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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

The thermal stability of coronal loops by nonlinear diffusion asymptotics

A nonlinear reaction-diffusion equation and some additional constraints are derived which describe the time-dependent behavior of the temperature structure of the plasma in coronal loops. The equation is analyzed using nonlinear diffusion asymptotics, in particular singular perturbation techniques, and the results are interpreted in the context of the physical problem of the thermal stability and temporal behavior of the plasma. The results are consistent with the possibility of cyclic thermal behavior of the plasma, as suggested by Kuin and Martens (1982).

Pakkert, J. W.↗
NASA NTRS1994

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Max J. Suarez↗
NASA NTRS1999

A Textbook for a First Course in Computational Fluid Dynamics

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Zingg, D. W.↗
NASA NTRS1975

Cratering and cosmogenic nuclides

A simple probabilistic model was constructed for the average value of a cosmogenic nuclide as a function of depth in a regolith. An arbitrary function was chosen for the size distribution of craters. The resulting integro-differential equation was found to reduce in limiting cases to the marching equation with a characteristic residence time and to the diffusion equation. The regolith diffusion constant is shown to be a simple integral of the cratering rate weighted by geometrical terms. This formal treatment provides a direct and general connection between cosmogenic nuclides and cratering rates and crater population in a simple analytical form. The validity of this model remains to be tested.

Blake, M. L.↗
DOE OSTI2016

STOCHASTIC PARTICLE ACCELERATION IN TURBULENCE GENERATED BY MAGNETOROTATIONAL INSTABILITY

We investigate stochastic particle acceleration in accretion flows. It is believed that magnetorotational instability (MRI) generates turbulence inside accretion flows and that cosmic rays (CRs) are accelerated by the turbulence. We calculate equations of motion for CRs in the turbulent fields generated by MRI with the shearing box approximation and without back reaction to the field. Our results show that the CRs randomly gain or lose their energy through interaction with the turbulent fields. The CRs diffuse in the configuration space anisotropically: the diffusion coefficient in the direction of the unperturbed flow is about 20 times higher than the Bohm coefficient, while those in the other directions are only a few times higher than the Bohm. The momentum distribution is isotropic and its evolution can be described by the diffusion equation in momentum space where the diffusion coefficient is a power-law function of the CR momentum. We show that the shear acceleration works efficiently for energetic particles. We also cautiously note that in the shearing box approximation, particles that cross the simulation box many times along the radial direction undergo unphysical runaway acceleration by the Lorentz transformation, which needs to be taken into account with special care.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

An improved iterative HDG approach for partial differential equations

Here we propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work [45] in several directions: 1) the improved iHDG approach converges in a finite number of iterations for the scalar transport equation; 2) it is unconditionally convergent for both the linearized shallow water system and the convection–diffusion equation; 3) it has improved stability and convergence rates; 4) we uncover a relationship between the number of iterations and time stepsize, solution order, meshsize and the equation parameters. This allows us to choose the time stepsize such that the number of iterations is approximately independent of the solution order and the meshsize; and 5) we provide both strong and weak scalings of the improved iHDG approach up to 16,384 cores. A connection between iHDG and time integration methods such as parareal and implicit/explicit methods are discussed. Extensive numerical results for linear (and nonlinear) PDEs are presented to verify the theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Derivation of the Point-Kinetics Parameters for the Coupled Reactors

The design of coupled reactors, which provide two distinct spectral zones (fast and thermal), has recently drawn attention because it can provide configurations that could not be met in current thermal neutron test reactors and thus allows versatile irradiation tasks. A coupled reactor core is characterized by the neutron multiplicity of each zone as well as by the coupling between the two zones. It is desired to evaluate the integral point kinetics parameters that characterize the neutron physics of the coupled system. This summary provides a derivation of the equations for evaluating these point kinetics parameters. Following the strong and the weak form of the multigroup diffusion equation, the weak forms for the partial forward and adjoint solutions, each for a particular active region of the reactor core, are derived. These partial solutions are then used to collapse the weak form into the coupled-reactor point kinetics equations with the approximation of equilibrium. It is noted that these parameters are not meant for transient analysis because of the equilibrium approximation. They are rather used for characterizing the coupled system. The derived reactivity equations are then compared with those in Ref. 1. The equations are implemented in Rattlesnake, the INL MOOSE-based radiation transport application for multi-physics simulations. Numerical results are presented for a simple two-group problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

AZTRAN and AZKIND verification with a BWR study case

The AZTLAN Platform project is a national initiative led by the National Institute of Nuclear Research which gather the main public institutions of higher education in Mexico: the National Polytechnic Institute, the National Autonomous University of Mexico and the Autonomous Metropolitan University. It consists in the development of a modeling platform for the analysis and design of nuclear reactors. This project aims to modernize, improve and integrate the neutronic, thermohydraulics and thermomechanical codes, developed in the national institutions, in a platform integrated and developed by Mexican experts. The development of AZTLAN Platform is divided technically into four working groups: neutronics, thermohydraulics, coupling and uncertainty analysis, and users group. The present work is the result of the activities of the Users Group focused on the follow-up, testing and use of the different codes (modules) being developed under the AZTLAN project; with the objective of providing feedback and to suggest development priorities to the team of developers, as well as to promote collaboration and synergy between the participating institutions. In particular, in this work, the AZTRAN and the AZKIND modules were verified and tested against the results of well-known codes of the nuclear industry for boiling water reactor (BWR) models. AZTRAN is a 3D transport code which solves numerically the multi-group time independent neutron transport equation in Cartesian geometry, based on the discrete ordinates (SN) method and the RTN-0 nodal scheme. AZKIND is a 3D diffusion code that solves numerically the time dependent neutron diffusion equations in Cartesian geometry, based on a Galerkin Finite Element Method using the RTN-0 polynomial nodal approximation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

An analytical method as a preconditioning modeling for systems of linear equations

In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection–diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Overcoming element quality dependence of finite elements with adaptive extended stencil FEM (AES‐FEM)

Summary The finite element methods (FEMs) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES‐FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial basis functions , which we construct using local weighted least‐squares approximations. The method preserves the theoretical framework of FEM and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES‐FEM can use higher‐degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES‐FEM and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poisson equation and a time‐independent convection–diffusion equation. The numerical results demonstrate that AES‐FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor‐quality meshes. Copyright © 2016 John Wiley & Sons, Ltd.

Conley, Rebecca↗
DOE OSTI2015

Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients

In this study, we extend some of the multilevel convergence results obtained by Xu and Zhu, to the case of second order linear reaction-diffusion equations. Specifically, we consider the multilevel preconditioners for solving the linear systems arising from the linear finite element approximation of the problem, where both diffusion and reaction coefficients are piecewise-constant functions. We discuss in detail the influence of both the discontinuous reaction and diffusion coefficients to the performance of the classical BPX and multigrid V-cycle preconditioner.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 1: The 1-D case

In this first part of two papers, we extend the C-method developed in for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities in one space dimension. For gas dynamics, the C-method couples the Euler equations to a scalar reaction-diffusion equation, whose solution C serves as a space-time smooth artificial viscosity indicator. The purpose of this paper is the development of a high-order numerical algorithm for shock-wall collision and bounce-back. Specifically, we generalize the original C-method by adding a new collision indicator, which naturally activates during shock-wall collision. Additionally, we implement a new high-frequency wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We show that our scheme improves the order of accuracy of our WENO algorithm, handles extremely strong discontinuities (ranging up to nine orders of magnitude), allows for shock collision and bounce back, and removes high frequency noise. The causes of the well-known “wall heating” phenomenon are discussed, and we demonstrate that this particular pathology can be effectively treated in the framework of the C-method. This method is generalized to two space dimensions in the second part of this work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Spatial Resolution Versus Data Acquisition Efficiency in Mapping an Inhomogeneous System with Species Diffusion

Traditionally, spatially-resolved photoluminescence (PL) has been performed using a point-by-point scan mode with both excitation and detection occurring at the same spatial location. But with the availability of high quality detector arrays like CCDs, an imaging mode has become popular for performing spatially-resolved PL. By illuminating the entire area of interest and collecting the data simultaneously from all spatial locations, the measurement efficiency can be greatly improved. However, this new approach has proceeded under the implicit assumption of comparable spatial resolution. We show here that when carrier diffusion is present, the spatial resolution can actually differ substantially between the two modes, with the less efficient scan mode being far superior. We apply both techniques in investigation of defects in a GaAs epilayer – where isolated singlet and doublet dislocations can be identified. A superposition principle is developed for solving the diffusion equation to extract the intrinsic carrier diffusion length, which can be applied to a system with arbitrarily distributed defects. The understanding derived from this work is significant for a broad range of problems in physics and beyond (for instance biology) – whenever the dynamics of generation, diffusion, and annihilation of species can be probed with either measurement mode.

14 SOLAR ENERGY↗
DOE OSTI2015

Interpretation of thermoreflectance measurements with a two-temperature model including non-surface heat deposition

We develop a solution to the two-temperature diffusion equation in axisymmetric cylindrical coordinates to model heat transport in thermoreflectance experiments. Our solution builds upon prior solutions that account for two-channel diffusion in each layer of an N-layered geometry, but adds the ability to deposit heat at any location within each layer. We use this solution to account for non-surface heating in the transducer layer of thermoreflectance experiments that challenge the timescales of electron-phonon coupling. A sensitivity analysis is performed to identify important parameters in the solution and to establish a guideline for when to use the two-temperature model to interpret thermoreflectance data. We then fit broadband frequency domain thermoreflectance (BB-FDTR) measurements of SiO{sub 2} and platinum at a temperature of 300 K with our two-temperature solution to parameterize the gold/chromium transducer layer. We then refit BB-FDTR measurements of silicon and find that accounting for non-equilibrium between electrons and phonons in the gold layer does lessen the previously observed heating frequency dependence reported in Regner et al. [Nat. Commun. 4, 1640 (2013)] but does not completely eliminate it. We perform BB-FDTR experiments on silicon with an aluminum transducer and find limited heating frequency dependence, in agreement with time domain thermoreflectance results. We hypothesize that the discrepancy between thermoreflectance measurements with different transducers results in part from spectrally dependent phonon transmission at the transducer/silicon interface.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Designing High-Efficiency Thin Silicon Solar Cells Using Parabolic-Pore Photonic Crystals

We demonstrate the efficacy of wave-interference-based light trapping and carrier transport in parabolic-pore photonic-crystal, thin-crystalline silicon (c -Si) solar cells to achieve above 29% power conversion efficiencies. Using a rigorous solution of Maxwell’s equations through a standard finite-difference time domain scheme, we optimize the design of the vertical-parabolic-pore photonic crystal (PhC) on a 10 μm -thick (c -Si) solar cell to obtain a maximum achievable photocurrent density (MAPD) of 40.6 mA/cm 2 beyond the ray-optical, Lambertian light-trapping limit. For a slanted-parabolic-pore PhC that breaks x-y symmetry, improved light trapping occurs due to better coupling into parallel-to-interface refraction modes. We achieve the optimum MAPD of 41.6 mA/cm 2 for a tilt angle of 10° with respect to the vertical axis of the pores. This MAPD is further improved to 41.72 mA/cm 2 by introducing a 75-nm SiO 2 antireflective coating on top of the solar cell. We use this MAPD and the associated charge-carrier generation profile as input for a numerical solution of Poisson’s equation coupled with semiconductor drift-diffusion equations using a Shockley-Read-Hall and Auger recombination model. Using experimentally achieved surface recombination velocities of 10 cm/s, we identify semiconductor doping profiles that yield power conversion efficiencies over 29%. Practical considerations of additional upper-contact losses suggest efficiencies close to 28%. This improvement beyond the current world record is largely due to an open-circuit voltage approaching 0.8 V enabled by reduced bulk recombination in our thin silicon architecture while maintaining a high short-circuit current through wave-interference-based light trapping.

14 SOLAR ENERGY↗
DOE OSTI2018

Longitudinal dynamics of high baryon density matter in high-energy heavy-ion collisions

In high-energy heavy-ion collisions, the two colliding nuclei pass through each other leaving behind an almost baryon-free central rapidity region. Most of the baryons are carried away by the nuclear remnants and are located in the so-called fragmentation regions. In previous papers, it has been argued that very high baryon densities, more than ten times larger than the normal nuclear density, can be achieved in these fragmentation regions. In this paper, we assume the high baryon density matter is thermalized at the same time as the baryon-free quark-gluon plasma in the central rapidity region. We perform a 1+1D (temporal + longitudinal) hydrodynamic simulation covering both the fragmentation regions and the central rapidity region with the baryon diffusion equation included. Baryons are found to diffuse from the fragmentation regions to the central rapidity region driven by fugacity gradients. Here, the baryon chemical potential at freezeout monotonically increases from the central rapidity region to the fragmentation regions, suggesting a rapidity scan in high-energy heavy-ion collisions might be helpful in searching for the critical point of the quantum chromodynamics phase diagram.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Ionization waves in low-current dc discharges in noble gases obtained with a hybrid kinetic-fluid model

A hybrid kinetic-fluid model is used to study ionization waves (striations) in a low-current plasma column of dc discharges in noble gases. Coupled solutions of a kinetic equation for electrons, a drift-diffusion equation for ions, and a Poisson equation for the electric field are obtained to clarify the nature of plasma stratification in the positive column. A simplified two-level excitation-ionization model is used for the conditions when the nonlinear effects due to stepwise ionization, gas heating, and Coulomb interactions among electrons are negligible. It is confirmed that the nonlocal effects are responsible for the formation of moving striations in dc discharges at low plasma densities and low values of pR (the product of gas pressure and tube radius). Here, the calculated properties of self-excited waves of S–, P–, and R types in neon and S type in argon agree with available experimental data. The reason for helium plasma stability to stratification is clarified. It is shown that sustaining stratified plasma is more efficient than striation-free plasma when the ionization rate is a nonlinear function of the electric field. However, the nonlinear dependence of the ionization rate on the electric field is not required for plasma stratification. Striations of S–, P–, and R types in neon exist with minimal or no ionization enhancement. Effects of the column length and plasma density on the wave properties are demonstrated.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗