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NASA NTRS1992

Phase-field model for isothermal phase transitions in binary alloys

A new phase field model is described which models isothermal phase transitions between ideal binary alloy solution phases. Equations are developed for the temporal and spatial variation of the phase field, which describes the identity of the phase, and of the composition. An asymptotic analysis, as the gradient energy coefficient of the phase field becomes small, was conducted. From the analysis, it is shown that the model recovers classical sharp interface models of this situation when the interfacial layers are thin, and they show how to relate the parameters appearing in the phase field model to material and growth parameters in real systems. Further, three stages of temporal evolution are identified: the first corresponding to interfacial genesis which occurs very rapidly; the second to interfacial motion controlled by the local energy difference across the interface and diffusion; the last taking place on a long time scale in which curvature effects are important and which correspond to Ostwald ripening. The results of the numerical calculations are presented.

Wheeler, A. A.↗

NASA NTRSDate not supplied

Modeling of Multicomponent Trace Contaminant Adsorption on Activated Carbon

Modeling of multicomponent trace contaminant adsorption on activated carbon for spacecraft life support applications presents challenges due to the very low contaminant concentrations in cabin air coupled with very strong adsorption of heavier components such as cyclic polydimethylsiloxanes. Both gas-phase and solid-phase micropore mass transfer resistances can be important, and competitive interactions between adsorbed components can result in behavior such as roll-up where lighter components displaced by heavier components have a higher concentration at the outlet than at the inlet. This paper describes the further development of a dynamic trace contaminant adsorption model based on Ideal Adsorbed Solution Theory (IAST). Alternative 1-dimensional and 2-dimensional versions of the model are described with different mass transfer resistance and driving force assumptions. Optimization of solution methods for speed and stability is also described. Mass balance equations are scaled to provide sensitivity over the wide range of component concentrations in cabin air. Model parameters are estimated from isotherm and breakthrough test data on single adsorbate and binary adsorbate systems. Multicomponent results are compared against predictions of a heritage model used extensively by NASA for trace contaminant control system (TCCS) carbon bed sizing. Finally, efforts to implement the model in a second software platform for wider access are described.

Kevin E Lange↗

NASA NTRS2000

Singular Isothermal Disks: Nonaxiymmetric Bifurcations and Equilibria - Paper 2

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance omega from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M = 2, 3, 4, ... separate bodies. On the basis of our experience in this paper, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Galli, Danielle↗

NASA NTRS2000

Singular Isothermal Disks and the Formation of Multiple Stars

A crucial missing ingredient in previous theoretical studies of fragmentation is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore consider the equilibrium configuration of isopedically magnetized, scale-free, singular isothermal disks, without the assumption of axial symmetry. We find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into separate bodies. We advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Galli, Daniele↗

NASA NTRS1980

Analysis and calculation of macrosegregation in a casting ingot. MPS solidification model. Volume 3: Operating manual

The operation of solidification model 1 is described. Model 1 calculates the macrosegregation in a rectangular ingot of a binary alloy as a result of horizontal axisymmetric bidirectional solidification. The calculation is restricted to steady-state solidification; there is no variation in final local average composition in the direction of isotherm movement. The physics of the model are given.

Maples, A. L.↗

NASA NTRS1984

The collapse of the cores of slowly rotating isothermal clouds

A generalized model which accounts for the effects of initially uniform and slow rotation is defined for the spherical collapse of a singular isothermal sphere such as protosolar and binary nebulae. An initial unstable equilibrium state is described for a sound speed of 0.35 km/sec and a rotation rate of 10 to the -14th/sec for the molecular cloud surrounding the accreting core. The total angular momentum and mass of the inner cloud is set equal to solar system values. The evolution of the collapse is traced by applying a perturbation analysis to the similarity solution for a nonrotating condition, and matched asymptotic expansions solve the hydrodynamic equations. The model is concluded a valid tool for studying star and nebular disk formation.

Terebey, S.↗

NASA NTRS1989

Thermosolutal convection during dendritic solidification

This paper presents a mathematical model for directional solidification of a binary alloy including a dendritic region underlying an all-liquid region. It is assumed initially that there exists a nonconvecting state with planar isotherms and isoconcentrates solidifying at a constant velocity. The stability of this system has been analyzed and nonlinear calculations are performed that show the effect of convection in the solidification process when the system is unstable. Results of calculations for various cases defined by the initial temperature gradient at the dendrite tips and varying strength of the gravitational field are presented for systems involving lead-tin alloys. The results show that the systems are stable for a gravitational constant of 0.0001 g(0) and that convection can be suppressed by appropriate choice of the container's size for higher values of the gravitational constant. It is also concluded that for the lead-tin systems considered, convection in the mushy zone is not significant below the upper 20 percent of the dendritic zone, if al all.

Heinrich, J. C.↗

NASA NTRS1984

Use of the Burton-prim-slichter Equation at High Growth Rates

The following must be assumed in order to derive the classic Burton-Prim-Slichter equation for segregation during crystal growth: isobaric, isothermal, isopotential or uncharged species, binary, planar interface, steady state, constant diffusion coefficient in fluid, no diffusion in crystal, no lateral convection within fluid film at interface with complete mixing beyond (stagnant film model), and either density, total concentration or partial molar volumes constant in the fluid phase. In addition, the effective distribution coefficient and the interfacial distribution coefficient must be defined properly. The velocity in the equation is the growth rate times a factor correcting for the difference in volumetric properties between crystal and fluid. The stagnant film thickness is found to be a function of freezing rate, with the precise functionality depending on the type of stirring occurring in the growth fluid.

Wilcox, W. R.↗

NASA NTRS1995

Simultaneous concentration and purification through gradient deformation chromatography

Mobile-phase additives, commonly used to modulate absorbate retention in gradient elution chromatography, are usually assumed to be either linearly retained or unretained. Previous theoretical work from our laboratory has shown that these modulators, such as salts in ion-exchange and hydrophobic interaction chromatography and organic modifiers in reversed-phase chromatography, can absorb nonlinearly, giving rise to gradient deformation. Consequently, adsorbate peaks that elute in the vicinity of the head of the deformed gradient may exhibit unusual shapes, form shoulders, and/or be concentrated. These effects for a reversed-phase sorbent with aqueous acetonitrile (ACN) as the modulator are verified experimentally. Gradient deformation is demonstrated experimentally and agrees with simulations based on ACN isotherm parameters that are independently determined from batch equilibrium studies using the layer model. Unusual absorbate peak shapes were found experimentally for single-component injections of phenylalanine, similar to those calculated by the simulations. A binary mixture of tryptophan and phenylalanine is used to demonstrate simultaneous concentration and separation, again in agreement with simulations. The possibility of gradient deformation in ion-exchange and hydrophobic interaction chromatography is discussed.

NASA Discipline Number 93-10↗

NASA NTRS1989

Finite element simulations of thermosolutal convection in vertical solidification of binary alloys

Dendritic vertical solidification of a binary alloy is modeled using the finite element method to assess the effect of thermosolutal convection in macrosegregation. The mathematical model assumes steady-state solidification with a planar, undeformable surface defined by the dendrite tips and the eutectic isotherm. The dendritic region is assumed to advance at a constant solidification velocity v. The stability of the modeled system has been investigated and nonlinear calculations performed that show finger-like convection when the system is unstable. Results for lead-tin alloys show that when the system is unstable, convection is only significant in the uppermost part of the mush and is entirely driven by convection in the bulk fluid.

Heinrich, J. C.↗

NASA NTRS1984

Angular momentum transfer by gravitational torques and the evolution of binary protostars

The efficiency of angular momentum transport by gravitational torques is investigated semianalytically for two idealized models. The first model, a rotating ellipsoid embedded within another ellipsoid, is compared with numerical results for the fission instability of a radpidly-rotating polytrope. The fission instability is aborted by the rapid transfer of angular momentum outward by gravitational torques. The global rates of angular momentum transfer by gravitational torques in rotating gas clouds such as the presolar nebula are shown to be comparable to the rates assumed to be appropriate for transfer by turbulent stresses. The second model is a binary system embedded within a rotating ellipsoid. The binary orbital angular momentum decreases significantly when the phase angle with the ellipsoid is constant; the binary separation may then decrease by a factor of 100 within about an orbital period. For a variable phase angle, little secular loss of orbital angular momentum occurs. Binaries which form in the isothermal regime of the theory of hierarchical fragmentation will not undergo orbital decay, whereas very close binaries composed of nonisothermal fragments may decay and merge into single objects.

Boss, A. P.↗

NASA NTRS2001

Understanding the Puzzling X-Ray Spectrum of the SO Galaxy NGC 4382; NGC 43819: Spectral Analysis of the Prototypical Early Merger and ASCA Observations of a Dynamically Young Elliptical: NGC 4125

We have analyzed the ASCA observations of NGC 4382, NGC 4038/9, NGC 4125 and produced papers for publication. NGC 4382 is one of the E and SO galaxies detected with the lowest X-ray to optical luminosity ratio. These galaxies have a peculiar X-ray (0.1-3 keV) spectrum, with a significant excess of counts in the lowest spectral channels (less than 1 keV) relative to the spectral count distributions of X-ray brihter E and SO galaxies. Analyzing the ROSAT PSPC observation of NGC 4382 it was unclear whether this soft excess was due to a real very soft component in a multi-component spectrum, or reflected an extremely low metal abundance in an isothermal hot gas. Our ASCA observations show that the low-abundance single-temperature model does not fit well to the X-ray spectrum, in agreement with our previous suggestions. A better explanation is a composite spectrum with a very soft component (0.3 keV) in addition to a harder (5 keV) component from X-ray binaries. In this model, the abundance cannot be constrained. More complex spectral models are also possible. The ASCA observations of The Antennae - (NGC4038/9) show that at least two spectral components are required to describe the emission-thermal emission from a plasma at 0.8 keV, and a component at higher energies. The hot gas contributes about half of the flux in the 0.5 to 6 keV band. If the column density to the higher energy component is greater than 2 x 10 (exp 21) per square centimeter, then the fitted abundance in the hot gas component is less than 0.2 solar. This low abundance is not expected for the hot interstellar medium in NGC4038/9 in which supernovae and star formation (expected to enrich and heat the gas) are ongoing. We do not detect any spatial variations in the spectrum. We relate these findings to data obtained by other satellites (Einstein, ROSAT) for this interacting galaxy pair. NGC4125's ASCA data was analyzed jointly with its Beppo-SAX observation. A hard component (kT /sim 4-10 keV) is observed together with a thermal component with line emission.

Fabbiano, Giuseppina↗

NASA NTRS1988

Directional solidification with heat losses

The upward directional solidification of a dilute binary alloy in a tall, thin, two-dimensional slot is considered. Heat losses from the sidewalls produce curved isotherms, interface deformations, and melt convection. An asymptotic approach is used which relates the small heat loss to the thinness of the solidification cell, and solutions are obtained for the resulting melt convection, interface deflection, and the distribution of heat and solute. The model is compared to the numerical results of Chang and Brown (1983) which exclude the effects of solute buoyancy and thermodynamic equilibrium at the interface. The radial segregation at the interface (consistent with both interface shapes and temperature fields) is computed, and it is found that the radial segregation is independent of interfacial shapes; the radial segregation cannot be calculated from only a knowledge of the interface shape.

Brattkus, K.↗

NASA NTRS1992

Models for Galaxy halos in an open universe

The properties of simple, self-consistent infall models which embed an 'isothermal' dark halo in an open universe are presented. These models depend on one scaling parameter and two shape parameters. The first may be taken to be the circular velocity in the inner regions, and the others to be the density of the universe, Omega, and a measure, e, of the shape of orbits. These models provide a useful description of ensembles of satellite galaxies, or of binary galaxies, because they allow explicitly for the fact that such systems have orbital periods approaching the age of the universe and so cannot have a random orbital phase.

White, Simon D. M.↗

NASA NTRS1990

The baroeffect and an appropriate momentum boundary condition

As disparate molecular weight gases isothermally diffuse between two ends of a capillary tube, they can support a pressure gradient. The magnitude of this pressure gradient depends critically on viscous wall stress and becomes a measure of the boundary condition. Here, a one-dimensional analytical model is proposed that allows for specular gas reflection from the wall. It explains anomalous (4/3) correction factors required previously to match experiment to baroeffect models. It predicts a new physical phenomenon, a surface-driven baroeffect for equal molecular weight gases. Diffusive slip contributions exceed the order of convective diffusion for Peclet number Pe less than 1 and approximately equal convective diffusion for Pe values between 1 and 4. For binary gases, this model further extends the baroeffect experiment as a means to find momentum accommodation coefficients, slip lengths, and external friction coefficients. A corrected binary diffusion coefficient is defined.

Noever, David A.↗

NASA NTRS1988

Interfacial tension and vapor-liquid equilibria in the critical region of mixtures

In the critical region, the concept of two-scale-factor universality can be used to accurately predict the surface tension between near-critical vapor and liquid phases from the singularity in the thermodynamic properties of the bulk fluid. In the present work, this idea is generalized to binary mixtures and is illustrated using the data of Hsu et al. (1985) for CO2 + n-butane. The pressure-temperature-composition-density data for coexisting, near-critical phases of the mixtures are fitted with a thermodynamic potential comprised of a sum of a singular term and nonsingular terms. The nonuniversal amplitudes characterizing the singular term for the mixtures are obtained from the amplitudes for the pure components by interpolation in a space of thermodynamic 'field' variables. The interfacial tensions predicted for the mixtures from the singular term are within 10 percent of the data on three isotherms in the pressure range (Pc - P)/Pc of less than 0.5. This difference is comparable to the combined experimental and model errors.

Moldover, Michael R.↗

NASA NTRS1990

Numerical Formulation for the Prediction of Solid/Liquid Change of a Binary Alloy

A computational model is presented for the prediction of solid/liquid phase change energy transport including the influence of free convection fluid flow in the liquid phase region. The computational model considers the velocity components of all non-liquid phase change material control volumes to be zero but fully solves the coupled mass-momentum problem within the liquid region. The thermal energy model includes the entire domain and uses an enthalpy like model and a recently developed method for handling the phase change interface nonlinearity. Convergence studies are performed and comparisons made with experimental data for two different problem specifications. The convergence studies indicate that grid independence was achieved and the comparison with experimental data indicates excellent quantitative prediction of the melt fraction evolution. Qualitative data is also provided in the form of velocity vector diagrams and isotherm plots for selected times in the evolution of both problems. The computational costs incurred are quite low by comparison with previous efforts on solving these problems.

Schneider, G. E.↗

NASA NTRS2021

X-ray Emission from Magnetized Neutron Star Atmospheres at Low Mass Accretion Rates

Recent observations of X-ray pulsars at low luminosities allow, for the first time, to compare theoretical models for the emission from highly magnetized neutron star atmospheres at low mass accretion rates ( M ≲ 10(exp 15) g s(exp -1)) with the broadband X-ray data. The purpose of this paper is to investigate the spectral formation in the neutron star atmosphere at low M and to conduct a parameter study of physical properties of the emitting region. We obtain the structure of the static atmosphere, assuming that Coulomb collisions are the dominant deceleration process. The upper part of the atmosphere is strongly heated by the braking plasma, reaching temperatures of 30–40 keV, while its denser isothermal interior is much cooler (~2 keV). We numerically solve the polarized radiative transfer in the atmosphere with magnetic Compton scattering, free-free processes, and non-thermal cyclotron emission due to possible collisional excitations of electrons. The strongly polarized emitted spectrum has a double-hump shape that is observed in low-luminosity X-ray pulsars. A low-energy “thermal” component is dominated by extraordinary photons that can leave the atmosphere from deeper layers due to their long mean free path at soft energies. We find that a high-energy component is formed due to resonant Comptonization in the heated non-isothermal part of the atmosphere even in the absence of collisional excitations. The latter, however, affect the ratio of the two components. A strong cyclotron line originates from the optically thin, uppermost zone. A fit of the model to NuSTAR and Swift/XRT observations of GX304􀀀1 provides an accurate description of the data with reasonable parameters. The model can thus reproduce the characteristic double-hump spectrum observed in low-luminosity X-ray pulsars and provides insights into spectral formation.

X-Ray binaries↗