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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 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

New concepts for Mercury orbiter missions

The next logical step in the exploration of Mercury is an orbiter mission. A conflict exists between those in the field of planetary sciences who desire a mission with a low circular orbit, and scientists in the fields and particles disciplines, who generally prefer a highly elliptical spacecraft orbit. The thermal environment imposed by the sun and planet render the low orbit intolerable for spacecraft using previous thermal control methods. A thermal control concept and a spacecraft mission concept have been developed which resolve these problems and promise a scientifically significant mission for the mid-1980s.

French, J. R.↗
NASA NTRS1978

Volumetric pattern analysis of airborne antennas

By blending together the roll and elevation plane high-frequency solutions, a very efficient technique has been developed for the volumetric pattern analysis of antennas mounted on the fuselage of a generalized aircraft. The fuselage is simulated by an infinitely long, perfectly conducting, elliptic cylinder in cross section and a composite elliptic cylinder in profile. The wings, nose section, stabilizers, and landing-gear doors may be modeled by finite flat or bent plates. Good agreement with accurate scale model measurements has been obtained for a variety of airborne antenna problems.

Yu, C. L.↗
NASA NTRS1993

A least-squares finite element method for 3D incompressible Navier-Stokes equations

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations, and results in symmetric, positive definite algebraic system. An additional compatibility equation, i.e., the divergence of vorticity vector should be zero, is included to make the first-order system elliptic. The Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. The flow in a half of 3D cubic cavity is calculated at Re = 100, 400, and 1,000 with 50 x 52 x 25 trilinear elements. The Taylor-Gortler-like vortices are observed at Re = 1,000.

Jiang, Bo-Nan↗
DOE OSTI2016

Blade Load Unsteadiness and Turbulence Statistics in an Actuator-Line Computed Turbine–Turbine Interaction Problem

The objective of this study is to investigate how different volumetric projection techniques used in actuator-line modeling affect the unsteady blade loads and wake turbulence statistics. The two techniques for the body-force projection radius are based on either (i) the grid spacing or (ii) the combination of grid spacing and an equivalent elliptic blade planform. An array of two National Renewable Energy Laboratory 5-MW turbines separated by seven rotor diameters is simulated for 2000s (about rotor 300 revolutions) within a large-eddy simulation (LES) solver of the neutral and moderately convective atmospheric boundary layer (ABL). The statistics of sectional angle of attack (AOA), blade loads, and turbine power histories are quantified. Moreover, the degree of unsteadiness of sectional blade loads in response to atmospheric and wake turbulence is computed via a reduced frequency based on the rate-of-change in sectional AOA. Finally, the goal of this work is to make the wind energy community aware of the uncertainties associated with actuator-line modeling approaches.

17 WIND ENERGY↗
DOE OSTI2020

Statistical Treatment of Inverse Problems Constrained by Differential Equations-based Models with Stochastic Terms

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is to formulate the inverse problem, in particular the objective function, to find the closest forward distribution (i.e., the output of the stochastic forward problem) that best explains the distribution of the observations in a certain metric. We use proper scoring rules, a concept employed in statistical forecast verification, namely energy, variogram, and hybrid (i.e., combination of the two) scores. We study the performance of the proposed formulation in the context of two applications: a coefficient field inversion for subsurface flow governed by an elliptic partial differential equation with a stochastic source and a parameter inversion for power grid governed by differential-algebraic equations. In both cases we show that the variogram and the hybrid scores produce better parameter inversion results than does the energy score, whereas the energy score leads to better probabilistic predictions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

Relaxation methods in fluid mechanics

The present work considers the iterative solution of a coupled set of difference equations and examines methods that carry successive approximates to a state that is invariant with further iteration and independent of the initial guess. Methods are studied with regard to their efficiency and economy of computer resources. The basic principles of classical relaxation are set forth, with attention confined to linear elliptic equations. This discussion involves the evaluation of the spectral radius that is the magnitude of the eigenvalue with largest modulus. The subject of relaxation is then related to the study of ordinary differential equations and hyperbolic partial differential equations. Problems that occur when linearly dependent eigenvectors appear in the relaxation matrix are discussed, leading to multiply connected eigenvalues in the Jordan canonical form. Finally, a brief survey of relaxation methods used in aerodynamics is given.

Lomax, H.↗
NASA NTRS1985

Stable boundary conditions and difference schemes for Navier-Stokes equations

The Navier-Stokes equations can be viewed as an incompletely elliptic perturbation of the Euler equations. By using the entropy function for the Euler equations as a measure of energy for the Navier-Stokes equations, it was possible to obtain nonlinear energy estimates for the mixed initial boundary value problem. These estimates are used to derive boundary conditions which guarantee L2 boundedness even when the Reynolds number tends to infinity. Finally, a new difference scheme for modelling the Navier-Stokes equations in multidimensions for which it is possible to obtain discrete energy estimates exactly analogous to those we obtained for the differential equation was proposed.

Dutt, P.↗
NASA NTRS1993

Study of supersonic intersection flowfield at modified wing-body junctions

The problem of supersonic flow control using fillets and sweep for a wing-body junction has been investigated numerically using a three-dimensional Navier-Stokes code, which employs the MacCormack's time-split finite volume technique. An elliptic grid generation technique with direct control over spacing has been developed for constructing the grid at a filleted wing-body junction. The computed results for pressure distribution, particle paths, and limiting streamlines on the flat plate and fin surface for a swept fin show a decrease in the peak pressure on the fin leading edge and in the extent of the separated flow region. Moreover, the results for filleted juncture clearly show that the flow streamline patterns lose much of their vortical character with proper filleting. It has been demonstrated that fillets with a radius of three-and-one-half times the fin leading-edge diameter are required to weaken the vorticity in the horseshoe vortex by a factor of three for the Mach number and Reynolds number considered in the present study.

Lakshmanan, B.↗
NASA NTRS1990

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

Shi, Yun. Y.↗
NASA NTRS1974

Vibration analysis of a completely free elliptical plate

The Ritz method is applied to the variation analysis of a completely free elliptical plate as an efficient alternative to a procedure using a truncated series of regular and modified Mathieu functions. It is shown that a solution as accurate as desired can be obtained with the Ritz method in solving thin plate vibration problems with difficult geometries.

Beres, D. P.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate than corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1992

Aerobraking Magellan

While the Magellan spacecraft is currently in an elliptical orbit around Venus, its orbit may be circularized by means of an aerobraking maneuver during which a minor amount of aerodynamic drag is applied to 1000-2000 orbits. An evaluation is presently undertaken of the thermal-control and operational problems arising from such a maneuver, in virtue of its not having been considered among the design requirements of the spacecraft. Attention is given to atmospheric erosion and contamination problems to which the spacecraft surfaces could be exposed.

Lyons, Daniel T.↗
NASA NTRS1999

Solving Upwind-Biased Discretizations: Defect-Correction Iterations

This paper considers defect-correction solvers for a second order upwind-biased discretization of the 2D convection equation. The following important features are reported: (1) The asymptotic convergence rate is about 0.5 per defect-correction iteration. (2) If the operators involved in defect-correction iterations have different approximation order, then the initial convergence rates may be very slow. The number of iterations required to get into the asymptotic convergence regime might grow on fine grids as a negative power of h. In the case of a second order target operator and a first order driver operator, this number of iterations is roughly proportional to h-1/3. (3) If both the operators have the second approximation order, the defect-correction solver demonstrates the asymptotic convergence rate after three iterations at most. The same three iterations are required to converge algebraic error below the truncation error level. A novel comprehensive half-space Fourier mode analysis (which, by the way, can take into account the influence of discretized outflow boundary conditions as well) for the defect-correction method is developed. This analysis explains many phenomena observed in solving non-elliptic equations and provides a close prediction of the actual solution behavior. It predicts the convergence rate for each iteration and the asymptotic convergence rate. As a result of this analysis, a new very efficient adaptive multigrid algorithm solving the discrete problem to within a given accuracy is proposed. Numerical simulations confirm the accuracy of the analysis and the efficiency of the proposed algorithm. The results of the numerical tests are reported.

Diskin, Boris↗
DOE OSTI2016

Summary Report: Multigrid for Systems of Elliptic PDEs

We are interested in determining if multigrid can be effectively applied to the system. The conclusion that I seem to be drawn to is that it is impossible to develop a blackbox multigrid solver for these general systems. Analysis of the system of PDEs must be conducted first to determine pre-processing procedures on the continuous problem before applying a multigrid method. Determining this pre-processing is currently not incorporated in black-box multigrid strategies. Nevertheless, we characterize some system features that will make the system more amenable to multigrid approaches, techniques that may lead to more amenable systems, and multigrid procedures that are generally more appropriate for these systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Sum-Frequency Generation from a Thin Spherical Layer: I. Analytical Solution

In the tensor form, using the generalized Rayleigh–Gans–Debye approximation, the problem of the sum-frequency generation from a thin nonlinear layer deposited on a dielectric spherical particle placed in a dielectric medium is solved. The second-order nonlinear dielectric susceptibility tensor is chosen in a general form containing chiral components. In the vector and tensor forms, expressions are obtained that describe the spatial distribution of the sum-frequency radiation field generated by two plane electromagnetic elliptically polarized waves. Limiting expressions that describe the spatial distribution of the sum-frequency harmonic at small and large radii of the spherical layer are obtained. It is revealed that, at small radii of the spherical layer, the radiation due to the chiral anisotropy coefficients makes a dominant contribution to the generation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1973

Long-term motion in a restricted problem of rotational motion

A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the long-term effects of gravity-gradient torque and orbital evolution on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is constrained to precess and spin with constant rates. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order in n/omega sub 0, where n is the orbital mean motion of the center of mass and omega sub 0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable, and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed, and a comparison of theoretical results with observations is made.

Cochran, J. E.↗
NASA NTRS1977

Simplified clustering of nonorthogonal grids generated by elliptic partial differential equations

A simple clustering transformation is combined with the Thompson, Thames, and Mastin (TTM) method of generating computational grids to produce controlled mesh spacings. For various practical grids, the resulting hybrid scheme is easier to apply than the inhomogeneous clustering terms included in the TTM method for this purpose. The technique is illustrated in application to airfoil problems, and listings of a FORTRAN computer code for this usage are included.

Sorenson, R. L.↗