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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗
NASA NTRS1977

The geopotential in nonsingular orbital elements

Singularities are eliminated from the geopotential and its partial derivatives for zero eccentricity and inclination, and an expression for the geopotential expansion based entirely on nonsingular orbital elements is developed. The argument relies on the treatments of the geopotential function given by Izsak (1964), Allan (1965) and Kaula (1966); the geopotential expansion developed does not involve mixed variables, and therefore does not require the chain rule to formulate the Lagrange planetary equations. The need for recursion relations to be used in conjunction with the nonsingular version of the geopotential expansion is also mentioned.

Nacozy, P. E.↗
DOE OSTI2014

Ground-state and dynamical properties of two-dimensional dipolar Fermi liquids

We study the ground-state properties of a two-dimensional spin-polarized fluid of dipolar fermions within the Euler–Lagrange Fermi-hypernetted-chain approximation. Our method is based on the solution of a scattering Schrödinger equation for the “pair amplitude” √(g(r)), where g(r) is the pair distribution function. A key ingredient in our theory is the effective pair potential, which includes a bosonic term from Jastrow–Feenberg correlations and a fermionic contribution from kinetic energy and exchange, which is tailored to reproduce the Hartree–Fock limit at weak coupling. Very good agreement with recent results based on quantum Monte Carlo simulations is achieved over a wide range of coupling constants up to the liquid-to-crystal quantum phase transition. Using the fluctuation–dissipation theorem and a static approximation for the effective inter-particle interactions, we calculate the dynamical density–density response function, and furthermore demonstrate that an undamped zero-sound mode exists for any value of the interaction strength, down to infinitesimally weak couplings. -- Highlights: •We have studied the ground state properties of a strongly correlated two-dimensional fluid of dipolar fermions. •We have calculated the effective inter-particle interaction and the dynamical density–density response function. •We have shown that an undamped zero sound mode exists at any value of the interaction strength.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Action principles for extended magnetohydrodynamic models

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

In situ transmission electron microscopy investigation of the interfacial reaction between Ni and Al during rapid heating in a nanocalorimeter

The Al/Ni formation reaction is highly exothermic and of both scientific and technological significance. In this report, we study the evolution of intermetallic phases in this reaction at a heating rate of 830 K/s. 100-nm-thick Al/Ni bilayers were deposited onto nanocalorimeter sensors that enable the measurement of temperature and heat flow during rapid heating. Time-resolved transmission electron diffraction patterns captured simultaneously with thermal measurements allow us to identify the intermetallic phases present and reconstruct the phase transformation sequence as a function of time and temperature. The results show a mostly unaltered phase transformation sequence compared to lower heating rates.

36 MATERIALS SCIENCE↗
NASA NTRS2006

Retrieving Storm Electric Fields from Aircrfaft Field Mill Data: Part II: Applications

The Lagrange multiplier theory developed in Part I of this study is applied to complete a relative calibration of a Citation aircraft that is instrumented with six field mill sensors. When side constraints related to average fields are used, the Lagrange multiplier method performs well in computer simulations. For mill measurement errors of 1 V m(sup -1) and a 5 V m(sup -1) error in the mean fair-weather field function, the 3D storm electric field is retrieved to within an error of about 12%. A side constraint that involves estimating the detailed structure of the fair-weather field was also tested using computer simulations. For mill measurement errors of 1 V m(sup -l), the method retrieves the 3D storm field to within an error of about 8% if the fair-weather field estimate is typically within 1 V m(sup -1) of the true fair-weather field. Using this type of side constraint and data from fair-weather field maneuvers taken on 29 June 2001, the Citation aircraft was calibrated. Absolute calibration was completed using the pitch down method developed in Part I, and conventional analyses. The resulting calibration matrices were then used to retrieve storm electric fields during a Citation flight on 2 June 2001. The storm field results are encouraging and agree favorably in many respects with results derived from earlier (iterative) techniques of calibration.

Koshak, William↗
NASA NTRS2010

A New Representative for Small-Body Gravity Estimation

One of the options proposed in the 2009 Review of the U. S. Human Spaceflight Plans Committee calls for the consideration of robotic and human missions to asteroids. Beginning in 2000, the NEAR Shoemaker spacecraft inserted into orbit about the asteroid 433 Eros, and studied it for a year before landing. The Hayabusa satellite journeyed to 25143 Itokawa, and operated in a proximity of the asteroid for several months before landing to collect a return sample. Additionally, the DAWN satellite, which was launched in 2007, will explore the dwarf-planet Ceres and the asteroid 4 Vesta in the next three years. These are just several examples of current interests in exploring asteroids. In this paper, we explore an alternative for estimating the gravity field of a small body using observations of an orbiting satellite. Our approach uses two new mathematical tools, the quadratures (on a sphere) invariant under the icosahedral group, and a multiresolution representation of the gravity potential. With the near optimal quadratures on the sphere, we minimize the number of parameters needed to recover a function. Also, instead of estimating the coefficients of the spherical harmonics, the new quadratures allow us to estimate directly the values of the gravity field since they offer an analogue of the Lagrange-type interpolation.

Jones, Brandon A.↗
DOE OSTI2019

Effect of Mach number and volume fraction in air-shock interacting with a bed of randomly distributed spherical particles

Shock-particle interaction is a fundamental problem in many engineering applications, with the dynamics being heavily influenced by the incident-shock Mach number and the particle volume fraction. In this paper we present fully resolved inviscid simulations of an incident-shock wave traveling through a bed of randomly distributed spherical particles. We vary the strength of the incident shock along with the particle volume fraction in order to study the complex wave interaction during shock-particle interaction. In this study we are interested in the early-time behavior during which the particles do not move and hence in our simulations all the particles are fixed in space. We compute the streamwise average of flow field quantities to generate the x - t contour plots to study the unsteady oscillations inside the particle bed. We observe that the transmitted shock slows down under certain conditions and it is partly due to tortuosity and partly due to weakening caused by energy dissipation. We also present the force histories of the streamwise drag and lift forces for all the particles. The random distribution of particles leads to high variability in the drag force experienced by the particles. We compute the mean peak drag force as a function of the streamwise location to study the mean behavior of the transmitted shock. Based on our findings, we propose simple modifications to improve the current point-particle models used in Euler-Lagrange simulations of shock interacting with a bed of particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility of the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 2

Two families of parametrized mixed variational principles for linear electromagnetodynamics are constructed. The first family is applicable when the current density distribution is known a priori. Its six independent fields are magnetic intensity and flux density, magnetic potential, electric intensity and flux density and electric potential. Through appropriate specialization of parameters the first principle reduces to more conventional principles proposed in the literature. The second family is appropriate when the current density distribution and a conjugate Lagrange multiplier field are adjoined, giving a total of eight independently varied fields. In this case it is shown that a conventional variational principle exists only in the time-independent (static) case. Several static functionals with reduced number of varied fields are presented. The application of one of these principles to construct finite elements with current prediction capabilities is illustrated with a numerical example.

Felippa, Carlos A.↗
DOE OSTI2018

On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains

Here, this work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function w:R → [0,1]. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Boundary node Petrov–Galerkin method in solid structures

Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Two charges on plane in a magnetic field: III. He{sup +} ion

The He{sup +} ion on a plane subject to a constant magnetic field B perpendicular to the plane is considered taking into account the finite nuclear mass. Factorization of eigenfunctions permits to reduce the four-dimensional problem to three-dimensional one. The ground state energy of the composite system is calculated in a wide range of magnetic fields from B=0.01 up to B=100a.u. and center-of-mass Pseudomomentum K from 0 to 1000 a.u. using a variational approach. The accuracy of calculations for B=0.1a.u. is cross-checked in Lagrange-mesh method and not less than five significant figures are reproduced in energy. Similarly to the case of moving neutral system on the plane a phenomenon of a sharp change of energy behavior as a function of K for a certain critical K{sub c} but a fixed magnetic field occurs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1997

The Nature and Evolutionary History of GRO J1744-28

GRO J1744-28 is the first known X-ray source to display bursts, periodic pulsations, and quasi-periodic oscillations. This source may thus provide crucial clues that will lead to an understanding of the differences in the nature of the X-ray variability from various accreting neutron stars. The orbital period is 11.8 days, and the measured mass function of 1.31 x 10(exp -4) solar mass is one of the smallest among all known binaries. If we assume that the donor star is a low-mass giant transferring matter through the inner Lagrange point, then we can show that its mass is lower than approximately 0.7 solar mass and probably closer to 0.25 solar mass. Higher mass, but unevolved, donor stars are shown to be implausible. We also demonstrate that the current He core mass of the donor star lies in the range of 0.20-0.25 solar mass. Thus, this system is most likely in the final stages of losing its hydrogen-rich envelope, with only a small amount of mass remaining in the envelope. If this picture is correct, then GRO J1744-28 may well represent the closest observational link that we have between the low-mass X-ray binaries and recycled binary pulsars in wide orbits. We have carried out a series of binary evolution calculations and explored, both systematically and via a novel Monte Carlo approach, the range of initial system parameters and input physics that can lead to the binary parameters of the present-day GRO J1744-28 system. The input parameters include both the initial total mass and the core mass of the donor star, the neutron-star mass, the strength of the magnetic braking, the mass-capture fraction, and the specifics of the core mass/radius relation for giants. Through these evolution calculations, we compute probability distributions for the current binary system parameters (i.e., the total mass, core mass, radius, luminosity, and K-band magnitude of the donor star, the neutron star mass, the orbital inclination angle, and the semimajor axis of the binary). Our calculations yield the following values for the GRO J1744-28 system parameters (with 95% confidence limits in parentheses): donor star mass: 0.24 solar mass (0.2-0.7 solar mass); He core mass of the donor star: 0.22 solar mass (0.20-0.25 solar mass); neutron-star mass: 1.7 solar mass (1.39-1.96 solar mass); orbital inclination angle: 18deg (7deg-22deg); semi- major axis: 64 lt-s (60-67 lt-s); radius of the donor star: 6.2 solar radius(6-9 solar radius); luminosity of donor star: 23 solar luminosity (15-49 solar luminosity), and long-term mass transfer rate at the current epoch: 5 x 10(exp -10)solar mass/yr (2 x 10(exp -10) to 5 x 10(exp -9)solar mass/yr). We deduce that the magnetic field of the underlying neutron star lies in the range of approximately 1.8 x 10(exp 11)G to approximately 7 x 10(exp 11)G, with a most probable value of 2.7 x 10(exp 11)G. This is evidently sufficiently strong to funnel the accretion flow onto the magnetic polar caps and suppress the thermonuclear flashes that would otherwise give rise to the type 1 X-ray bursts observed in most X-ray bursters. We present a simple paradigm for magnetic accreting neutron stars where X-ray pulsars, GRO J1744-28, the Rapid Burster, and the type 1 X-ray bursters may form a continuum of possible behaviors among accreting neutron stars, with the strength of the neutron-star magnetic field serving as a crucial parameter that determines the mode of X-ray variability from a given object.

Rappaport, S.↗
DOE OSTI2021

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1967

Program for calculating optimum dimensions of alpha radioisotope capsules exposed to varying stress and temperature

A method and computer program were developed for calculating the creep and optimizing the dimensions of capsules filled with alpha-emitting radioisotopes. The method solves an integral equation that was developed assuming linear accumulation of partial creep lives and relating life to time-dependent stress and temperature using the Larson-Miller parameter. The computer program, CAPSUL, is written in Fortran language for the IBM 360/75 computer. The program makes a least squares fit of the creep life function using conventional constant stress, constant temperature creep data. Dimensions of capsules having maximum thermal power per unit of weight, volume, or area are calculated for a given creep life and pressure-temperature history using a numerical Lagrange Multiplier formulation. The program also calculates the life to a prescribed strain for capsules of given dimensions and pressure-temperature history. The method has been used to analyze creep data for the alloys 304 stainless steel, Hastelloy N, Cb-1% Zr, FS-85, and T-222.

J. P. Nichols↗
NASA NTRS1995

Structural Optimization Using the Newton Modified Barrier Method

The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program.

Khot, N. S.↗
NASA NTRS1994

Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control

The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when possible, and initial conclusions regarding the accuracy and limitations of these models are given.

Heyliger, P. R.↗