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At least 595 records · Page 33

A new formulation of the conservation equations of fluid dynamics

The computation of time-dependent flows has inspired a new, higher-dimensional formulation of the conservation equations of fluid dynamics in which time is treated as a fourth coordinate. The formulation is derived for a constant-density flow, and then extended to a variable-density flow by introducing a fifth, fictitious coordinate. This new coordinate can also act as a source coordinate, so that external source terms can be included. The analysis is carried out for both incompressible, stratified flow, and compressible equilibrium flow. The results are then extended to non-equilibrium and magnetohydrodynamic flows. Several applications of the new formulation to the computation of time-dependent flows are discussed.

Vinokur, M.↗

Carbon dioxide catastrophes: Past and future menace

Carbon dioxide is important in its role as coupler of the terrestrial biosphere to inorganic chemical processes and as the principal greenhouse gas controlling Earth's surface temperature. The hypothesis that atmospheric CO2 levels have diminished with time, with the resulting cooling effect offsetting an increase in the solar constant, seems firmly established, and it is shown that feedback mechanisms exist which can maintain the terrestrial surface in a relatively narrow temperature range over geological time. Of the factors involved in such CO2 variation, the oceanic reservoir appears the most important. Surface waters are probably in approximate equilibrium with regard to CO2 exchange with the ambient atmosphere in most regions, but data from deep-ocean water sampling indicates that such waters are somewhat undersaturated in the sense that they would tend to absorb CO2 from the atmosphere if brought to the surface without change in composition or temperature. If major impacts into the ocean can result in loss of a substantial portion of the atmospheric CO2 reservoir, then any such future event could imperil the continuation of most higher forms of life on Earth. The most likely candidate for an inverse Nyos global event in previous Earth history is the Cretaceous-Tertiary terminal extinction event. The Cretaceous was characterized by warm, equable temperatures presumably indicative of relatively high CO2 levels and an intense greenhouse heating. Cooling of the oceans in absence of massive transfer of CO2 to the oceanic reservoir in itself would promote a condition of CO2 undersaturation in abyssal waters, and this is made even more extreme by the pattern of ocean water circulation. It is possible to envision a situation in which deep ocean waters were at least occasionally profoundly undersaturated with regard to CO2. Turnover of a major fraction of such an ocean would then remove, on a very short time scale, as much as 90 percent of the atmospheric CO2 inventory.

Baur, Mario E.↗

A rapid-pressure correlation representation consistent with the Taylor-Proudman theorem materially-frame-indifferent in the 2D limit

A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.

Ristorcelli, J. R.↗

Heliospheric Termination Shock Motion Due to Fluctuations in the Solar Wind Upstream Conditions: Spherically Symmetric Model

Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Ratkiewicz, R.↗

Impact of microstructure on elastic properties in the alloy Ti-42Al-8.5 Nb

The microstructure of a γ-TiAl alloy containing niobium undergoes continuous transformations during annealing at 550 °C. These take place within the α 2 -phase of lamellar (α 2 +γ) colonies. We have characterized these changes by transmission electron microscopy and made a correlation to the elastic constants determined by resonant ultrasonic spectroscopy during in-situ annealing at the same temperature. Further, the results show a continuous increase of the E-modulus. This can be attributed to elastic strains acting within α 2 lamellae as a result of lattice transformations. After 5000h, a thermodynamic equilibrium was established with equal fractions of α 2 -phase and O-phase that differ only in lattice symmetry and Nb content. Generally, the presence of O-phase should contribute to lower elastic moduli, however in the present case the evolving microstructural characteristics were responsible for the observed increase in the E-modulus.

36 MATERIALS SCIENCE↗

In-situ measurement of irradiation behavior in LiNbO 3

In-situ measurement of LiNbO 3 based surface acoustic wave (SAW) crystal resonator device under irradiation was demonstrated and used to characterize the impact of radiation on physical properties of this material. The resonant frequency of the SAW device was monitored as the output power of the reactor was varied. Upon step increase of the reactor power, a gradual shift in the device’s resonant frequency was observed. This frequency shift initially exhibits a linear growth and eventually reaches an equilibrium value proportional to the reactor power. The observed behavior can be attributed to two competing processes: increase of temperature due to gamma heating or accumulation of irradiation induced defects. In both cases, the response is attributed to changes in the physical properties of LiNbO 3 , particularly the elastic constants. This demonstrated ability to measure materials properties under irradiation is attractive for development of sensors and performing materials science under irradiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Determination of Thermal Expansion, Defect Formation Energy, and Defect-Induced Strain of α-U Via ab Initio Molecular Dynamics

Uranium (U) is often alloyed with molybdenum (Mo) or zirconium (Zr) in order to stabilize its high-temperature body-centered cubic phase for use in nuclear reactors. However, in all metallic fuel forms, the α phase of U remains in some fraction. This phase decomposition due to temperature or compositional variance can play an outsized role on fuel performance and microstructural evolution. Relatively little is known about fundamental point defect properties in α -U at non-zero temperatures, from either computational or experimental studies. This work performs the first thorough evaluation of the α phase of U via ab initio molecular dynamics (AIMD). A number of thermophysical properties are calculated as a function of temperature, including equilibrium lattice parameters, thermal expansion, and heat capacity. These results indicate a two-region behavior, with the transition at 400 K. The thermal expansion/contraction in the a / b direction occurs rapidly from 100 up to 400 K, after which a more linear and gradual change in the lattice constant takes place. The volumetric expansion matches experiments quantitatively, but the individual lattice constant expansion only matches experiments qualitatively. Point defect formation energies and induced lattice strains are also determined as a function of temperature, providing insight on defect populations and the fundamentals of irradiation growth in α -U. Interstitials induce significantly more strain than vacancies, and the nature of that strain is highly dependent on the individual lattice directions. The direction of point defect-induced lattice strain is contrary to the irradiation growth behavior of α -U. This work shows that isolated point defects cannot be the primary driving force responsible for the significant irradiation-induced growth of α -U observed experimentally.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The quiet time structure of energetic /35-560 keV/ radiation belt electrons

Detailed Explorer 45 observations of quiet time pitch angle distributions and equatorial radial profiles of energetic radiation belt electrons are presented. The observed pitch angle distributions in the slot region and the outer regions of the plasmasphere are found to agree with the values expected from resonant interactions with the plasmaspheric whistler mode wave band, and Coulomb collisions are found to be the dominant electron loss mechanism in the inner zone. The overall structure of quiet time radial profiles is shown to agree with the equilibrium structure expected to result from a balance between pitch angle scattering losses and radial diffusion from an outer zone source, and this agreement suggests that the dominant quiet time source and loss mechanisms have been correctly identified. Electron fluxes in the inner plasmasphere are found to remain nearly constant during the quiet periods due to their decoupling from magnetic activity variations in the outer plasmasphere.

Lyons, L. R.↗

Tables and charts of equilibrium thermodynamic properties of carbon dioxide for temperatures from 100 K to 25,000 K

Equilibrium thermodynamic properties for pure carbon dioxide are presented in tabulated and graphical form for temperatures from 100 K to 25,000 K and pressures from 40 mN/sq m to 1 GN/sq m. Properties include pressure, temperature, density, enthalpy, speed of sound, entropy, molecular weight ratio, specific heat at constant pressure, specific heat at constant volume, isentropic exponent, and species mole fractions.

Miller, C. G., III↗

Evolution of rotating interstellar clouds. II - The collapse of protostars of 1, 2, and 5 solar masses

Numerical calculations have been made for the early stages of collapse of axisymmetric rotating protostars of 1, 2, and 5 solar masses. The calculations employ a range of values of total angular momentum, as well as two types of initial density distribution. The effects of boundary conditions are tested by using constant volume and constant surface pressure with identical initial conditions. The principal result of the calculations is that, in all cases tried, the collapse leads to the formation of a ring structure in the interior of the cloud, with a local density minimum at the center of the cloud. The rings approach equilibrium with a structure consistent with that of previous analytic determinations, after which they undergo further gravitational collapse. The collapse of a two-solar-mass cloud, similar to that assumed by Cameron and Pine (1973), does not appear to lead to the equilibrium nebula these authors construct.

Black, D. C.↗

On the anticorrelation of the electric field and peak electron energy within an auroral arc

The present investigation is concerned with an example of a strongly anticorrelated electric field and particle precipitation, taking into account an application of an extended version of the model of Evans et al. (1977) to the data. A striking feature of the data reported is the high degree of anticorrelation between electric field strength and peak precipitating electron energy. A simple model consisting of a constant current traversing a region in which the conductivities increase in proportion to ionospheric energy deposition provides a qualitative explanation of the observations. However, when the effects of neutral winds, ionization transport, Hall currents, and arc motion, and the nonlinearity of the relationship between peak precipitating electron energy and equilibrium are considered, the conclusions become less clear.

Mallinckrodt, A. J.↗

Equilibrium carbon isotope fractionation factors of hydrocarbons: Semi-empirical force-field method

Here, we have calculated the reduced partition function ratios for carbon isotopes (β-factor) of 67 hydrocarbons (alkanes, alkenes, alkynes, cycloalkanes, and aromatics), including their 267 single-substituted isotopomers. The calculations were performed using the harmonic oscillator – rigid rotator model and the Urey / Bigeleisen-Mayer approach. Normal frequencies of molecular vibrations of the isotopologues were calculated from the molecular structures data and valence field force constants stored in the Light-handled Elucidation of Vibrations (LEV) database elaborated by Dr. Gribov and his colleagues in Russia. The LEV database is constructed from experimental spectroscopic and structural data by solving inverse problems of molecular vibrations. The LEV is internally consistent and the most comprehensive database available to date. The β-factor were calculated in the temperature range of 200–800 K with a 10 K step. Our calculations predict that the β-factors increase with an increasing number of C atoms within the same groups of hydrocarbons (e.g., alkanes). Our calculations also show a general descending order of 13 C enrichments among the different groups of hydrocarbons: cycloalkanes, aromatics, alkenes (double bonds) and isoalkanes, alkanes, alkynes (triple bonds). Position-specific, intramolecular isotope effects within hydrocarbons are determined by the β-factors of C in the different functional groups in the order: quaternary (C), tertiary (methine, CH), secondary (methylene, CH 2 ), primary (methyl, CH 3 ) and double bond (C=C), saturated bond (C - C), triple bond (HC≡). Our calculations on bulk and position-specific carbon isotope β-factors of the hydrocarbons, which are generally consistent with very limited ab initio calculations in the literature, are internally consistent and the most comprehensive to date for future applications to position-specific isotope geochemistry of hydrocarbons.

58 GEOSCIENCES↗

Nonlinear Reynolds stress model for turbulent shear flows

A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

Barton, J. Michael↗

The mass and speed dependence of meteor air plasma temperatures

The speed and mass dependence of meteor air plasma temperatures is perhaps the most important data needed to understand how small meteoroids chemically change the ambient atmosphere in their path and enrich the ablated meteoric organic matter with oxygen. Such chemistry can play an important role in creating prebiotic compounds. The excitation conditions in various air plasma emissions were measured from high-resolution optical spectra of Leonid storm meteors during NASA's Leonid Multi-Instrument Aircraft Campaign. This was the first time a sufficient number and range of temperature measurements were obtained to search for meteoroid mass and speed dependencies. We found slight increases in temperature with decreasing altitude, but otherwise nearly constant values for meteoroids with speeds between 35 and 72 km/s and masses between 10(-5) g and 1 g. We conclude that faster and more massive meteoroids produce a larger emission volume, but not a higher air plasma temperature. We speculate that the meteoric plasma may be in multiphase equilibrium with the ambient atmosphere, which could mean lower plasma temperatures in a CO(2)-rich early Earth atmosphere.

Temperature↗

Behavior of Langmuir Probes in Non-Equilibrium Plasmas

Langmuir probes are diagnostic tools used to determine electron temperature, number density, and plasma potential. Irving Langmuir first used an electrostatic probe in the 1920s to find these characteristics in ionized gases. Single, double, and triple Langmuir probes are commonly used in plasma diagnostics because of their relative simplicity. In the single probe, a swept voltage is applied between the probe tip and circuit common to acquire a waveform showing the collected current as a function of applied voltage. A double Langmuir probe consists of two tips, both inserted into the plasma, with a voltage applied between them. As this voltage is swept, a current-voltage characteristic is measured. In a triple probe three probe tips are electrically coupled to each other with constant non-swept voltages applied between each of the tips. The voltages are selected to represent three points on the single Langmuir probe I-V curve. Elimination of the voltage sweep makes it possible to measure time-varying plasma properties in transient plasmas. Triple Langmuir probe measurements have been widely employed for various types of plasmas, including pulsed and time-varying plasmas such as those seen in pulsed plasma thrusters (PPTs), dense plasma focus devices, plasma flows, and fusion experiments. The typical Langmuir probe analysis for determining electron temperature and number density of the plasma (for a single, double, or triple Langmuir probe) includes an assumption that the plasma is in thermal equilibrium. While the this assumption may be justified for some applications, it is unlikely that it is fully justifiable for pulsed and time-varying plasmas or for the entire time a plasma device is in use. In the present work, we model the responses of Langmuir probes as they are inserted into a range of simple equilibrium and non-equilibrium plasmas. We return to basic governing equations of probe current collection and compute the current to the probes for a distribution function consisting of two Maxwellian distributions with different temperatures (the two-temperature Maxwellian). A variation of this method is also employed, where one of the Maxwellians is offset from zero (in velocity space) to add a suprathermal beam of electrons to the tail of the main Maxwellian distribution (the bump-on-the-tail distribution function). For a range of parameters in these non-Maxwellian distributions, we compute the current collection to the probes. Comparing the distribution function that was assumed a priori with the plasma density and temperature one would infer when applying standard probe theory to analyze the collected currents serves to illustrate the effect a non- Maxwellian plasma would have on results interpreted using the equilibrium probe current collection theory, allowing us to state the magnitudes of these deviations as a function of the assumed distribution function properties.

Polzin, Kurt A.↗

Combined DSC/TGA Analysis to Rationalize the As-Sintered Microstructure in Binder Jet Additively Manufactured H13 Tool Steel

In this study, a combined DSC/TGA analysis has been used to rationalize the constant liquid channel width at higher sintering temperatures in H13 tool steel manufactured by binder jet additive manufacturing. Using enthalpy conservation along with coupled DSC + TGA analysis, the phase fractions of liquid and austenite phases during heating and cooling respectively were estimated. The estimates from the DSC/TGA analysis were compared with equilibrium phase fraction predictions from ThermoCalc. The resulting phase evolution was correlated to the as-sintered microstructure to rationalize the unexpected lack of change in liquid channel width at higher sintering temperatures.

Kannan, Rangasayee↗

Egg yolk as a model for gelation: From rheometry to flow physics

Egg yolks are an excellent model for studying sol-gel transitions, particularly the power law viscoelasticity that defines the critical point of gelation. However, prior studies lack comprehensive datasets and fail to visualize flow behavior linked to temperature and time-dependent linear and nonlinear rheology. Here, we present a detailed dataset characterizing egg yolk viscoelasticity across temperature, time, and forcing amplitude using oscillatory shear, step strain, step stress, and constant high strain rate. Novel protorheology visualizations link rheological properties with observable flow behavior. Our findings highlight the nuanced determination of the critical gel point, emphasizing observation timescale dependencies. We compare methods to identify critical temperatures for gelation, including power law viscoelasticity, moduli crossover, diverging zero-shear viscosity, and emerging equilibrium elastic modulus, while visualizing flow consequences near these transitions. Egg yolk is an accessible, realistic, and nontoxic material relevant to the physicist and the chef alike, making it ideal for understanding the rheology of critical gels. By integrating protorheology photos and videos with rigorous rheometric data, we deepen the understanding of critical gels, with broader impacts for studying other materials with sol-gel transitions.

Marsh, Maxwell C. [Department of Mechanical Scienc↗

Scale covariant gravitation. V - Kinetic theory. VI - Stellar structure and evolution

A scale covariant kinetic theory for particles and photons is developed. The mathematical framework of the theory is given by the tangent bundle of a Weyl manifold. The Liouville equation is derived, and solutions to corresponding equilibrium distributions are presented and shown to yield thermodynamic results identical to the ones obtained previously. The scale covariant theory is then used to derive results of interest to stellar structure and evolution. A radiative transfer equation is derived that can be used to study stellar evolution with a variable gravitational constant. In addition, it is shown that the sun's absolute luminosity scales as L approximately equal to GM/kappa, where kappa is the stellar opacity. Finally, a formula is derived for the age of globular clusters as a function of the gravitational constant using a previously derived expression for the absolute luminosity.

Hsieh, S.-H.↗