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Results for “diffusion equation”

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 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Investigation of carbon segregation during low temperature tempering in a medium carbon steel

Low temperature tempering is important in improving the mechanical properties of steels. In this study, the thermoelectric power method was employed to investigate carbon segregation during low temperature tempering ranging from 110 °C to 170 °C of a medium carbon alloyed steel, combined with micro-hardness, transmission electron microscopy and atom probe tomography. Evolution of carbon dissolution from martensite and segregation to grain boundaries/interfaces and dislocations were investigated for different tempering conditions. Carbon concentration variation was quantified from 0.33 wt.% in quenching sample to 0.15 wt.% after long time tempering. The kinetic of carbon diffusion during tempering process was discussed through Johnson-Mehl-Avrami equation. - Highlights: • The thermoelectric power (TEP) was employed to investigate the low temperature tempering of a medium carbon alloyed steel. • Evolution of carbon dissolution was investigated for different tempering conditions. • Carbon concentration variation was quantified from 0.33 wt.% in quenching sample to 0.15 wt.% after long time tempering.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Modeling the relative dynamics of DNA-coated colloids

Here, we construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1 μm colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger than the corresponding coefficient of hydrodynamic friction. We use a mean-field extension of the model to higher dimensions to estimate the friction tensor for a disc rotating and translating horizontally along a line. When the DNA strands are very stiff and short, the friction coefficient for the disc rolling approaches zero while the friction for the disc sliding remains large. Together, these results could have significant implications for the dynamics of DNA-coated colloids or other ligand-receptor systems, implying that DNA-induced friction between colloids can be stronger than hydrodynamic friction and should be incorporated into simulations, and that it depends nontrivially on the type of relative motion, possibly causing the particles to assemble into out-of-equilibrium metastable states governed by the pathways with the least friction.

36 MATERIALS SCIENCE↗
DOE OSTI2020

From synchrotrons for XFELs: the soft x-ray near-edge spectrum of the ESCA molecule

A predictive understanding of soft x-ray near-edge absorption spectra of small molecules is an enduring theoretical challenge and of current interest for x-ray probes of molecular dynamics. We report the experimental absorption spectrum for the electron spectroscopy for chemical analysis (ESCA) molecule (ethyl trifluoroacetate) near the carbon 1s absorption edge between 285-300 eV. Furthermore, the ESCA molecule with four chemically distinct carbon sites has previously served as a theoretical benchmark for photoelectron spectra and now for photoabsorption spectra. We report a simple edge-specific approach for systematically expanding standard basis sets to properly describe diffuse Rydberg orbitals and the importance of triple excitations in equation-of-motion coupled-cluster calculations of the energy interval between valence and Rydberg excitations.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

A multifluid model extended for strong temperature nonequilibrium

We present a multifluid model in which the material temperature is strongly affected by the degree of segregation of each material. In order to track temperatures of segregated form and mixed form of the same material, they are defined as different materials with their own energy. This extension makes it necessary to extend multifluid models to the case in which each form is defined as a separate material. Statistical variations associated with the morphology of the mixture have to be simplified. Simplifications introduced include combining all molecularly mixed species into a single composite material, which is treated as another segregated material. Relative motion within the composite material, diffusion, is represented by material velocity of each component in the composite material. Compression work, momentum and energy exchange, virtual mass forces, and dissipation of the unresolved kinetic energy have been generalized to the heterogeneous mixture in temperature nonequilibrium. The present model can be further simplified by combining all mixed forms of materials into a composite material. Molecular diffusion in this case is modeled by the Stefan-Maxwell equations.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Entropy Stable Discretization of Compressible Flows in Thermochemical Nonequilibrium

Entropy stable numerical methods for compressible flow have been demonstrated to exhibit better robustness than purely linearly stable methods and need less overall artificial dissipation for long simulations in subsonic and transonic flows. In this work we seek to extend these benefits to multicomponent, multitemperature flows in thermochemical nonequilibrium such as combustion and hypersonic flight. We first derive entropy functions that symmetrize the governing equations and allow stability proofs for such systems. The impact of diffusion model selection on provable entropy stability is considered in detail, including both rigorous models of irreversible thermodynamics and simplified models of greater practical interest. Based on the proven entropy functions we develop affordable, entropy conservative two-point flux functions for solution in conservation form. We derive entropy conservative fluxes for calorically and thermally perfect mixtures, with heat capacities described by either polynomials of the temperature or formulas from statistical thermodynamics.

42 ENGINEERING↗
DOE OSTI2024

Predicting the Slowing of Stellar Differential Rotation by Instability-driven Turbulence

Abstract Differentially rotating stars and planets transport angular momentum (AM) internally due to turbulence at rates that have long been a challenge to predict reliably. We develop a self-consistent saturation theory, using a statistical closure approximation, for hydrodynamic turbulence driven by the axisymmetric Goldreich–Schubert–Fricke instability at the stellar equator with radial differential rotation. This instability arises when fast thermal diffusion eliminates the stabilizing effects of buoyancy forces in a system where a stabilizing entropy gradient dominates over the destabilizing AM gradient. Our turbulence closure invokes a dominant three-wave coupling between pairs of linearly unstable eigenmodes and a near-zero frequency, viscously damped eigenmode that features latitudinal jets. We derive turbulent transport rates of momentum and heat and provide them in analytic forms. Such formulae, free of tunable model parameters, are tested against direct numerical simulations; the comparison shows good agreement. They improve upon prior quasi-linear or “parasitic saturation” models containing a free parameter. Given model correspondences, we also extend this theory to heat and compositional transport for axisymmetric thermohaline-instability-driven turbulence in certain regimes.

Astronomy & Astrophysics↗
NASA NTRS1966

Gunn domain dynamics.

Carrier motion equation in Gunn diode in terms of average drift velocity and diffusion coefficient

DIFFUSION COEFFICIENT↗
NASA NTRS1972

Comments on ""Contact Diffusion Interaction of Materials with Cladding''

A Russian paper by A. A. Babad-Zakhryapina contributes much to the understanding of fuel, clad interactions, and thus to nuclear thermionic technology. In that publication the basic diffusion expression is a simple one. A more general but complicated equation for this mass transport results from the present work. With appropriate assumptions, however, the new relation reduces to Babad-Zakhryapina's version.

Morris, J. F.↗
NASA NTRS1973

Fission-gas release from uranium nitride at high fission rate density

A sweep gas facility has been used to measure the release rates of radioactive fission gases from small UN specimens irradiated to 8-percent burnup at high fission-rate densities. The measured release rates have been correlated with an equation whose terms correspond to direct recoil release, fission-enhanced diffusion, and atomic diffusion (a function of temperature). Release rates were found to increase linearly with burnups between 1.5 and 8 percent. Pore migration was observed after operation at 1550 K to over 6 percent burnup.

Weinstein, M. B.↗
NASA NTRS1974

Experimental determination of turbulence in a GH2-GOX rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient for a gaseous rocket combustion chamber have been determined from the experimental measurements of the tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and Spalding's numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber. An exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the maximum value of the intensity of turbulence is about 15% and the Lagrangian correlation coefficient drops to about 0.12 in one inch of the chamber length.

Tou, P.↗
NASA NTRS1981

An extended classical solution of the droplet growth problem

Problems of applying the classical kinetic theory to the growth of small droplets from vapor are examined. A solution for the droplet growth equation is derived which is based on the assumption of a diffusive field extending to the drop surface. The method accounts for partial thermal and mass accommodation at the interface and the kinetic limit to the mass and heat fluxes, and it avoids introducing the artifact of a discontinuity in the thermal and vapor field near the droplet. Consideration of the environmental fields in spherical geometry utilizing directional fluxes yields boundary values in terms of known parameters and a new Laplace transform integral.

Anderson, B. J.↗
NASA NTRS1981

Cosmology

The current view of the universe is summarized. The equations used to described it and the means of interpreting the diffuse gamma radiation which might result from phenomena which occurred in the distant past are described. The Friedmann model is described in detail.

Source record↗
NASA NTRS1981

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

Palusinski, O. A.↗
NASA NTRS1983

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Strelkov, S. A.↗
NASA NTRS1985

Assessment of discretization schemes to reduce numerical diffusion in the calculation of complex flows

Comprehensive criteria for evaluating finite-difference schemes to reduce numerical diffusion in the solution of the Reynolds averaged Navier-Stokes equations have been established in this study. Several candidate schemes have been examined, based on these criteria. Taylor series analyses, model problem studies and examination of the difference equations have been used to assess the schemes. Two schemes, which showed the most promise, and satisfied a majority of the criteria, are recommended for incorporation into two dimensional and three dimensional computer codes for further evaluation.

Syed, S. A.↗
NASA NTRS1990

Catalytic ignition model in a monolithic reactor with in-depth reaction

Two transient models have been developed to study the catalytic ignition in a monolithic catalytic reactor. The special feature in these models is the inclusion of thermal and species structures in the porous catalytic layer. There are many time scales involved in the catalytic ignition problem, and these two models are developed with different time scales. In the full transient model, the equations are non-dimensionalized by the shortest time scale (mass diffusion across the catalytic layer). It is therefore accurate but is computationally costly. In the energy-integral model, only the slowest process (solid heat-up) is taken as nonsteady. It is approximate but computationally efficient. In the computations performed, the catalyst is platinum and the reactants are rich mixtures of hydrogen and oxygen. One-step global chemical reaction rates are used for both gas-phase homogeneous reaction and catalytic heterogeneous reaction. The computed results reveal the transient ignition processes in detail, including the structure variation with time in the reactive catalytic layer. An ignition map using reactor length and catalyst loading is constructed. The comparison of computed results between the two transient models verifies the applicability of the energy-integral model when the time is greater than the second largest time scale of the system. It also suggests that a proper combined use of the two models can catch all the transient phenomena while minimizing the computational cost.

Tien, Ta-Ching↗