Search NASA⌕ Search

SEARCH · Search NASA

Results for “Higher order calculations”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Evaluating Shallow Convection Parameterization Assumptions With a q t – w Quadrant Analysis

Abstract Uncertainties associated with the response of shallow clouds to global warming remain a great challenge for climate projection. Due to the small size of these clouds, parameterizations are required to represent them in both current‐ and next‐generation climate models. We present a quantitative evaluation of several important assumptions used in both mass‐flux and Assumed‐PDF Higher‐Order Closure parameterizations of shallow convection. We use large‐eddy simulations (LESs) of four different shallow convection regimes as benchmarks and apply a q t (total moisture)– w (vertical velocity) quadrant analysis technique to identify the “coherent structures” of moist and dry up/down‐drafts. The statistics of these coherent structures and the environment are then used to evaluate commonly used assumptions in mass‐flux parameterizations related to (a) the convective downdrafts and (b) the subplume variability of convective updrafts. For quantitative evaluation of the PDF closure used in AP‐HOCs, we perform offline calculations with the PDF closure used in the Cloud Layers Unified By Bi‐normals and the Simplified Higher‐Order Closure schemes by supplying the closure with statistical quantities directly calculated from the LESs. Then, the impact of parameterization assumptions embedded in the PDF closure in the same two categories is analyzed and understood through comparisons of the output from the closure with the statistics of the moist and dry up/down‐drafts from the LESs.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1980

Investigations of medium wavelength magnetic anomalies in the eastern Pacific using MAGSAT data

The computer program package for dealing with MAGSAT data was refined and a program listing and deck of cards was forwarded for use by interested investigators. Instead of doing equivalent source calculations, it is proposed to use spherical harmonics to model the observed data since spherical harmonic functions are orthogonal and addition of higher degree and order harmonics can be done without recalculation of the harmonics of lower degree and order already calculated. These functions are much more easy to manipulate in that the height of the term of the observation can be taken care of with great facility. Downward calculation (after suitable filtering) can also be performed very simply.

Harrison, C. G. A.↗
DOE OSTI2023

Thermodynamic modeling of KCl-PrCl 3 and KCl-LiCl-PrCl 3 systems

Molten salt electrolysis can recover the actinides from spent nuclear fuels, and it involves a eutectic LiCl-KCl in molten form as an electrolyte. During reprocessing, the concentration of fission products such as La, Nd, Pr, etc., increases and affects the recovery efficiency of the electrolyte. In this work, thermodynamic modeling of KCl-PrCl 3 and KCl-LiCl-PrCl 3 systems was carried out using the CALPHAD (Calculation of Phase Diagrams) approach for the first time. The thermodynamic functions for the pure salts were taken from the SGTE (Scientific Group Thermodata Europe) Substances (SSUB) database. The experimental thermochemical and phase equilibria data available in the literature were used as input for the assessment of KCl-PrCl 3 and KCl-LiCl-PrCl 3 systems. The model parameters for the KCl-LiCl system were adjusted to include the new Gibbs energy descriptions for the pure salts. In addition, the sublattice model for the liquid phase in the LiCl-PrCl 3 system was modified and reassessed to ensure the model compatibility for higher-order extrapolation. There is a good agreement between the experimental and calculated thermochemical and phase diagram data for all the optimized constituent binaries and the ternary system. Furthermore, this work will be beneficial for determining the solubility limit of PrCl 3 in molten LiCl-KCl electrolytes and their thermodynamic properties for improving the efficiency of the pyrochemical process.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Time-interval distributions in a digital gamma multi-channel analyzer at extreme input rates

Here, this study explores the relationship between experimentally observed inter-event time-interval distributions (TIDs) and measured dead times for pulses generated by a HPGe gamma detector and processed by a digital spectrometer. The system utilizes a fast and slow channel, pile-up rejector, trapezoid filtering, and flash analog-to-digital converter. The experimentally derived TIDs were compared with theory for validation. The results demonstrate that the theoretical model reliably describes measured TIDs up to 40% dead time. However, significant distortion effects become increasingly pronounced at higher input rates. It appears that the deviation between the measured and calculated time-interval distributions take the shape of higher-order convolutions of the TID, which represent the time difference between counts for more than two successive events. In this work, theoretical functions for the TID are expanded to reproduce measurements up to 90%. This refinement in the interpretation and treatment of the measured TIDs provides improved accuracy and precision in the prediction of the true event rate and measured dead time in the counter. Even though it reflects occasional count loss that is specific to the set-up, it is expected that a similar adjustment may be applicable to other detection systems as well.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1988

A comparison between onestep and other multiconic trajectory propagation methods

The paper presents an optimized version of the one-step multiconic method of spacecraft trajectory propagation in the presence of two attracting bodies. This method is compared to eleven other methods ranging from simple conic propagation to full integration of the equations of motion by applying the methods to a wide variety of test cases taken from planned space missions. This optimize one-step method is shown to be an order of magnitude better than other single-step methods for interplanetary and most lunar trajectories. Multistep multiconics methods and integration of the state offer another order of magnitude improvement, but at a proportionally higher cost and calculation time.

Kiedron, Krystyna↗
NASA NTRS1990

Dynamic Analysis and Control of Lightweight Manipulators with Flexible Parallel Link Mechanisms

The objective is the theoretical analysis and the experimental verification of dynamics and control of a two link flexible manipulator with a flexible parallel link mechanism. Nonlinear equations of motion of the lightweight manipulator are derived by the Lagrangian method in symbolic form to better understand the structure of the dynamic model. The resulting equation of motion have a structure which is useful to reduce the number of terms calculated, to check correctness, or to extend the model to higher order. A manipulator with a flexible parallel link mechanism is a constrained dynamic system whose equations are sensitive to numerical integration error. This constrained system is solved using singular value decomposition of the constraint Jacobian matrix. Elastic motion is expressed by the assumed mode method. Mode shape functions of each link are chosen using the load interfaced component mode synthesis. The discrepancies between the analytical model and the experiment are explained using a simplified and a detailed finite element model.

Lee, Jeh Won↗
NASA NTRS1991

Toward a formal verification of a floating-point coprocessor and its composition with a central processing unit

Discussed here is work to formally specify and verify a floating point coprocessor based on the MC68881. The HOL verification system developed at Cambridge University was used. The coprocessor consists of two independent units: the bus interface unit used to communicate with the cpu and the arithmetic processing unit used to perform the actual calculation. Reasoning about the interaction and synchronization among processes using higher order logic is demonstrated.

Pan, Jing↗
NASA NTRS1995

Parametric studies of stitching effectiveness for preventing substructure disbond

A methodology is desired that will allow a designer to select appropriate amounts of through-thickness reinforcement needed to meet design requirements. The goal is to use a relatively simple analysis to minimize the amount of testing that needs to be performed, and to make test results from simple configurations applicable to more general structures. Using this methodology one should be able to optimize the selection of stitching materials, the weight of the yarn, and the stitching density. The analysis approach is to treat substructure disbond as a crack propagation problem. In this approach, the stitches have little influence until a delamination begins to grow. Once the delamination reaches, or extends beyond a stitch, the stitch serves to reduce the strain-energy-release-rate (G) at the crack tip for a given applied load. The reduced G can then be compared to the unstitched materials toughness to predict the load required to further extend the crack. The current model treats the stitch as a simple spring which responds to displacements in the vertical (through-thickness) direction. In concept, this approach is similar to that proposed by other authors. Test results indicate that the model should be refined to include the shearing stiffness of the stitch. The strain-energy-release-rate calculations are performed using a code which uses interconnected higher-order plates to model built-up composite cross-sections. When plates are stacked vertically, the interfacial tractions between the plates can be computed. The plate differential equations are solved in closed-form. The code, called SUBLAM, was developed as part of this section in one dimension. Because of this limitation, rows of stitches are treated as a two-dimensional sheet. The spring stiffness of a row of stitches can be estimated from the stitch material, weight, and density. As a practical and conservative approach, we can assume that the stitch is bonded until a crack passes the stitch location. After the crack passes, it is fully bonded. A series of tests were performed to exercise this methodology and incorporated an attached flange such that the sudden change in thickness initiated a delamination. The analysis was used to estimate the materials' critical G from that of the unstitched specimens. With this data, a prediction was made for the load required to delaminate the stitched specimens. Using the methodology, design charts have been created for simplified geometries. These charts give stitch force, along with G(sub 1) and G(sub 2) as as function of the stitch spring stiffness. Using the charts, it should be possible to determine the stitch spring stiffness and strength required to reduce the G to a desired level. From these parameters, the actual stitching material, weight, and density can be computed.

Flanagan, Gerry↗
NASA NTRS1994

Higher order moments of the matter distribution in scale-free cosmological simulations with large dynamic range

We calculate reduced moments (xi bar)(sub q) of the matter density fluctuations, up to order q = 5, from counts in cells produced by particle-mesh numerical simulations with scale-free Gaussian initial conditions. We use power-law spectra P(k) proportional to k(exp n) with indices n = -3, -2, -1, 0, 1. Due to the supposed absence of characteristic times or scales in our models, all quantities are expected to depend on a single scaling variable. For each model, the moments at all times can be expressed in terms of the variance (xi bar)(sub 2), alone. We look for agreement with the hierarchical scaling ansatz, according to which ((xi bar)(sub q)) proportional to ((xi bar)(sub 2))(exp (q - 1)). For n less than or equal to -2 models, we find strong deviations from the hierarchy, which are mostly due to the presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also found in n greater than or equal to -1 models. The wide range of spectra considered and the large dynamic range, with careful checks of scaling and shot-noise effects, allows us to reliably detect evolution away from the perturbation theory result.

Lucchin, Francesco↗
NASA NTRS1977

A critical study of higher-order numerical methods for solving the boundary-layer equations

A fourth-order box method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations. The efficiency of the present method is compared with other two-point and three-point higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, and the three-point spline methods. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.

Wornom, S. F.↗
DOE OSTI2024

A precise measurement of the Z -boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS experiment at $\sqrt{s}=8$ TeV

This paper presents for the first time a precise measurement of the production properties of the Z boson in the full phase space of the decay leptons. This is in contrast to the many previous precise unfolded measurements per formed in the fiducial phase space of the decay leptons. The measurement is obtained from proton–proton collision data collected by the ATLAS experiment in 2012 at $\sqrt{s}$ = 8 TeV at the LHC and corresponding to an integrated luminosity of 20.2 fb -1 . The results, based on a total of 15.3 million Z boson decays to electron and muon pairs, extend and improve a previous measurement of the full set of angular coefficients describing Z-boson decay. The double-differential cross section distributions in Z-boson transverse momentum pT and rapidity y are measured in the pole region, defined as 80 < m ℓℓ < 100 GeV, over the range |y| < 3.6. The total uncertainty of the normalised cross-section measurements in the peak region of the pT distribution is dominated by statistical uncertainties over the full range and increases as a function of rapidity from 0.5–1.0% for |y| < 2.0 to 2 - 7% at higher rapidities. The results for the rapidity-dependent transverse momentum distributions are compared to state of-the-art QCD predictions, which combine in the best cases approximate N 4 LL resummation with N 3 LO fixed-order per turbative calculations. The differential rapidity distributions integrated over pT are even more precise, with accuracies from 0.2–0.3% for |y| < 2.0 to 0.4–0.9% at higher rapidities, and are compared to fixed-order QCD predictions using the most recent parton distribution functions. The agreement between data and predictions is quite good in most cases.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1990

Postbuckling response of long thick isotropic plates loaded in compression including higher order transverse shearing effects

Buckling and postbuckling results for aluminum plates loaded in compression are presented. The buckling results were plotted to show the effects of thickness on the stress coefficient. Buckling results are given for various length-to-width ratios. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. The plates are considered to be long with side edges simply supported, with edges free of stress and the plates are subjected to longitudinal compressive displacement. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman, first-order shear deformation, higher-order shear deformation, and three-dimensional flexibility. Present results indicate that the three-dimensional flexibility theory gives the lowest and therefore, most accurate results. The higher-order shear deformation theory has fewer unknowns than the three-dimensional flexibility but is not as accurate. The figures presented show that small differences occur in the maximum stress resultants and the transverse displacements calculated when the effects of transverse shear are included.

Stein, Manuel↗
NASA NTRS1972

Corrections to vibrational transition probabilities calculated from a three-dimensional model.

Corrections to the collision-induced vibration transition probability calculated by Hansen and Pearson from a three-dimensional semiclassical model are examined. These corrections come from the retention of higher order terms in the expansion of the interaction potential and the use of the actual value of the deflection angle in the calculation of the transition probability. It is found that the contribution to the transition cross section from previously neglected potential terms can be significant for short range potentials and for the large relative collision velocities encountered at high temperatures. The correction to the transition cross section obtained from the use of actual deflection angles will not be appreciable unless the change in the rotational quantum number is large.

Stallcop, J. R.↗
NASA NTRS1974

Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method. Part 2. User's manual for computer program

The surface-source method of calculating potential flow is improved by refining the underlying numerical analysis. The present analysis uses parabolic elements and linearly-varying source density which results in a large increase in computing speed and accuracy. The computer program including all relevant input and output is described.

Friedman, D. M.↗
DOE OSTI2024

Patterned dielectric back contact design for GaAs thermophotovoltaic devices

-Patterned-dielectric back contact structures in optoelectronic devices are designed to boost the reflectance of light from the device back surface while retaining a low-resistance pathway for electrical conductance. Their reduced light absorption at near- and sub-bandgap photon energies leads to improved luminescence in light-emitting diodes, greater photon recycling, voltage, and efficiency in photovoltaic cells, and greater recuperation of unabsorbed sub-bandgap light in thermophotovoltaic (TPV) systems. However, diffraction from the patterned features can deflect incident light in propagation directions that lead to light trapping and parasitic absorption in the cell. Here, in this article, we use rigorous coupled-wave analysis (RCWA) to study three-dimensional diffractive scattering of electromagnetic waves by periodic metal point-contact gratings on 1.42-eV GaAs TPV cells, to analyze their effect on unwanted sub-bandgap absorption in order to achieve higher TPV system efficiency. Solutions of Maxwell's equations calculated using RCWA are compared to measured sub-bandgap reflectance in experimental GaAs TPV devices with varying metal point-contact diameters and spacing. Modeling and experiments indicate decreased total reflectance due to these diffractive effects for a small point contact diameter of 1 μm, and this effect is much stronger at higher contact coverage fractions.

14 SOLAR ENERGY↗
NASA NTRS1989

Numerical simulation of rotorcraft

The objective of the research is to develop and validate accurate, user-oriented viscous CFD codes (with inviscid options) for three-dimensional, unsteady aerodynamic flows about arbitrary rotorcraft configurations. Unsteady, three-dimensional Euler and Navier-Stokes codes are developed, adapted, and extended to rotor-body combinations. Flow solvers are coupled with zonal grid topologies, including rotating and nonrotating blocks. Special grid clustering and wave-fitting techniques were developed to capture low-level radiating acoustic waves. Significant progress was made in computing the propagation of acoustic waves due to the interaction of a concentrated vortex and a helicopter airfoil. The need for higher-order schemes was firmly established in relatively inexpensive two-dimensional calculations. In three dimensions, the number of grid points required to capture the low-level acoustic waves becomes very large, so that large supercomputer memory becomes essential. Good agreement was obtained between the numerical results obtained with a thin-layer Navier-Stokes code and experimental data from a model rotor. In addition, several nonrotating configurations that are sometimes proposed to simulate rotor blade tips in conventional wind tunnels were examined, and the complex flow around the radical tip shape of the world's fastest helicopter is under investigation. These studies demonstrate the flexibility and power of CFD to gain physical insight, study novel ideas, and examine various possibilities that might be difficult or impossible to set up in physical experiments. As a prelude to studies of rotor-body aerodynamic interactions, a preliminary grid topology and moving-interface strategy were developed. A new Euler/Navier-Stokes code using these techniques computes the vortical wake directly, rather than modeling it, as in most previous rotorcraft studies. Several hover cases were run for conventional and advanced-geometry blades. Numerical schemes using multi-zones and/or adaptive grids appear to be necessary to simulate the complex vortical flows in rotor wakes.

Mccroskey, William J.↗
NASA NTRS1974

Analysis of finite-size phased arrays of circular waveguide elements

A derivation is presented for the calculation of the interelement mutual coupling in a finite-size planar array of waveguide-fed apertures covered by a multilayered dielectric and/or plasma. The general mutual admittance expression is evaluated for circular apertures and the mutual coupling calculations are verified experimentally for two transverse electric circular waveguide mode excited apertures. A parametric study of higher order mode aperture fields indicates that the only significant change in the circular aperture mutual coupling is due to the transverse magnetic mode, which introduces an additional phase shift. Qualitative agreement between calculations for a 183-element array of circular apertures and an infinite array establishes the validity of the finite-array theoretical model.

Bailey, M. C.↗
DOE OSTI2020

Exciton energy transfer reveals spectral signatures of excited states in clusters

Electronic excitation and concomitant energy transfer leading to Penning ionization in argon–acetylene clusters generated in a supersonic expansion are investigated with synchrotron-based photoionization mass spectrometry and electronic structure calculations. Spectral features in the photoionization efficiency of the mixed argon–acetylene clusters reveal a blue shift from the 2 P 1/2 and 2 P 3/2 excited states of atomic argon. Analysis of this feature suggests that excited states of argon clusters transfer energy to acetylene, resulting in its ionization and successive evaporation of argon. Theoretically calculated Ar n (n = 2–6) cluster spectra are in excellent agreement with experimental observations, and provide insight into the structure and ionization dynamics of the clusters. A comparison between argon–acetylene and argon–water clusters reveals that argon solvates water better, allowing for higher-order excitons and Rydberg states to be populated. Furthermore, these results are explained by theoretical calculations of respective binding energies and structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗