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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fast estimation of reaction rates in spherical and non-spherical porous catalysts

Here we present a methodology for modeling multi-step reaction rates in porous catalyst particles for use in CFD-DEM and two fluid models. Single-step effectiveness factors based on a Thiele modulus, while useful, cannot accurately capture the cascading reaction systems common in high temperature vapor-phase chemical reactors like fluidized catalytic cracking units and catalytic biomass fast pyrolysis systems. Instead, multi-step effectiveness vectors derived from steady-state solutions to the governing reaction-diffusion equations are needed. Solutions for various catalyst shapes are presented, including spheres, cylinders, and prisms. Computational challenges inherent in repeated evaluation of reaction rates with diffusion limitations are discussed, and an efficient implementation based on pre-computed lookup tables is proposed and demonstrated on a simulation of a fluidized bed reactor. Open-source code is provided for the compilation of reaction rate tables for use in ODE, DEM, and two-fluid models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Application of implicit numerical techniques to the solution of the three-dimensional diffusion equation

Implicit techniques for calculating three-dimensional, time-dependent heat diffusion in a cube are tested with emphasis on storage efficiency, accuracy, and speed of calculation. For this purpose, a tensor product technique with both Chebyshev collocation and finite differences and a generalized conjugate gradient technique with finite differences are used in conjunction with Crank-Nicolson discretization. An Euler explicit finite difference calculation is performed for use as a benchmark. The implicit techniques are found to be competitive with the Euler explicit method in terms of storage efficiency and speed of calculation and offer advantages both in accuracy and stability. Mesh stretching in the finite difference calculations is shown to markedly improve the accuracy of the solution.

Peltier, Leonard Joel↗
NASA NTRS2000

Application of the Space-Time Conservation Element and Solution Element Method to One-Dimensional Convection-Diffusion Problems

In the space-time conservation element and solution element (CE/SE) method, the independent marching variables used comprise not only the mesh value of the physical dependent variables but also, in contrast to it typical numerical method, the Mesh values of the spatial derivatives of the physical variables The use of the extra marching variables results from the need to construct the two-level explicit and nondissipative schemes which are at the core of the CE/SE development. It also results from the need to minimize the stencil while maintaining accuracy. In this paper using the 1D(sub (alpha)-mu) scheme as an example, the effect of this added complication on consistency, accuracy and operation count is assessed. As part of this effort, an equivalent yet more efficient form of the alpha-mu scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced. Also, the intriguing relations that exist among the alpha-mu. Leapfrog, and DuFort-Frankel schemes are further explored. In addition, the redundance of the Leapfrog, DUFort-Frankel, and Lax scheme and the remedy for this redundance are discussed. This paper is concluded with the construction and evaluation of a CE/SE solver for the inviscid Burger equation.

Chang, Sin-Chung↗
NASA NTRS1982

Radiation effects studies for the high-resolution spectrograph

The generation and collection of charge carriers created during the passage of energetic protons through a silicon photodiode array are modeled. Pulse height distributions of noise charge collected during exposure of a digicon type diode array to 21 and 75 MeV protons were obtained. The magnitude of charge collected by a diode from each proton event is determined not only by diffusion, but by statistical considerations involving the ionization process itself. Utilizing analytical solutions to the diffusion equation for transport of minority carriers, together with the Vavilov theory of energy loss fluctuations in thin absorbers, simulations of the pulse height spectra which follow the experimental distributions fairly well are presented and an estimate for the minority carrier diffusion length L sub d is provided.

Smith, L. C.↗
NASA NTRS1987

Heat transfer to and from vegetated surfaces - An analytical method for the bulk exchange coefficients

The semianalytical model outlined in a previous study (Massman, 1987) to describe momentum exchange between the atmosphere and vegetated surfaces is extended to include the exchange of heat. The methods employed are based on one-dimensional turbulent diffusivities, and use analytical solutions to the steady-state diffusion equation. The model is used to assess the influence that the canopy foliage structure and density, the wind profile structure within the canopy, and the shelter factor can have upon the inverse surface Stanton number (kB exp -1), as well as to explore the consequences of introducing a scalar displacement height which can be different from the momentum displacement height. In general, the triangular foliage area density function gives results which agree more closely with observations than that for constant foliage area density. The intended application of this work is for parameterizing the bulk aerodynamic resistances for heat and momentum exchange for use within large-scale models of plant-atmosphere exchanges.

Massman, William J.↗
NASA NTRS2005

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

Atkins, H. L.↗
NASA NTRS1992

An analytic model of the neutral cloud evolution in the earth's atmosphere

An analytic model for the expansion of a chemically reacting gas in the upper atmosphere is discussed. The spatial-temporal distribution of released particles in the initial regime is described on the basis of self-similar solutions of Euler's equations. In the case of transition to the diffusion regime an approximate solution of the kinetic equation with the collision integral in the form of BGK is performed. Gravitation and the atmospheric inhomogeneity are taken into account, The diffusion regime is described by an analytic solution of the diffusion equation in an exponential atmosphere taking account of possible losses of the gas due to chemical reactions. Some peculiarities of the expansion of various gases as well as the possibility of applying the model for describing ionospheric 'holes' are discussed.

Bruskin, L. G.↗
NASA NTRS1992

A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

Felici, Helene Marie↗
NASA NTRS1973

Dynamics of moisture diffusion through a partially liquid filled porous matrix.

Models for unsteady water transport in fuel cell configurations of Bacon-Pratt and Whitney type are derived. Tests with a specially constructed isothermal cell producing no water and order of magnitude analysis show that diffusion through the liquid alone cannot account for the observed behavior. An analytical solution which includes diffusion in both the liquid and the gas spaces of the matrix is in better agreement with the data than models which consider diffusion in either the liquid or in the gas phase alone.

Murty, B. G. K.↗
NASA NTRS1986

Medium-energy electrons and heavy ions in Jupiter's magnetosphere - Effects of lower hybrid wave-particle interactions

A theory of medium-energy (about keV) electrons and heavy ions in Jupiter's magnetosphere is presented. Lower hybrid waves are generated by the combined effects of a ring instability of neutral wind pickup ions and the modified two-stream instability associated with transport of cool Iogenic plasma. The quasi-linear energy diffusion coefficient for lower hybrid wave-particle interactions is evaluated, and several solutions to the diffusion equation are given. Calculations based on measured wave properties show that the noise substantially modifies the particle distribution functions. The effects are to accelerate superthermal ions and electrons to keV energies and to thermalize the pickup ions on time scales comparable to the particle residence time. The S(2+)/S(+) ratio at medium energies is a measure of the relative contribution from Iogenic thermal plasma and neutral wind ions, and this important quantity should be determined from future measurements. The theory also predicts a preferential acceleration of heavy ions with an accleration time that scales inversely with the root of the ion mass. Electrons accelerated by the process contribute to further reionization of the neutral wind by electron impact, thus providing a possible confirmation of Alfven's critical velocity effect in the Jovian magnetosphere.

Barbosa, D. D.↗
NASA NTRS1972

Diffusion models for Jupiter's radiation belt

Solutions are given for the diffusion of trapped particles in a planetary magnetic field in which the first and second adiabatic invariants are preserved but the third is not, using as boundary conditions a fixed density at the outer boundary (the magnetopause) and a zero density at an inner boundary (the planetary surface). Losses to an orbiting natural satellite are included and an approximate evaluation is made of the effects of the synchrotron radiation on the energy of relativistic electrons. Choosing parameters appropriate to Jupiter, the electrons required to produce the observed synchrotron radiation are explained. If a speculative mechanism in which the diffusion is driven by ionospheric wind is the true explanation of the electrons producing the synchrotron emission it can be concluded that Jupiter's inner magnetosphere is occupied by an energetic proton flux that would be a serious hazard to spacecraft.

Jacques, S. A.↗
DOE OSTI2022

Heat conduction in an irregular magnetic field. Part 2. Heat transport as a measure of the effective non-integrable volume

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyse critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa _{\perp } \rightarrow 0$ , where $\kappa_{\perp}$ is the perpendicular diffusion coefficient. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Vacancy-mediated transport and segregation tendencies of solutes in FCC Ni under diffusional creep

Nickel-based alloys are known for their excellent corrosion resistance and high-temperature strength. However, at high temperatures, polycrystals experience grain boundary-stress-driven vacancy diffusion leading to diffusion-driven creep. Understanding the fundamentals of defect migration is essential to predict diffusion creep behavior. In this talk, we explore the Nabarro-Herring diffusion creep and the associated solute segregation that is likely to result from the different diffusivities of the solute and solvent elements. Density functional theory calculations are performed to determine the formation, migration and binding energies of the solute and vacancy defects in stress-free and stressed states. The dilute-limit transport coefficients are then calculated using the self-consistent mean field theory as implemented in the Kinetic Cluster Expansion (KineCluE) code. Predictions of diffusion creep strain rates and solute segregation are then presented for various solutes, stress and temperatures. This work opens research avenues for exploration of diffusion creep via characterization of elemental segregation to grain boundaries.

36 MATERIALS SCIENCE↗
NASA NTRS2023

Homogeneity Study of ZrC, NbC, and TaC Binary Carbide Fuels for the Application of Nuclear Thermal Propulsion

In alignment with NASA and DARPA goals, efforts towards Nuclear Thermal Propulsion (NTP) have increased in recent years. As progress is made, a main challenge still exists; the fuel in an NTP system must survive the extreme environment experienced during operating conditions. Three fuel forms have been studied including a ceramic-metallic matrix, a ceramic-ceramic matrix, and solid solution carbides. Solid solution carbides were studied previously as a fuel for NTP and was shown to be a promising technology; however, the programs were canceled before demonstration in an NTP engine test. Of the refractory metal carbides of interest, zirconium carbide (ZrC), niobium carbide (NbC) and tantalum carbide (TaC) were studied. ZrC, NbC, and TaC powders were consolidated in monocarbide (ZrC, NbC, TaC) and bi-carbide (ZrC-NbC, ZrC-TaC, NbC-TaC) forms using spark plasma sintering (SPS), with 50-50 mol% compositions of the bi-carbides of interest. The time and temperature conditions to achieve a completely homogeneous solid solution for the mixed carbides is of interest for NTP fuel applications, since this homogeneity is considered to be essential for this fuel form. Homogeneity is typically not achieved during sintering, as surface diffusion (predominant for sintering to near ideal density) tends to occur at lower temperatures than bulk volumetric diffusion (required for solute interdiffusion to achieve a homogeneous solid solution). High temperature isochronal annealing was performed to identify the conditions to achieve a chemically homogeneous sample. The solute interpenetration vs annealing temperature was quantified using energy dispersion spectroscopy (EDS) in a scanning electron microscope (SEM). X-ray diffraction (XRD) was used to accurately measure the phase stability and lattice parameter as a function of annealing conditions. The diffusion data from each sample was then used to determine self-diffusion coefficients for interdiffusion of the Nb, Zr, and Ta solutes and compared to existing literature values. The minimum annealing conditions to achieve complete chemical homogeneity for each carbide was determined.

nuclear thermal propulsion↗
DOE OSTI2020

A Particle-Based Conditional Sampling Scheme for the Simulation of Transport in Fractured Rock With Diffusion Into Stagnant Water and Rock Matrix

In situ experiments and field-scale characterization studies have pointed out that, in fractured crystalline media, groundwater flow is highly channelized. This implies that, at the scale of a single fracture, only part of the fracture surface area is in contact with flowing water, while the rest of in-plane water is essentially stagnant and can be accessed by solutes via molecular diffusion. Despite their importance for contaminant retention, to date, there are no numerical or analytical approaches that could be used to assess the implication of stagnant water zones on solute transport in realistic large-scale Discrete Fracture Network-based models. In this study, we present an efficient and flexible algorithm for the simulation of transport in fractured rock with diffusion into stagnant water and rock matrix. The algorithm is a generalization of a previously developed numerical framework for time domain particle tracking in sparsely fractured rock. The key of the generalization is that total time in fracture (τ f ) is first evaluated using a Monte Carlo sampling and then a second sampling is performed conditioned on τ f . The algorithm has been successfully validated against existing independent solutions and the implication of diffusion into stagnant water and secondary diffusion into the matrix has been assessed for a realistic modeling scenario. The results show that, due to diffusion into stagnant water, contaminants are more strongly retarded. This increased retention is more significant for sorbing species, as a larger number of sorption sites is accessible. A high sensitivity to the flowing channel/stagnant water zone geometry has also been observed.

54 ENVIRONMENTAL SCIENCES↗