A new approach to the homogenization of heterogeneous media for neutron diffusion calculations
Mathematical formulation for homogenization of heterogeneous media for neutron diffusion transport theory
DIFFUSION THEORY↗
SEARCH · Search NASA
Results for “Heterogeneous media”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
A New Approach to the Homogenization of Heterogeneous Media for Neutron Diffusion Calculations
Mathematical model for neutron diffusion mechanics in heterogeneous media with vacuum channels
VACUUM SYSTEM↗
Problems related to the determination of land surface parameters and fluxes over heterogeneous media from satellite data
Problems encountered in the definition of relevant parameters which can describe heterogeneous media as a whole are discussed. A procedure to extend the definition of parameters from local to regional scales via inversion of appropriate models is tentatively proposed. The adequacy of these models for describing physical processes at the earth/atmosphere interface as observed with satellite systems is addressed.
Becker, F.↗
First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.
Michael I Mishchenko↗
Mechanistic Studies of Combustion and Structure Formation During Synthesis of Advanced Materials
Combustion in a variety of heterogeneous systems, leading to the synthesis of advanced materials, is characterized by high temperatures (2000-3500 K) and heating rates (up to 10(exp 6) K/s) at and ahead of the reaction front. These high temperatures generate liquids and gases which are subject to gravity-driven flow. The removal of such gravitational effects is likely to provide increased control of the reaction front, with a consequent improvement in control of the microstructure of the synthesized products. Thus, microgravity (mu-g) experiments lead to major advances in the understanding of fundamental aspects of combustion and structure formation under the extreme conditions of the combustion synthesis (CS) wave. In addition, the specific features of microgravity environment allow one to produce unique materials, which cannot be obtained under terrestrial conditions. The current research is a logic continuation of our previous work on investigations of the fundamental phenomena of combustion and structure formation that occur at the high temperatures achieved in a CS wave. Our research is being conducted in three main directions: 1) Microstructural Transformations during Combustion Synthesis of Metal-Ceramic Composites. The studies are devoted to the investigation of particle growth during CS of intermetallic-ceramic composites, synthesized from nickel, aluminum, titanium, and boron metal reactants. To determine the mechanisms of particle growth, the investigation varies the relative amount of components in the initial mixture to yield combustion wave products with different ratios of solid and liquid phases, under 1g and mu-g conditions; 2) Mechanisms of Heat Transfer during Reactions in Heterogeneous Media. Specifically, new phenomena of gasless combustion wave propagation in heterogeneous media with porosity higher than that achievable in normal gravity conditions, are being studied. Two types of mixtures are investigated: clad powders, where contact between reactants occurs within each particle, and mixtures of elemental powders, where interparticle contacts are important for the reaction; and 3) Mechanistic Studies of Phase Separation in Combustion of Thermite Systems. Studies are devoted to experiments on thermite systems (metal oxide-reducing metal) where phase separation processes occur to produce alloys with tailored compositions and properties. The separation may be either gravity-driven or due to surface forces, and systematic studies to elucidate the true mechanism are being conducted. The knowledge obtained will be used to find the most promising ways of controlling the microstructure and properties of combustion-synthesized materials. Low-gravity experiments are essential to create idealized an environment for insights into the physics and chemistry of advanced material synthesis processes.
Varma, A.↗
Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations
In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.
Dlugach, Janna M.↗
The Linear Bicharacteristic Scheme for Electromagnetics
The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on electromagnetic wave propagation problems. This paper extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for one-dimensional model problems on both uniform and nonuniform grids, and the FDTD algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has approximately one-third the phase velocity error. The LBS is also more accurate on nonuniform grids.
Beggs, John H.↗
The Linear Bicharacteristic Scheme for Computational Electromagnetics
The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on electromagnetic wave propagation problems. This paper extends the Linear Bicharacteristic Scheme for computational electromagnetics to treat lossy dielectric and magnetic materials and perfect electrical conductors. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media, and treatment of perfect electrical conductors (PECs) are shown to follow directly in the limit of high conductivity. Heterogeneous media are treated through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for one-dimensional model problems on both uniform and nonuniform grids, and the FDTD algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has approximately one-third the phase velocity error. The LBS is also more accurate on nonuniform grids.
Beggs, John H.↗
A Two-Dimensional Linear Bicharacteristic Scheme for Electromagnetics
The upwind leapfrog or Linear Bicharacteristic Scheme (LBS) has previously been implemented and demonstrated on one-dimensional electromagnetic wave propagation problems. This memorandum extends the Linear Bicharacteristic Scheme for computational electromagnetics to model lossy dielectric and magnetic materials and perfect electrical conductors in two dimensions. This is accomplished by proper implementation of the LBS for homogeneous lossy dielectric and magnetic media and for perfect electrical conductors. Both the Transverse Electric and Transverse Magnetic polarizations are considered. Computational requirements and a Fourier analysis are also discussed. Heterogeneous media are modeled through implementation of surface boundary conditions and no special extrapolations or interpolations at dielectric material boundaries are required. Results are presented for two-dimensional model problems on uniform grids, and the Finite Difference Time Domain (FDTD) algorithm is chosen as a convenient reference algorithm for comparison. The results demonstrate that the two-dimensional explicit LBS is a dissipation-free, second-order accurate algorithm which uses a smaller stencil than the FDTD algorithm, yet it has less phase velocity error.
Beggs, John H.↗
Adaptation of Combustion Principles to Aircraft Propulsion: Basic Considerations in the Combustion of Hydrocarbon Fuels with Air - Volume I
The report summarizes source material on combustion for flight-propulsion engineers. First, several chapters review fundamental processes such as fuel-air mixture preparation, gas flow and mixing, flammability and ignition, flame propagation in both homogenous and heterogenous media, flame stabilization, combustion oscillations, and smoke and carbon formation. The practical significance and the relation of these processes to theory are presented. A second series of chapters describes the observed performance and design problems of engine combustors of the principal types. An attempt is made to interpret performance in terms of the fundamental processes and theories previously reviewed. Third, the design of high-speed combustion systems is discussed. Combustor design principles that can be established from basic considerations and from experience with actual combustors are described. Finally, future requirements for aircraft engine combustion systems are examined.
THEORIES - COMBUSTION↗
Surface Plasmon Resonance Evaluation of Colloidal Metal Aerogel Filters
We have fabricated aerogels containing gold, silver, and platinum nanoparticles for gas catalysis applications. By applying the concept of an average or effective dielectric constant to the heterogeneous interlayer surrounding each particle, we extend the technique of immersion spectroscopy to porous or heterogeneous media. Specifically, we apply the predominant effective medium theories for the determination of the average fractional composition of each component in this inhomogeneous layer. Hence, the surface area of metal available for catalytic gas reaction is determined. The technique is satisfactory for statistically random metal particle distributions but needs further modification for aggregated or surfactant modified systems. Additionally, the kinetics suggest that collective particle interactions in coagulated clusters are perturbed during silica gelation resulting in a change in the aggregate geometry.
Smith, David D.↗
Noble Metal Immersion Spectroscopy of Silica Alcogels and Aerogels
We have fabricated aerogels containing gold and silver nanoparticles for gas catalysis applications. By applying the concept of an average or effective dielectric constant to the heterogeneous interlayer surrounding each particle, we extend the technique of immersion spectroscopy to porous or heterogeneous media. Specifically, we apply the predominant effective medium theories for the determination of the average fractional composition of each component in this inhomogeneous layer. Hence, the surface area of metal available for catalytic gas reaction is determined. The technique is satisfactory for statistically random metal particle distributions but needs further modification for aggregated or surfactant modified systems. Additionally, the kinetics suggest that collective particle interactions in coagulated clusters are perturbed during silica gelation resulting in a change in the aggregate geometry.
Smith, David D.↗
Integrated Structural/Acoustic Modeling of Heterogeneous Panels
A model for the dynamic response of heterogeneous media is presented. A given medium is discretized into a number of subvolumes, each of which may contain an elastic anisotropic material, void, or fluid, and time-dependent boundary conditions are applied to simulate impact or incident pressure waves. The full time-dependent displacement and stress response throughout the medium is then determined via an explicit solution procedure. The model is applied to simulate the coupled structural/acoustic response of foam core sandwich panels as well as aluminum panels with foam inserts. Emphasis is placed on the acoustic absorption performance of the panels versus weight and the effects of the arrangement of the materials and incident wave frequency.
Bednarcyk, Brett, A.↗
A Semi-Numerical Method for Elastic Wave Scattering Calculations
This paper is concerned with the calculation of elastic wavefields in strongly heterogeneous media containing scatters of arbitrary shape and size.
NDE↗
Verification and Validation of Elastodynamic Simulation Software for Aerospace Research
Physics-based simulation of nondestructive evaluation (NDE) inspection can help to advance the inspectability and reliability of mechanical systems. However, NDE simulations applicable to non-idealized mechanical components often require large compute domains and long run times. This has prompted development of custom NDE simulation software tailored to high performance computing (HPC) hardware. Verification and validation (V&V) is an integral part of developing this software to ensure implementations are robust and applicable to inspection problems, producing tools and simulations suitable for computational NDE research. This presentation addresses factors common to V&V of several elastodynamic simulation codes applicable to ultrasonic NDE. Examples are drawn from in-house simulation software at NASA Langley Research Center, ranging from ensuring reliability in a 1D heterogeneous media wave equation solver to the V&V needs of 3D cluster-parallel elastodynamic software. Factors specific to a research environment are addressed, where individual simulation results can be as relevant as the software product itself. Distinct facets of V&V are discussed including testing to establish software reliability, employing systematic approaches for consistency with fundamental conservation laws, establishing the numerical stability of algorithms, and demonstrating concurrence with empirical data. This talk also addresses V&V practices for small groups of researchers. This includes establishing resources (e.g. time and personnel) for V&V during project planning to mitigate and control the risk of setbacks. Similarly, we identify ways for individual researchers to use V&V during simulation software development itself to both speed up the development process and reduce incurred technical debt.
NDE↗
Polarimetric scattering from layered media with multiple species of scatterers
Geophysical media are usually heterogeneous and contain multiple species of scatterers. In this paper a model is presented to calculate effective permittivities and polarimetric backscattering coefficients of multispecies-layered media. The same physical description is consistently used in the derivation of both permittivities and scattering coefficients. The strong permittivity fluctuation theory is extended to account for the multiple species of scatterers with a general ellipsoidal shape whose orientations are randomly distributed. Under the distorted Born approximation, polarimetric scattering coefficients are obtained. These calculations are applicable to the special cases of spheroidal and spherical scatterers. The model is used to study effects of scatterer shapes and multispecies mixtures on polarimetric signatures of heterogeneous media. The multispecies model accounts for moisture content in scattering media such as snowpack in an ice sheet. The results indicate a high sensitivity of backscatter to moisture with a stronger dependence for drier snow and ice grain size is important to the backscatter. For frost-covered saline ice, model results for bare ice are compared with measured data at C band and then the frost flower formation is simulated with a layer of fanlike ice crystals including brine infiltration over a rough interface. The results with the frost cover suggest a significant increase in scattering coefficients and a polarimetric signature closer to isotropic characteristics compared to the thin saline ice case.
Nghiem, S. V.↗
Diffusion NMR methods applied to xenon gas for materials study
We report initial NMR studies of (i) xenon gas diffusion in model heterogeneous porous media and (ii) continuous flow laser-polarized xenon gas. Both areas utilize the pulsed gradient spin-echo (PGSE) techniques in the gas phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients--a brief overview of this area is provided in the Introduction. The heterogeneous or multiple-length scale model porous media consisted of random packs of mixed glass beads of two different sizes. We focus on observing the approach of the time-dependent gas diffusion coefficient, D(t) (an indicator of mean squared displacement), to the long-time asymptote, with the aim of understanding the long-length scale structural information that may be derived from a heterogeneous porous system. We find that D(t) of imbibed xenon gas at short diffusion times is similar for the mixed bead pack and a pack of the smaller sized beads alone, hence reflecting the pore surface area to volume ratio of the smaller bead sample. The approach of D(t) to the long-time limit follows that of a pack of the larger sized beads alone, although the limiting D(t) for the mixed bead pack is lower, reflecting the lower porosity of the sample compared to that of a pack of mono-sized glass beads. The Pade approximation is used to interpolate D(t) data between the short- and long-time limits. Initial studies of continuous flow laser-polarized xenon gas demonstrate velocity-sensitive imaging of much higher flows than can generally be obtained with liquids (20-200 mm s-1). Gas velocity imaging is, however, found to be limited to a resolution of about 1 mm s-1 owing to the high diffusivity of gases compared with liquids. We also present the first gas-phase NMR scattering, or diffusive-diffraction, data, namely flow-enhanced structural features in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack. c2002 John Wiley & Sons, Ltd.
NASA Discipline Life Sciences Technologies↗
Polarimetric Scattering from Layered Media with Multiple Species of Scatterers
Geophysical media are usually heterogeneous and contain multiple species of scatterers.
backscattering↗