Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Diffusion problems”

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.

At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

A spectral collocation method for the Navier-Stokes equations

A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

Malik, M. R.↗
NASA NTRS1978

Rocket exhaust plume impingement on the Voyager spacecraft

In connection with the conduction of the long-duration Voyager missions to the outer planets and the sophisticated propulsion systems required, it was necessary to carry out an investigation to avoid exhaust plume impingement problems. The rarefied gas dynamics literature indicates that, for most engineering surfaces, the assumption of diffuse reemission and complete thermal accommodation is warranted in the free molecular flow regime. This assumption was applied to an analysis of a spacecraft plume impingement problem in the near-free molecular flow regime and yielded results to within a few percent of flight data. The importance of a correct treatment of the surface temperature was also demonstrated. Specular reflection, on the other hand, was shown to yield results which may be unconservative by a factor of 2 or 3. It is pointed out that one of the most difficult portions of an exhaust plume impingement analysis is the simulation of the impinged hardware. The geometry involved must be described as accurately and completely as possible.

Baerwald, R. K.↗
NASA NTRS1995

The Interstellar Medium

The Interstellar Medium (ISM) forms an integral part of the lifecycle of stars and the galaxy. Stars are formed by gravitational contraction of interstellar clouds. Over their life, stars return much of their mass to the ISM through winds and supernova explosions, resulting in a slow enrichment in heavy elements. Understanding the origin and evolution of the ISM is a key problem within astrophysics. The KAO has made many important contributions to studies of the interstellar medium both on the macro and on the micro scale. In this overview, I will concentrate on two breakthroughs in the last decade in which KAO observations have played a major role: (1) the importance of large Polycyclic Aromatic Hydrocarbon (PAH) molecules for the ISM (section 3) and (2) the study of Photodissociation Regions (PDRs) as an analog for the diffuse ISM at large (section 4). Appropriately, the micro and macro problem are intricately interwoven in these problems. Finally, section 5 reviews the origin of the (CII) emission observed by COBE.

Tielens, Alexander G. G. M.↗
DOE OSTI2020

Efficient smoothed particle radiation hydrodynamics I: Thermal radiative transfer

This work presents efficient solution techniques for radiative transfer in the smoothed particle hydrodynamics discretization. Two choices that impact efficiency are how the material and radiation energy are coupled, which determines the number of iterations needed to converge the emission source, and how the radiation diffusion equation is solved, which must be done in each iteration. The coupled material and radiation energy equations are solved using an inexact Newton iteration scheme based on nonlinear elimination, which reduces the number of Newton iterations needed to converge within each time step. During each Newton iteration, the radiation diffusion equation is solved using Krylov iterative methods with a multigrid preconditioner, which abstracts and optimizes much of the communication when running in parallel. The code is verified for an infinite medium problem, a one-dimensional Marshak wave, and a two and three-dimensional manufactured problem, and exhibits first-order convergence in time and second-order convergence in space. For these problems, the number of iterations needed to converge the inexact Newton scheme and the diffusion equation is independent of the number of spatial points and the number of processors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Solving the small-scale structure puzzles with dissipative dark matter

Small-scale structure is studied in the context of dissipative dark matter, arising for instance in models with a hidden unbroken Abelian sector, so that dark matter couples to a massless dark photon. The dark sector interacts with ordinary matter via gravity and photon-dark photon kinetic mixing. Mirror dark matter is a theoretically constrained special case where all parameters are fixed except for the kinetic mixing strength, ε. In these models, the dark matter halo around spiral and irregular galaxies takes the form of a dissipative plasma which evolves in response to various heating and cooling processes. It has been argued previously that such dynamics can account for the inferred cored density profiles of galaxies and other related structural features. Here we focus on the apparent deficit of nearby small galaxies (''missing satellite problem'), which these dissipative models have the potential to address through small-scale power suppression by acoustic and diffusion damping. Using a variant of the extended Press-Schechter formalism, we evaluate the halo mass function for the special case of mirror dark matter. Considering a simplified model where M {sub baryons} ∝ M {sub halo}, we relate the halo mass function to more directly observable quantities, and find that for ε ≈ 2 × 10{sup −10} such a simplified description is compatible with the measured galaxy luminosity and velocity functions. On scales M {sub halo} ∼< 10{sup 8} M {sub ⊙}, diffusion damping exponentially suppresses the halo mass function, suggesting a nonprimordial origin for dwarf spheroidal satellite galaxies, which we speculate were formed via a top-down fragmentation process as the result of nonlinear dissipative collapse of larger density perturbations. This could explain the planar orientation of satellite galaxies around Andromeda and the Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Generalization of NESTLE into a Multi-Energy N-Group Formulation

The NESTLE code is a few-group, diffusion-based core simulation code that employs the Nodal Expansion Method (NEM). NESTLE has the capability to solve both steady-state and transient problems, using either Cartesian or hexagonal geometry, and to apply thermal-hydraulic feedback including single and two-phase flow. A modern version of the NESTLE nodal-diffusion simulator is currently maintained and developed at the University of Tennessee. The original version of the code was limited to only two or four neutron energy groups, therefore, this article describes recent work carried out to expand NESTLE into a general multi-group solver. Generalization of a fixed group finite-difference diffusion theory into arbitrary N groups is a well-known problem [3], however, this paper describes the intricacies associated with the generalization of the Nodal Expansion Method, and the methodical and computational challenges encountered and managed along the way.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

On Integral of a Semi-Markov Diffusion Process

Let (X(t)) (t ≥ 0) be a semi-Markov diffusion process. The process (J(T )) (T ≥ 0) equal to the integral of (X(t)) on interval [0, T ) is studied. The relation between one-dimensional differential equation of the second order of elliptical type and asymptotics of a solution to Dirichlet problem on an interval with length tending to zero is established. This relation is used to derive a differential equation for the Laplace transform of the semi-Markov generating function of the process (J(t)).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Time-dependent approximation schemes for some problems of parameter estimation in distributed systems

A parameter estimation method that can be used to estimate functional parameters in delay differential equations and moving boundary problems is discussed. In either problem, the original model equation (which is infinite-dimensional) is approximated by a system of ordinary differential equations that can be solved numerically in an efficient way. The approximation scheme is based on time-dependent spline elements. For the delay equation with time-varying delay, convergence results are presented that indicate the estimates obtained using the approximating system. Numerical test examples converge in some sense to a best-fit parameter for the original system are included by means of which time-varying and state-dependent delays and a time-varying diffusion coefficient in a one-phase, one-dimensional Stefan problem are estimated.

Murphy, K. A.↗
DOE OSTI2022

Hand Calculations for Nuclear Criticality Safety – Primer Revision

The document “ Hand Calculation Methods for Criticality Safety – A Primer, ” was published by the authors (Los Alamos National Laboratory report LA-14244-M) in December 2006 to provide an overview of the most common hand calculation methods used for criticality safety analysis. Hand calculation methods can be used as a starting point for more advanced calculations, and in many circumstances, they can provide sensitivity and perturbation information quicker than using a criticality code, such as KENO or MCNP. This report has been revised to augment existing basis information and example problems for each of the methods discussed: 1-group and modified 1- group diffusion theory, core-density conversions, buckling conversions, limiting surface density method, density analog method, surface density method, and solid angle method. This primer discusses the applicability of the various methods, illustrates how they are used, and provides an interpretation of the example problem results. The example problems provided are simple, practical problems, and the reference data to solve each example problem is provided. This paper will provide an overview of the Primer revision and how it can be useful for new Nuclear Criticality Safety practitioners.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Hand Calculations for Nuclear Criticality Safety — Primer Revision [Abstract]

The document “ Hand Calculation Methods for Criticality Safety –A Primer, ” was published by the authors (Los Alamos National Laboratory report LA-14244-M) in December 2006 to provide an overview of the most common hand calculation methods used for criticality safety analysis. Hand calculation methods can be used as a starting point for more advanced calculations, and in many circumstances, they can provide sensitivity and perturbation information quicker than using a criticality code, such as KENO or MCNP. This report has been revised to augment existing basis information and example problems for each of the methods discussed: 1-group and modified 1-group diffusion theory, core-density conversions, buckling conversions, limiting surface density method, density analog method, surface density method, and solid angle method. This primer discusses the applicability of the various methods, illustrates how they are used, and provides an interpretation of the example problem results. The example problems provided are simple, practical problems, and the reference data to solve each example problem is provided. This paper will provide an overview of the Primer revision and how it can be useful for new Nuclear Criticality Safety practitioners.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2018

An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

The chaotic diffusion for a family of Hamiltonian mappings whose angles diverge in the limit of vanishingly action is investigated by using the solution of the diffusion equation. The system is described by a two-dimensional mapping for the variables action, I, and angle, θ and controlled by two control parameters: (i) ϵ, controlling the nonlinearity of the system, particularly a transition from integrable for ϵ=0 to non-integrable for ϵ≠0 and; (ii) γ denoting the power of the action in the equation defining the angle. For ϵ≠0 the phase space is mixed and chaos is present in the system leading to a finite diffusion in the action characterized by the solution of the diffusion equation. The analytical solution is then compared to the numerical simulations showing a remarkable agreement between the two procedures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

New discretization of Caputo–Fabrizio derivative

We derive a numerical approximation, namely L1–2 formula, to the Caputo–Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1–2 formulas using Lagrange interpolation, respectively. We compute Caputo–Fabrizio derivatives of some known functions both theoretically and numerically. In addition, we solve non/linear sub-diffusion equations to test theoretical findings. Numerical results confirm the theoretically observed convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assessment the leaching characteristics and long-term leaching behavior of some radionuclides from synthesized zeolite cement matrix

Highlights: • Synthesis and characterization of zeolite cement synthesized from fly ash • Leaching tests were used to assess the release rate of {sup 85}Sr and {sup 60}Co radionuclides. • Simple mathematical models were used to detect leaching mechanisms. • Long-term leaching behavior of {sup 85}Sr and {sup 60}Co from cementitious matrix was assessed. The development of cementitious materials remains a vital goal to produce valuable products with good mechanical, physical and chemical properties suitable for the safe disposal of concentrated radionuclides resulted from the treatment of contaminated solutions. In this paper, zeolite cement with good properties was laboratory synthesized from industrial by-products fly ash and characterized using various characterization techniques. The leaching characteristics of strontium and cobalt radionuclides from the synthesized zeolite cement were scrutinized conforming with the standard leaching methodology of International Atomic Energy Authority (IAEA). A mechanical strength assessment was executed to characterize the extent of immobilization process of the solidified matrices. The cumulative leaching fraction (φ) of the two studied radionuclides was found to be less than 5% in all examined conditions, which implies the applicability of the IAEA-recommended methodology for estimating the diffusion coefficient. The experimental leaching data were regressed nonlinearly to various mathematical kinetic models to assess the controlling leaching mechanism and to determine the leaching parameters. The regression results indicated that strontium ({sup 85}Sr) and cobalt ({sup 60}Co) leaching resulted from two succeeding mechanisms: as first order kinetic reaction, and then diffusion. The calculated values of leachability indices signify that the performance of each of the studied matrices is within an acceptable range. A simplified mathematical model, rooted in the first order reaction and diffusion mechanisms, was simulated to predict the radionuclides leaching rates from zeolite cement matrices. By comparing the synthesized zeolite cement with other cementitious materials, it can be concluded that the synthesized material can be classified as an efficient material suitable to immobilize {sup 85}Sr and {sup 60}Co from radioactive wastes. The acquired findings demonstrated that the studied immobilized waste matrices have acceptable mechanical effectiveness.

36 MATERIALS SCIENCE↗
DOE OSTI2019

The HANDE-QMC Project: Open-Source Stochastic Quantum Chemistry from the Ground State Up

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Electrostatic Barriers to Nanoparticle Accessibility of a Porous Matrix

Translocation from one cavity to another through a narrow constriction (i.e., a “hole”) represents the fundamental elementary process underlying hindered mass transport of nanoparticles and macromolecules within many natural and synthetic porous materials, including intracellular environments. This process is complex and may be influenced by long-range (e.g., electrostatic) particle–wall interactions, transient adsorption/desorption, surface diffusion, and hydrodynamic effects. In this study, we used a three-dimensional (3D) tracking method to explicitly visualize the process of nanoparticle diffusion within periodic porous nanostructures, where electrostatic interactions were mediated via ionic strength. The effects of electrostatic interactions on nanoparticle transport were surprisingly large. For example, an increase in the Debye length of only a few nanometers (in a material with a hole diameter of ~100 nm) increased the mean cavity escape time 3-fold. A combination of computational and experimental analyses indicated that this hindered cavity escape was due to an electrostatic energy barrier in the region of the hole, which was quantitatively explained using DLVO theory. These findings explicitly demonstrate that the cavity escape process was barrier-limited and dominated by electrostatic effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Kinetic theory of phase space plateaux in a non-thermal energetic particle distribution

The transformation of kinetically unstable plasma eigenmodes into hole-clump pairs with temporally evolving carrier frequencies was recently attributed to the emergence of an intermediate stage in the mode evolution cycle, that of an unmodulated plateau in the phase space distribution of fast particles. The role of the plateau as the hole-clump breeding ground is further substantiated in this article via consideration of its linear and nonlinear stability in the presence of fast particle collisions and sources, which are known to affect the production rates and subsequent frequency sweeping of holes and clumps. In particular, collisional relaxation, as mediated by e.g. velocity space diffusion or even simple Krook-type collisions, is found to inhibit hole-clump generation and detachment from the plateau, as it should. On the other hand, slowing down of the fast particles turns out to have an asymmetrically destabilizing/stabilizing effect, which explains the well-known result that collisional drag enhances holes and their sweeping rates but suppresses clumps. It is further demonstrated that relaxation of the plateau edge gradients has only a minor quantitative effect and does not change the plateau stability qualitatively, unless the edge region extends far into the plateau shelf and the corresponding Landau pole needs to be taken into account.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Entropic and gradient flow formulations for nonlinear diffusion

Nonlinear diffusion ∂{sub t}ρ = Δ(Φ(ρ)) is considered for a class of nonlinearities Φ. It is shown that for suitable choices of Φ, an associated Lyapunov functional can be interpreted as thermodynamic entropy. This information is used to derive an associated metric, here called thermodynamic metric. The analysis is confined to nonlinear diffusion obtainable as hydrodynamic limit of a zero range process. The thermodynamic setting is linked to a large deviation principle for the underlying zero range process and the corresponding equation of fluctuating hydrodynamics. For the latter connections, the thermodynamic metric plays a central role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗