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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Interactive application of quadratic expansion of chi-square statistic to nonlinear curve fitting

This report contains a detailed theoretical description of an all-purpose, interactive curve-fitting routine that is based on P. R. Bevington's description of the quadratic expansion of the Chi-Square statistic. The method is implemented in the associated interactive, graphics-based computer program. Taylor's expansion of Chi-Square is first introduced, and justifications for retaining only the first term are presented. From the expansion, a set of n simultaneous linear equations is derived, then solved by matrix algebra. A brief description of the code is presented along with a limited number of changes that are required to customize the program of a particular task. To evaluate the performance of the method and the goodness of nonlinear curve fitting, two typical engineering problems are examined and the graphical and tabular output of each is discussed. A complete listing of the entire package is included as an appendix.

Badavi, F. F.↗
NASA NTRS1987

Separating Peaks in X-Ray Spectra

Deconvolution algorithm assists in analysis of x-ray spectra from scanning electron microscopes, electron microprobe analyzers, x-ray fluorescence spectrometers, and like. New algorithm automatically deconvolves x-ray spectrum, identifies locations of spectral peaks, and selects chemical elements most likely producing peaks. Technique based on similarities between zero- and second-order terms of Taylor-series expansions of Gaussian distribution and of damped sinusoid. Principal advantage of algorithm: no requirement to adjust weighting factors or other parameters when analyzing general x-ray spectra.

Nicolas, David↗
NASA NTRS1974

Approximate techniques of structural reanalysis

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Noor, A. K.↗
NASA NTRS1982

Power series expansions for the frequency and period of the limit cycle of the van der Pol equation

An equation reported by van der Pol (1926) in connection with relaxation-oscillations studies is considered. The equation contains the factor epsilon which can assume values in the range from zero to infinity. The period T(epsilon), or equivalently the frequency nu(epsilon) of the limit cycle has been studied. However, to date there has been little success in discovering the analytical structure of T(epsilon) as a function of epsilon. The present investigation has the objectives to present the Taylor series expansion of nu(epsilon), to locate the singularities which determine the radius of convergence of that expansion, to introduce a new damping variable in terms of which the expansion converges for all epsilon, to form a new expansion for the period T(epsilon) which improves the rate of convergence of the series, to attempt to 'complete' the series, and to compare the obtained results with the numerically determined values of T(epsilon) and with the asymptotic approximation valid for large epsilon.

Andersen, C. M.↗
NASA NTRS1995

A hybrid neurocomputing/numerical strategy for nonlinear structural analysis

A hybrid neurocomputing/numerical strategy is presented for geometrically nonlinear analysis of structures. The strategy combines model-free data processing capabilities of computational neural networks with a Pade approximants-based perturbation technique to predict partial information about the nonlinear response of structures. In the hybrid strategy, multilayer feedforward neural networks are used to extend the validity of solutions by using training samples produced by Pade approximations to the Taylor series expansion of the response function. The range of validity of the training samples is taken to be the radius of convergence of Pade approximants and is estimated by setting a tolerance on the diverging approximants. The norm of residual vector of unbalanced forces in a given element is used as a measure to assess the quality of network predictions. To further increase the accuracy and the range of network predictions, additional training data are generated by either applying linear regression to weight matrices or expanding the training data by using predicted coefficients in a Taylor series. The effectiveness of the hybrid strategy is assessed by performing large-deflection analysis of a doubly-curved composite panel with a circular cutout, and postbuckling analyses of stiffened composite panels subjected to an in-plane edge shear load. In all the problems considered, the hybrid strategy is used to predict selective information about the structural response, namely the total strain energy and the maximum displacement components only.

Szewczyk, Z. Peter↗
DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗
DOE OSTI2022

A coupling approach for linear elasticity problems with spatially non-coincident discretized interfaces

Here we present a new method for coupled linear elasticity problems whose finite element discretization may lead to spatially non-coincident discretized interfaces. Our approach combines the classical Dirichlet–Neumann coupling formulation with a new set of discretized interface conditions obtained through Taylor series expansions. We show that these conditions ensure linear consistency of the coupled finite element solution. We then formulate an iterative solution method for the coupled discrete system and apply the new coupling approach to two representative settings for which we also provide several numerical illustrations. The first setting is a mesh-tying problem in which both coupled structures have the same Lamé parameters whereas the second setting is an interface problem for which the Lamé parameters in the two coupled structures are different.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential (µB) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature T and µ B to the universal properties of the second order chiral phase transition were determined by lattice QCD calculations. Motivated by these advances, first, we discuss the analytic structure of the partition function - the so-called Yang-Lee edge singularity - in the QCD crossover regime, solely based on universal properties. Then, utilizing the lattice calculated non-universal parameters, we map this singularity to the real T and complex µ B plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around µ B = 0 in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around µ B = 0; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the T - µ B plane.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Connection Between Mass Flux Transport and Eddy Diffusivity in Convective Atmospheric Boundary Layers

Turbulence parameterizations for convective boundary layer in coarse-scale atmospheric models usually consider a combination of the eddy-diffusive transport and a non-local transport, typically in the form of a mass flux term, such as the widely adopted eddy-diffusivity mass-flux (EDMF) approach. These two types of turbulent transport are generally considered to be independent of each other. Using results from large-eddy simulations, here, we show that a Taylor series expansion of the updraft and downdraft mass-flux transport can be used to approximate the eddy-diffusivity transport in the atmospheric surface layer and the lower part of the mixed layer, connecting both eddy-diffusivity and mass-flux transport theories in convective conditions, which also quantifies departure from the Monin-Obukhov similarity (MOS) in the surface layer. This study provides a theoretical support for a unified EDMF parameterization applied to both the surface layer and mixed layer and highlights important correction required for surface models relying on MOS

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Multiscale Temporal Variability of the Global Air‐Sea CO 2 Flux Anomaly

Abstract The global air‐sea CO 2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO 2 ), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO 2 effect controlled by the ∆pCO 2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO 2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO 2 effect was closely connected with the relative strength of atmospheric pCO 2 and the nonthermal component of oceanic pCO 2 anomaly associated with dissolved inorganic carbon and alkalinity.

Environmental Sciences & Ecology↗
DOE OSTI2023

A Gradient Based Subgrid-Scale Parameterization for Ocean Mesoscale Eddies

Mesoscale eddies play an important role in transport of heat and biogeochemical tracers in the global ocean circulation. Resolving these energetic eddies, however, is challenging in ocean general circulation models (OGCM) because it requires a horizontal grid spacing of ≲1/8° that is computationally expensive. As a result, we are required to parameterize mesoscale eddy effects on large-scale ocean flows. In this work, we introduce a new subgrid-scale (SGS) model that is developed based on a Taylor series expansion of resolved variables to parameterize subgrid mesoscale eddy transports and momentum fluxes in OGCM. We have performed an a priori study to evaluate the performance of our new gradient model using high-resolution ocean simulations. Our results show that the gradient model well predicts the actual SGS thickness fluxes in the zonal and meridional directions in coarse-resolution simulations with the grid spacing ≳1/4°. The unresolved kinetic energy at the ocean surface is also skillfully estimated. More importantly, unlike current mesoscale eddy parameterizations, which are mainly developed based on an assumption of flat bottom ocean, our new SGS model can capture the structure of unresolved standing meanders at the ocean surface. We have also developed a dynamic procedure for setting in non-dimensional parameters in our new parameterization through a non-ad hoc and tuning-free method. Overall, this work suggests that implementing the gradient model in OGCM can improve the model accuracy with an affordable computational cost in eddy-permitting and non-eddying simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Generalized quasiharmonic approximation via space group irreducible derivatives

The quasiharmonic approximation (QHA) is the simplest nontrivial approximation for interacting phonons under constant pressure, bringing the effects of anharmonicity into temperature-dependent observables. Nonetheless, the QHA is often implemented with additional approximations due to the complexity of computing phonons under arbitrary strains, and the generalized QHA, which employs constant stress boundary conditions, has not been completely developed. In this work we formulate the generalized QHA, providing a practical algorithm for computing the strain state and other observables as a function of temperature and true stress. We circumvent the complexity of computing phonons under arbitrary strains by employing irreducible second-order displacement derivatives of the Born-Oppenheimer potential and their strain dependence, which are efficiently and precisely computed using the lone irreducible derivative approach. We formulate two complementary strain parametrizations: a discretized strain grid interpolation and a Taylor series expansion in symmetrized strain. We illustrate our approach by evaluating the temperature and pressure dependence of select elastic constants and the thermal expansion in thoria (ThO 2 ) using density functional theory with three exchange-correlation functionals. The QHA results are compared to our measurements of the elastic constant tensor using time-domain Brillouin scattering and inelastic neutron scattering. Our irreducible derivative approach simplifies the implementation of the generalized QHA, which will facilitate reproducible, data-driven applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dynamic Phasor Modeling of Various Multipulse Rectifiers and a VSI Fed by 18-Pulse Asymmetrical Autotransformer Rectifier Unit for Fast Transient Analysis

To study the fast modelling of dynamic characteristics caused by power electronic switching, the dynamic phasor (DP) theory based on the time-varying Fourier decomposition and frequency shifting is firstly applied to the modelling of various multipulse rectifiers. The DP model for symmetrical 12-pulse phase-shifting reactor rectifier unit (PSR-RU) is derived with model order reduction, relations between ac and dc terminals, and Taylor series expansion. The DP model of asymmetrical 18-pulse autotransformer rectifier unit (AT-RU) is proposed based on the switching functions expressed in the DP domain. Meanwhile, the DP model of voltage source inverter (VSI) fed by asymmetrical 18-pulse AT-RU is built with the harmonic state-space (HSS) equations. Under both balanced and unbalanced conditions, the good calculation accuracy and rapid simulation speed of the developed DP models are validated by the detailed time-domain (TD) simulation.

42 ENGINEERING↗
DOE OSTI2023

A New Analytical Expression for Estimating the Adiabatic Temperature Rise in Lithium-Ion Batteries During High-Power Pulses

A coupled, thermal-electrochemical model is used to explain why the Joule heating assumption (i.e., I 2 R) does not provide a good representation of the temperature rise during high power pulses in lithium-ion batteries, even in cases where the reversible heat generation can be neglected. The poor agreement occurs because the internal resistance changes during the pulse due to the opposing effects of mass transport in the electrolyte, which raises the resistance, and heat generation (temperature rise), which lowers the resistance. These insights are used to propose a new analytical expression for predicting the temperature rise during adiabatic pulses with limited experimental and physical data. The expression accounts for thermal effects using a Taylor series expansion of an Arrhenius-type equation. It accounts for transport effects using an approximate solution to the one-dimensional diffusion equation. The new expression is shown to accurately estimate the simulated, adiabatic temperature rise across a range of loadings (1 to 4 mAh cm -2 ) and C-rates (1C to 10C) for cells containing LiNi 0.5 Mn 0.3 Co 0.2 O 2 positive electrodes and graphite negative electrodes. In conclusion, it is also shown to accurately estimate the experimental, adiabatic temperature rise measured for cells with LiFePO 4 positive electrodes and mesocarbon negative electrodes with minimal changes to the fitted parameters.

25 ENERGY STORAGE↗