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NASA NTRS1992

Radiative shocks and hydrogen molecules in pregalactic gas - The effects of postshock radiation

Previous calculations of radiative shocks in pregalactic gas are generalized and substantially improved. The hydrodynamical conservations are solved, along with the rate equations for nonequilibrium ionization, recombination, and molecule formation, and the equation of radiative transfer, for steady-state shocks in a gas of primordial compositions. This calculation self-consistently includes the effects of the diffuse postshock emission as well as a possible external radiation flux on the postshock flow and the preshock ionization levels. A previous result is confirmed that the shocked gas cools faster than it can recombine and, as a result, is able to form an H2 concentration as high as 0.003 via the formation of H(-) and H2(+) intermediaries due to the enhanced nonequilibrium ionization fraction at 10,000 K. It is shown that, as the level of the external radiation flux is increased, the formation of and cooling by H2 molecules can be inhibited and delayed. The detailed radiation spectra and ionizing photon number fluxes emergent from these shocks are presented.

Kang, Hyesung↗

NASA NTRS1991

The computation of standard solar models

Procedures for calculating standard solar models with the usual simplifying approximations of spherical symmetry, no mixing except in the surface convection zone, no mass loss or gain during the solar lifetime, and no separation of elements by diffusion are described. The standard network of nuclear reactions among the light elements is discussed including rates, energy production and abundance changes. Several of the equation of state and opacity formulations required for the basic equations of mass, momentum and energy conservation are presented. The usual mixing-length convection theory is used for these results. Numerical procedures for calculating the solar evolution, and current evolution and oscillation frequency results for the present sun by some recent authors are given.

Ulrich, Roger K.↗

NASA NTRS2003

Theory of Transport of Long Polymer Molecules through Carbon Nanotube Channels

A theory of transport of long chain polymer molecules through carbon nanotube (CNT) channels is developed using Fokker-Planck equation and direct molecular dynamics (MD) simulations. The mean transport or translocation time tau is found to depend on the chemical potential energy, entropy and diffusion coefficient. A power law dependence tau approx. N(sup 2)is found where N is number of monomers in a molecule. For 10(exp 5)-unit long polyethylene molecules, tau is estimated to be approx. 1micro-s. The diffusion coefficient of long polymer molecules inside CNTs, like that of short ones, are found to be few orders of magnitude larger than in ordinary silicate based zeolite systems.

Wei, Chenyu↗

NASA NTRS2005

Linear Stability Analysis of Gravitational Effects on a Low-Density Gas Jet Injected into a High-Density Medium

Lawson, Anthony L.↗

NASA NTRS2001

Instability Analysis of a Low-Density Gas Jet Injected into a High-Density Gas

The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis and a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas were performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. It was found that the presence of variable density within the shear layer resulted in an increase in the temporal amplification rate of the disturbances and an increase in the range of unstable frequencies, accompanied by a reduction in the phase velocities of the disturbances. Also, the temporal growth rates of the disturbances were increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity. The spatio-temporal stability analysis was performed to determine the nature of the absolute instability of the jet. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the jet s absolute instability were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be. Experiments were carried out to observe the qualitative differences between a round low-density gas jet injected into a high-density gas (helium jet injected into air) and a round constant density jet (air jet injected into air). Flow visualizations and velocity measurements in the near-injector region of the helium jet show more mixing and spreading of the helium jet than the air jet. The vortex structures develop and contribute to the jet spreading causing the helium jet to oscillate.

Lawson, Anthony Layiwola↗

NASA NTRS2002

Linear Temporal Stability Analysis of a Low-Density Round Gas Jet Injected into a High-Density Gas

It has been observed in previous experimental studies that round helium jets injected into air display a repetitive structure for a long distance, somewhat similar to the buoyancy-induced flickering observed in diffusion flames. In order to investigate the influence of gravity on the near-injector development of the flow, a linear temporal stability analysis of a round helium jet injected into air was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The temporal growth rates and the phase velocity of the disturbances were obtained. The temporal growth rates of the disturbances increased as the Froude number was reduced (i.e. gravitational effects increased), indicating the destabilizing role played by gravity.

Lawson, Anthony L.↗

DOE OSTI2024

Comprehensive Dynamics in a Polyelectrolyte Complex Coacervate

The linear viscoelastic response, LVR, of a hydrated polyelectrolyte complex coacervate, PEC, was evaluated over a range of frequencies, temperatures, and salt concentrations. The PEC was a nearly stoichiometric blend of a quaternary ammonium poly([3-(methacrylamido)propyl]trimethylammonium chloride), PMAPTAC, and poly(2-acrylamido-2-methyl-1-propanesulfonic acid sodium salt), PAMPS, an aliphatic sulfonate, selected because they remain fully charged over the conditions of use. Narrow molecular weight distribution polyelectrolytes were prepared using fractionation techniques. A partially deuterated version of PMAPTAC was incorporated to determine its coil radius of gyration, R g , within PECs using small-angle neutron scattering. Chain dimensions were determined to be Gaussian with a Kuhn length of 2.37 nm, which remained constant from 25 to 65 °C. The LVR for a series of matched molecular weight PECs, mostly above the entanglement threshold, exhibited crossovers of modulus versus frequency classically attributed to the reptation time, relaxation between entanglements, and the relaxation of a Kuhn length of units (the “monomer” time). The scaling for zero shear viscosity, η 0 , versus chain length, N, was η 0 ~ N 3.1 , in agreement with “sticky reptation” theory. The lifetime and activation energy, E p , of a pair between polyanion and polycation repeat units, Pol + Pol – , were determined from diffusion coefficients of salt ions within the PEC. The activation energy for LVR of salt-free PECs was 2E p , showing that the key mechanism limiting the dynamics of undoped PECs is pair exchange. An FTIR technique was used to distinguish whether SCN– acts as a counterion or a co-ion within PECs. Doping of PECs with NaSCN breaks Pol + Pol – pairing efficiently, which decreases effective cross-linking and decreases viscosity. Finally, an equation was derived that quantitatively predicts this effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1975

Diffusion in liquid metal systems

Physical properties of twenty liquid metals are reported; some of the data on such liquid metal properties as density, electrical resistivity, thermal conductivity, and heat capacity are summarized in graphical form. Data on laboratory handling and safety procedure are summarized for each metal; heat-transfer-correlations for liquid metals under various conditions of laminar and turbulent flow are included. Where sufficient data were available, temperature equations of properties were obtained by the method of least-squares fit. All values of properties given are valid in the given liquid phase ranges only. Additional tabular data on some 40 metals are reported in the appendix. Included is a brief description of experiments that were performed to investigate diffusion in liquid indium-gallium systems.

Ukanwa, A. O.↗

NASA NTRS2017

Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.

reynolds averaging↗

NASA NTRS1994

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

Cho, Soo-Yong↗

NASA NTRS1995

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗

DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗

DOE OSTI2025

A compartmentalized model of multiphase chemical kinetics

There are significant challenges in predicting multiphase chemical kinetics due to the complex coupling of reaction and mass transport across a phase boundary (i.e., interface). Here, we describe a framework for predicting multiphase kinetics that embeds the elementary kinetic steps of reaction, solvation, and diffusion into a coarse grain spatial description of two phases. The model is constructed to bridge the short-timescale interfacial dynamics observed in molecular simulations with the longer timescales observed in kinetic experiments. A simple set of governing differential equations is derived, which, when solved numerically or analytically, yield accurate predictions of multiphase kinetics in microdroplets. Although the equations are formulated for gas-liquid reactions, the underlying conceptual framework is general and can be applied to transformations in other two-phase systems (solid-liquid, liquid-liquid, etc.).

Chemical kinetics and dynamics↗

NASA NTRS1989

Analysis of opposed jet hydrogen-air counter flow diffusion flame

A computational simulation of the opposed-jet diffusion flame is performed to study its structure and extinction limits. The present analysis concentrates on the nitrogen-diluted hydrogen-air diffusion flame, which provides the basic information for many vehicle designs such as the aerospace plane for which hydrogen is a candidate as the fuel. The computer program uses the time-marching technique to solve the energy and species equations coupled with the momentum equation solved by the collocation method. The procedure is implemented in two stages. In the first stage, a one-step forward overal chemical reaction is chosen with the gas phase chemical reaction rate determined by comparison with experimental data. In the second stage, a complete chemical reaction mechanism is introduced with detailed thermodynamic and transport property calculations. Comparison between experimental extinction data and theoretical predictions is discussed. The effects of thermal diffusion as well as Lewis number and Prandtl number variations on the diffusion flame are also presented.

Ho, Y. H.↗

DOE OSTI2021

A multifidelity method for a nonlocal diffusion model

Nonlocal models feature a finite length scale, referred to as the horizon, such that points separated by a distance smaller than the horizon interact with each other. Such models have proven to be useful in a variety of settings. However, due to the reduced sparsity of discretizations, they are also generally computationally more expensive compared to their local differential equation counterparts. In this work, we introduce a multifidelity Monte Carlo method that combines the high-fidelity nonlocal model of interest with surrogate models that use coarser grids and/or smaller horizons and thus have lower fidelities and lower costs. Using the multifidelity method, the overall computational cost of uncertainty quantification is reduced without compromising accuracy. It is shown for a one-dimensional nonlocal diffusion example that speedups of up to two orders of magnitude can be achieved using the multifidelity method to estimate the expectation of an output of interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Thermal Shape Stability of fcc Metal Nanocrystals Synthesized with Faceted Nonequilibrium Shapes

Highly refined capabilities of the shape-controlled solution-phase synthesis of metal nanocrystals (NCs) allow the generation of NCs with faceted nonequilibrium shapes, which optimize properties for target applications such as catalysis and plasmonics. Often, for such applications and also for TEM analysis, the NCs are removed from the solution-phase environment. We explore the postsynthesis evolution of these metastable NCs in a high-vacuum TEM environment. Specifically, here we analyze their reshaping toward the equilibrium Wulff shapes mediated by surface diffusion, where such reshaping degrades the above-mentioned optimized properties. Typical sizes for these NCs range from 5 to 30 nm or 10 3 –10 6 atoms, and reshaping often occurs on the time scale of minutes for temperatures around, say, 400 °C. We discuss the development of predictive stochastic atomistic-level models for NC evolution with a realistic description of surface diffusion. These models, in contrast to Molecular Dynamics, can naturally address the relevant time and length scales for these systems. KMC simulation results for the stochastic models are described, focusing on the reshaping of slightly elongated nanorods and of mildly truncated octahedra and nanocubes. In addition, we review appropriate theoretical formulations for reshaping, which involves the nucleation and growth on 2D islands or layers on outer facets of the NC. We note the limitations of classical nucleation theory in some scenarios and demonstrate the successes of a more fundamental and general master equation-based analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1962

Pitfalls in thermal emission studies

Attention is called to several pitfalls that often beset investigators who make thermal emittance studies. The pitfalls mentioned include the following: (1) conflicting meanings of several frequently used terms as found in the literature, each meaning having authoritative sponsorship; (2) incomplete and hence potentially misleading descriptions of specimens on which reported data arc based; (3) reference to emissivity or remittance as a property of a surface rather than a volume property (influenced by the surface); (4) occasional omission of diffuse reflection from analyses of the optical properties of inhomogeneous bodies; (5) failure to observe the restrictions upon conditions that are required for validity of basic equations; (6)uncertainties as to the effective temperature, peculiar to specimens having low absorption indices; and (7) lack of suitable physical standards. Several suggestions are made for avoiding or minimizing the consequences of the pitfalls discussed.

THERMAL RADIATION↗

NASA NTRS1972

Normal evaporation of binary alloys

In the study of normal evaporation, it is assumed that the evaporating alloy is homogeneous, that the vapor is instantly removed, and that the alloy follows Raoult's law. The differential equation of normal evaporation relating the evaporating time to the final solute concentration is given and solved for several important special cases. Uses of the derived equations are exemplified with a Ni-Al alloy and some binary iron alloys. The accuracy of the predicted results are checked by analyses of actual experimental data on Fe-Ni and Ni-Cr alloys evaporated at 1600 C, and also on the vacuum purification of beryllium. These analyses suggest that the normal evaporation equations presented here give satisfactory results that are accurate to within an order of magnitude of the correct values, even for some highly concentrated solutions. Limited diffusion and the resultant surface solute depletion or enrichment appear important in the extension of this normal evaporation approach.

Li, C. H.↗