactic midplane, which is superimposed on the small eccentricity, near-Keplerian motion in the plane having epicycle period approximately equal to 150 m.y. In the process the galactic tidal field on the Sun/cloud system will vary causing a modulation of the observable Oort cloud flux. We have created a model of the galactic matter distribution as it affects the solar motion over a time interval ranging from 300 m.y. in the past to 100 m.y. into the future. As constraints on the disk's compact dark matter component we require consistency with the following: (1) the observed galactic rotation curve, (2) today's flux distribution of new comets, (3) the studies of K-giant distributions, and (4) the periodicity found in the terrestrial cratering record. The adiabatically varying galactic tidal torque is then determined and used to predict the time dependence of the flux. We find that a model in which approximately half the disk matter is compact is consistent with these constraints. Under such circumstances the peak-to-trough flux variation will be approx. equal to 5:1 with a full width of 9 m.y. This variability will manifest in the terrestrial cratering record and is consistent with the observed cratering periodicity, if over half of the impacts on Earth are caused by comets or asteroids that originate in the outer Oort cloud.

Matese, J. J.↗
NASA NTRS1989

The diffusion approximation and transport theory for cosmic rays in relativistic flows

Equations describing the transport of cosmic rays in relativistic flows in the diffusion approximation are obtained. The analysis is based on the zeroth, first, and second differential moment equations of the relativistic Boltzmann equation with a BGK collision term. A perturbation solution of the moment equations in the diffusion approximation yields both the co-moving frame particle current and viscous stresses. The resultant cosmic-ray continuity equation contains three readily recognized energy change terms: the adiabatic energy change term; the viscous shear energy change term; and a term proportional to the scalar product of the acceleration vector of the scattering frame and the heat flux.

Webb, G. M.↗
NASA NTRS1997

Lateral Shock of the R Aquarii Jet

The R Aqr jet was observed with the VLA B-configuration at two epochs separated by approximately 13.2 yr. Comparison of the resulting 6 cm continuum images show that the radio jet has undergone a lateral counterclockwise rotation of approximately 6 deg-12 deg on the plane of the sky. The model of jet parcels on independent trajectories is difficult to reconcile with these observations and leads us to consider a path-oriented jet (i.e., younger parcels follow the same path as older parcels). Comparison of the most recent radio image with a nearly contemporaneous HST/FOC ultraviolet image at approximately 2330 Angstroms suggests that the ultraviolet emission lies along the leading side of the rotating radio jet. In conjunction with a proper motion analysis of the jet material that yields empirical space-velocity and resulting acceleration-magnitude relationships as a function of distance from the central source, we evaluate the observational results in terms of a schematic model in which the jet emission consists of plane-parallel isothermal shocks along the leading edge of rotation. In such a radiating shock, the ultraviolet-emitting region is consistent with the adiabatic region in the form of a high-temperature, low-density sheath that surrounds the cooled postshock radio-emitting region. Within the context of the schematic model, we obtain the temperatures, densities, and pressures within the preshock, adiabatic, and postshock regions as a function of distance from the central source; the physical parameters so derived compare favorably to previously published estimates. We obtain a total jet mass of 3.1 x 10(exp -5) solar mass and an age of approximately 115 yr. We evaluate the model in the context of its density-boundary condition, its applicability to an episodic or quasi-continuous jet, and angular momentum considerations.

Hollis, J. M.↗
NASA NTRS1976

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.

Chandra, N.↗
NASA NTRS1980

Time-resolved imaging and spectral studies of an X-ray burst from the globular cluster Terzan

The first image of an X-ray burst was recorded with the HRI detector at the Einstein Observatory while observing the globular cluster Terzan 2. The burst was coincident with a persistent X-ray source located near the center of the cluster (thus confirming an earlier suggested identification) and reached a peak luminosity exceeding 5 x 10 to the 38th (d/10 kpc) squared. After a rapid rise to peak luminosity, a double-peaked spectral variation was observed over the next approximately 20 s with anticorrelated changes in the apparent emission region radius and temperature derived from blackbody (and modified blackbody) spectral fits. A shell or disk geometry, which undergoes adiabatic expansion and contraction, may be implied for the burst emission region. Alternatively, Comptonization is required. It is also shown that the peak burst luminosity must exceed the Eddington limit.

Grindlay, J. E.↗
DOE OSTI2025

A tale of two polarization paradoxes: The diamagnetic polarization paradox

An accurate calculation of the total polarization charge density in a plasma is essential for a self-consistent determination of the electric field. Yet, the “diamagnetic polarization paradox” refers to the fact that there is a paradoxical factor of 1/2 difference between the pressure-driven “diamagnetic polarization” density calculated using real space drift theory vs action-angle space guiding center and gyrokinetic theory that has not been explained before. Here, we show that both results can be made consistent with one another. Half of the diamagnetic polarization is due to the transformation from the guiding center density to the real space density. The other half is due to the fact that, within the drift kinetic ordering assumptions, the guiding center density should be expressed as the gyroaverage of the density in the limit of vanishing Larmor radius. A comprehensive review of polarization is presented to complete the derivation, and then we derive results that are required for the polarization calculations to agree. Expressions for the diamagnetic polarization density are given that are accurate to first order in amplitude and all orders in gyroradius within the gyrokinetic theory for a constant magnetic field. Applications to Maxwell–Boltzmann particle distribution functions (PDFs), including anisotropic temperature, are presented. Local invariants, like total energy and toroidal momentum, do not generate net polarization effects; the electric and thermodynamic polarizations must precisely cancel. In contrast, anisotropic dependence on the magnetic moment generates a net polarization proportional to the temperature anisotropy. Finally, when sources are present, the equilibrium PDF is approximately the ratio of two orbit averages.

adiabatic theory↗
NASA NTRS1994

Low-frequency modes and nonbarotropic effects in pseudo-Newtonian accretion disks

A recently developed formalism is used to reexamine the question of the existence of hydrodynamical modes that pulsate with very low frequencies in the inner regions of accretion disks. The formalism is valid in an exact sense for the adiabatic pulsations of rotating Newtonian fluids that are generally nonbarotropic (such as those with 'nonadiabatic temperature gradients,' for example), and hence its application in the present context represents an improvement over previous analyses that are more approximate. The formalism is applied to thin non-self-gravitating disks, with the gravitational potential of the central source modified in the usual way in order to simulate relativistic effects. In the barotropic limit, the analyses indicate that in many cases nearly Keplerian disks exhibit nonaxisymmetric modes of pulsation that are trapped in the inner disk regions, with pulsation periods much longer than the dynamical timescale. These results are similar to those of earlier calculations that assume disks pulsate without changing the temperature distribution. A method is developed for including lowest order nonbarotropic effects. Previous analyses have been incapable of accurately treating the nonbarotropic regime. The application of the present method to the low-frequency modes reveals that, due to unexpected cancellations among terms, the nonbarotropic correction to the pusation frequency omega is only of order tilde-omega(sub BV exp 2) omega, where tilde-omega(sub BV) is the appropriate dimensionless Brunt-Vaisala frequency. This correction is much smaller than the expected correction of order tilde-omega(sub BV) Omega, where Omega is the rotation angular velocity. The important conclusion drawn from this is that nonbarotropic corrections are generally small and hence that low-frequency modes persist into the nonbarotropic regime. For disk temperatures appropriate to X-ray emission, the adiabatic frequencies of trapped modes are of the same order as the frequencies associated with quasi-periodic oscillations (QPOs) of certain low-mass X-ray binaries and other X-ray sources. It is suggested that further consideration be given to the possiblity that modulation of emission processes by these modes can explain at least some of the QPO phenomena.

Ipser, James R.↗
NASA NTRS1975

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.

Chandra, N.↗
NASA NTRS1989

Why DA and DB white dwarfs do not show coronal activity and p-mode oscillations

The problems of nonradiative heating of outer atmospheric layers and p-mode oscillations in white dwarfs caused by acoustic waves generated in convective zones are discussed. These effects have been studied by calculating the cutoff periods for adiabatic and isothermal waves propagating in atmospheres of DA and DB stars with Teff greater than or equal 20,000 K and log g = 6-9. The obtained cutoff periods are approximately bounded by 0.01 and 40 sec for high- and low-gravity white dwarfs, respectively. Expected amplitudes of p-mode oscillations corresponding to trapped acoustic waves with small angular wave numbers are estimated, indicating that the amplitudes could be observed as Doppler shifts of spectral lines which might be detectable if adequate spectral resolution were available. The luminosity variations corresponding to these amplitudes are unlikely to be observable when all damping processes are accounted for. Results also indicate that the present theory of convection predicts some irregularities in the behavior of physical parameters.

Musielak, Z. E.↗
DOE OSTI2025

New Methods for Predicting Non-Born-Oppenheimer Chemistry

Current methods for modeling non-adiabatic molecular dynamics face fundamental limitations when treating geometric phase effects: quantum mechanical phenomena where nuclear wavepackets acquire phase shifts when encircling conical intersections. Existing approaches either neglect these effects entirely or rely on potential energy surfaces arising from the Born-Oppenheimer approximation, which introduce artificial singularities and can overestimate geometric phase contributions. This project developed a new theoretical framework based on exact factorization (XF) methods to overcome these limitations. We derived mathematical formulations for hybrid quantum-classical XF dynamics that selectively treat critical nuclear degrees of freedom quantum mechanically while propagating others classically. This approach addresses the computational intractability that has previously limited exact methods to toy systems. Key innovations include a new approach to systematically identifying nuclear coordinates requiring quantum treatment, as well as novel implementation strategies that interface with existing quantum chemistry codes. The project also developed a proof-of-concept code for treating Jahn-Teller systems and creation of educational materials on non-adiabatic dynamics geared at the graduate level. The theoretical framework developed will enable future systematically improvable calculations of nuclear quantum effects in realistic molecular systems, filling a critical gap in non-adiabatic dynamics methods. This foundation supports future development of predictive tools for designing energy-relevant photochemical processes where quantum coherence effects may be exploited to control reaction outcomes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
NASA NTRS1972

Application of the adiabatic-nuclei theory to vibrational excitation.

The adiabatic-nuclei theory is shown to be quantitatively applicable to vibrational excitation of diatomic molecules by electron impact. When the dependence of the fixed-nuclei phase shifts on internuclear separation is approximated by a two-term Taylor series, the resulting formulas are transparent and easily evaluated. Application to e-H2 excitation is made, phase-shift derivatives are estimated, and the theory is found to fit experimental data.

Faisal, F. H. M.↗
NASA NTRS1972

Computation of pressure effects of inert-gas mixtures on atomic line shapes.

Recent line-shape experiments on the absorption series of cesium pressurized by various concentration ratios of argon and helium provide an opportunity to study the additivity of perturber interactions. Calculations which assume additivity and which assume additive adiabatic collisions agree well with the reported data. The results suggest that a systematic study of such experiments using accurate digitized data can furnish criteria for the valid applications of the additivity approximation.

Jacobson, H. C.↗
NASA NTRS1994

Resonantly driven nonlinear density waves in protostellar disks

Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance, and that the propagation distance (and therefore the region of the disk to which angular momentum is redistributed) is set by the distance at which the wavelength becomes comparable to the disk thickness.

Yuan, Chi↗