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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 289 records · Page 16

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NASA NTRS2002

Elliptic Grid Generation of Spiral-Bevel Pinion Gear Typical of OH-58 Helicopter Transmission

This paper discusses the source term treatment in the numerical solution of elliptic partial differential equations for an interior grid generation problem in generalized curvilinear coordinates. The geometry considered is that of a planar cross-section of a generic spiral-bevel gear tooth typical of a pinion in the OH-58 helicopter transmission. The source terms used are appropriate for an interior grid domain where all the boundaries are prescribed via a combination of Dirichlet and Neumann boundary conditions. New constraints based on the Green's Theorem are derived which uniquely determine the coefficients in the source terms. These constraints are designed for boundary clustered grids where gradients in physical quantities need to be resolved adequately. However, it is seen that the present formulation works satisfactorily for mild clustering also. Thus, a fully automated elliptic grid generation technique is made possible where there is no need for a parametric study of these parameters since the new relations fix these free parameters uniquely.

Kaul, Upender K.↗

DOE OSTI2024

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

The present study is an extension of the work done by Peddle, Haut, and Wingate and Haut and Wingate, where a two-level Parareal method with mapping and averaging is examined. The method proposed in this paper is a multilevel Parareal method with arbitrarily many levels, which is not restricted to the two-level case. We give an asymptotic error estimate which reduces to the two-level estimate for the case when only two levels are considered. Introducing more than two levels has important consequences for the averaging procedure, as we choose separate averaging windows for each of the different levels, which is an additional new feature of the present study. The different averaging windows make the proposed method especially appropriate for nonlinear multiscale problems, because we can introduce a level for each intrinsic scale of the problem and adapt the averaging procedure such that we reproduce the behavior of the model on the particular scale resolved by the level. The method is applied to nonlinear differential equations. The nonlinearities can generate a range of frequencies in the problem. The computational cost of the new method is investigated and studied on several examples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Joint Modeling of Quasar Variability and Accretion Disk Reprocessing Using Latent Stochastic Differential Equations

Quasars are bright active galactic nuclei powered by the accretion of matter around supermassive black holes at the center of galaxies. Their stochastic brightness variability depends on the physical properties of the accretion disk and black hole. The upcoming Rubin Observatory Legacy Survey of Space and Time (LSST) is expected to observe tens of millions of quasars, so there is a need for efficient techniques like machine learning that can handle the large volume of data. Quasar variability is believed to be driven by an X-ray corona, which is reprocessed by the accretion disk and emitted as UV/optical variability. We are the first to introduce an auto-differentiable simulation of the accretion disk and reprocessing. We use the simulation as a direct component of our neural network to jointly model the driving variability and reprocessing, trained with supervised learning on simulated LSST-like 10 yr quasar light curves. We encode the light curves using a transformer encoder, and the driving variability is reconstructed using latent stochastic differential equations, a physically motivated generative deep learning method that can model continuous-time stochastic dynamics. By embedding the physical processes of the driving signal and reprocessing into our network, we achieve a model that is more robust and interpretable. We demonstrate that our model outperforms a Gaussian process regression baseline and can infer accretion disk parameters and time delays between wave bands, even for out-of-distribution driving signals. Our approach provides a powerful framework that can be adapted to solve other inverse problems in multivariate time series.

Fagin, Joshua [City Univ. of New York (CUNY), NY (↗

DOE OSTI2024

Neural Networks for Prediction of Complex Chemistry in Water Treatment Process Optimization

Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The effect of NN architecture on optimization is evaluated by optimizing hypothetical black-box desalination processes using a range of feed compositions from USGS brackish water data set, tracking the number of successful optimizations, and testing the impact of initial guess on the final solution. Our results clearly demonstrate that data generation and architecture impact NN accuracy and viability for use in equation-oriented optimization problems.

Dudchenko, Alexander V↗

NASA NTRS1967

Heat generation in a viscoelastic solid.

Temperature distributions and heat generation in viscoelastic isotropic solid resulting from mechanical deformations determined by energy equation

ENERGY EQUATION↗

NASA NTRS1971

ELAS8 - Computer program for linear structure equilibrium problems

Program generates and solves governing equations for unknown deflection of mesh points as if problem were to locate stationary point of total potential function associated with given loading and unknown deflections. Solution is obtained by means of displacement method and finite element technique.

Utku, S.↗

NASA NTRS1969

Stellar structure theory

Stellar structure theory, examining particle aggregates gravitational and pressure forces, energy flow, generation and opacity and equations of state

Iben, I., Jr.↗

NASA NTRS1971

Feasibility study of scanning celestial Attitude System (SCADS) for Earth Resources Technology Satellite (ERTS)

The feasibility of using the Scanning Celestial Attitude Determination System (SCADS) during Earth Resources Technology Satellite (ERTS) missions to compute an accurate spacecraft attitude by use of stellar measurements is considered. The spacecraft is local-vertical-stabilized. A heuristic discussion of the SCADS concept is first given. Two concepts are introduced: a passive system which contains no moving parts, and an active system in which the reticle is caused to rotate about the sensor's axis. A quite complete development of the equations of attitude motions is then given. These equations are used to generate the true attitude which in turn is used to compute the transit times of detectable stars and to determine the errors associated with the SCADS attitude. A more complete discussion of the analytical foundation of SCADS concept and its use for the geometries particular to this study, as well as salient design parameters for the passive and active systems are included.

Source record↗

NASA NTRS1972

Decision surface estimate of nonlinear system stability domain by Lie series method.

The Lie series recursive algorithm for Zubov's partial differential equation is used to generate two sets of points, where one represents the exact asymptotic stability boundary of an equilibrium state of the nonlinear system under consideration and the other is interior to it. Based on these two sets of data as training samples of two classes, a decision hypersurface can be determined such that it is a close approximation of the asymptotic stability boundary.

Kormanik, J.↗

NASA NTRS1973

Digital modeling of vibroacoustical processes generated by gearing

The statistical nature of vibroacoustical processes in transmission gears was studied using mathematical models. Special attention was given to high frequency components of vibroacoustical processes generated by spur gearing. Equations are given for describing torsional and tranverse vibrations of pairs of gear wheels when meshing, taking into account the flexibility of their supports.

Balitskiy, F. Y.↗

NASA NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗

NASA NTRS1977

Gravitational effects on chemically reacting laminar boundary layer flows over a horizontal flat plate

A theoretical study of the chemically reacting laminar boundary layer flow over a horizontal flat plate with gravitationally induced buoyant force is presented. A diffusion flame sheet model was used to describe the combustion process. The effects of gravity on the purely force convection flow can be characterized by a dimensionless coordinate quantity, which is involved in the generation of the governing equations. A numerical solution of the zero and first order governing equations subject to the appropriate physical boundary conditions was obtained. It is shown that the cross stream buoyancy induced body force acts effectively to produce a streamwise pressure gradient in the fluid adjacent to the plate surface. It is concluded that buoyancy plays an important role in boundary layer diffusion flames.

Lavid, M.↗

NASA NTRS1977

Analytic theory of orbit contraction

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

Vinh, N. X.↗

NASA NTRS1978

A simple method of calculating Stirling engines for engine design optimization

A calculation method is presented for a rhombic drive Stirling engine with a tubular heater and cooler and a screen type regenerator. Generally the equations presented describe power generation and consumption and heat losses. It is the simplest type of analysis that takes into account the conflicting requirements inherent in Stirling engine design. The method itemizes the power and heat losses for intelligent engine optimization. The results of engine analysis of the GPU-3 Stirling engine are compared with more complicated engine analysis and with engine measurements.

Martini, W. R.↗

NASA NTRS1979

Observations of Pc 1-2 waves in the outer magnetosphere

High time resolution measurements made inside the magnetopause from L = 7 to L = 14 by the flux gate magnetometer aboard the Ogo 5 satellite, which demonstrate that the Pc 1-2 magnetic field oscillations are present in the outer magnetosphere, are examined. The solar wind dynamic pressure and the magnetospheric cold plasma were enhanced, and the IMF had a southward component 2 hours before the events, but there was no significant correlation between the time of the events and either storm recovery phase or substorm onset. The magnetic field perturbations in each event were transverse to the ambient field with amplitudes from 2 to 8 gamma, and most of the transverse perturbations showed left-handed polarization. Excursions into the magnetosheath during two events revealed a disturbed magnetic field with significant power in frequencies of minimum 0.1 Hz, and although the magnetosheath was a source of free energy for waves at Pc 1-2 frequencies, the data within the magnetosphere suggest that the observed pulsations were ion cyclotron waves generated at the geomagnetic equator at large radial distances.

Kaye, S. M.↗

NASA NTRS1979

Development of LACIE CCEA-1 weather/wheat yield models

The advantages and disadvantages of the casual (phenological, dynamic, physiological), statistical regression, and analog approaches to modeling for grain yield are examined. Given LACIE's primary goal of estimating wheat production for the large areas of eight major wheat-growing regions, the statistical regression approach of correlating historical yield and climate data offered the Center for Climatic and Environmental Assessment the greatest potential return within the constraints of time and data sources. The basic equation for the first generation wheat-yield model is given. Topics discussed include truncation, trend variable, selection of weather variables, episodic events, strata selection, operational data flow, weighting, and model results.

Strommen, N. D.↗

NASA NTRS1980

Stress concentrations in screw threads

The concept of stress concentration in screw threads was defined using the sheer transfer rate as the fundamental quantity. The stress concentration is plotted for a fixed geometry. The Heywood equation was used to generate the basic plots and NASTRAN was used to extend the analysis to the case both where flanks of an individual thread tooth are in contact. The case where a finite axial stress is superimposed is discussed.

Ohara, G. P.↗

NASA NTRS1980

Stability boundaries for systems with frequency-model feedback and complacency filter

General parameter-plane equations were derived to generate boundaries for a class of systems characterized by a feedback loop that contains a complementary filter and a model for either the low- or high-frequency portion of the plant. This combination allows those frequencies of the part of the plant that is modeled to be fed back for control while suppressing other frequencies. For all specific examples considered, the stability regions obtained using the complementary filter and frequency model were larger (and in some cases, considerably larger) than those obtained using a low pass filter in the feedback of the system output. Furthermore, higher gain control was possible.

Barker, L. K.↗