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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 469 records · Page 26

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NASA NTRS1977

Comment on 'Drag coefficient of spheres in continuum and rarefied flows'

A paper by Henderson (1976) provides a method of predicting experimental sphere drag data. This approach uses two equations for the drag coefficient, one for relative Mach number less than one, one for relative Mach number greater than 1.75. For relative Mach numbers between these limits a linear interpolation procedure is followed. In a comment on this paper, it is claimed, on the basis of comparing predictions with experimental results, that a method proposed by Walsh (1975) gives better predictions of the drag coefficient for relative Mach numbers less than 1.75, provided that a modification of the procedure is made for relative Mach numbers less than 0.1. For values over 1.75, both methods are considered equally accurate. In a reply to this comment, it is agreed that the Walsh method is more accurate when Reynolds numbers are within a range between 20 and 200, and Mach numbers are between 0.5 and 1.25. Presumed errors and possible limitations in the Walsh procedure for predicting drag coefficients are discussed.

Walsh, M. J.↗

NASA NTRS1977

Temperature distribution from radiosonde and satellite measurements

Since air temperatures derived from satellite radiance measurements often contain large errors, a method is suggested for combining radiosonde and satellite measurements to achieve better accuracy. In particular, when geostationary satellite radiances become available, it would be possible to use the satellite measurements to interpolate geographically between the radiosonde stations, and also to extrapolate in time from one radiosonde launch time until the next launch time. Simulated radiance data were used to test this method in a region of possible severe local storm development, and the accuracy obtained by using real scanning microwave spectrometer data was determined.

Fritz, S.↗

NASA NTRS1988

Theoretical studies of solar-pumped lasers

The investigation of stimulated emission causing transitions from the B(1) pi sub u state of sodium to the overlapping 2(1) sigma(+) sub g electronic state has been continued. A new method of estimating the Franck-Condon factors has been developed which instead of fitting the molecular potential curves with Morse functions, estimates the V(r) dependence by interpolation from given potential curves. The results for the sum of the rates from one vibrational level in the upper state to all the levels in the lower state show good agreement with the previous method, implying that curve crossing by stimulated emission due to photons from the oven is an important mechanism in sodium.

Harries, Wynford L.↗

NASA NTRS1985

Mixed models and reduction method for dynamic analysis of anisotropic shells

A time-domain computational procedure is presented for predicting the dynamic response of laminated anisotropic shells. The two key elements of the procedure are: (1) use of mixed finite element models having independent interpolation (shape) functions for stress resultants and generalized displacements for the spatial discretization of the shell, with the stress resultants allowed to be discontinuous at interelement boundaries; and (2) use of a dynamic reduction method, with the global approximation vectors consisting of the static solution and an orthogonal set of Lanczos vectors. The dynamic reduction is accomplished by means of successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate the global approximation vectors. Then the Rayleigh-Ritz technique is used to generate a reduced system of ordinary differential equations in the amplitudes of these modes. The temporal integration of the reduced differential equations is performed by using an explicit half-station central difference scheme (Leap-frog method). The effectiveness of the proposed procedure is demonstrated by means of a numerical example and its advantages over reduction methods used with the displacement formulation are discussed.

Noor, A. K.↗

NASA NTRS1989

An algebraic homotopy method for generating quasi-three-dimensional grids for high-speed configurations

A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.

Moitra, Anutosh↗

NASA NTRS1994

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Gottlieb, David↗

NASA NTRS1974

Optimal rocket thrust profile shaping using third degree spline function interpolation

Optimal solid-rocket thrust profiles for the parallel-burn, solid-rocket-assisted space shuttle are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The profiles are optimized parametrically, using the Davidon-Fletcher-Powell penalty function method, by minimizing propellant weight subject to state and control inequality constraints and to terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degree spline function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners, which is realistic in nature, makes this method attractive from the viewpoint of solid rocket grain design.

Johnson, I. L.↗

NASA NTRS1982

On the geodetic applications of simultaneous range-differencing to LAGEOS

The possibility of improving the accuracy of geodetic results by use of simultaneously observed ranges to Lageos, in a differencing mode, from pairs of stations was studied. Simulation tests show that model errors can be effectively minimized by simultaneous range differencing (SRD) for a rather broad class of network satellite pass configurations. The methods of least squares approximation are compared with monomials and Chebyshev polynomials and the cubic spline interpolation. Analysis of three types of orbital biases (radial, along- and across track) shows that radial biases are the ones most efficiently minimized in the SRC mode. The degree to which the other two can be minimized depends on the type of parameters under estimation and the geometry of the problem. Sensitivity analyses of the SRD observation show that for baseline length estimations the most useful data are those collected in a direction parallel to the baseline and at a low elevation. Estimating individual baseline lengths with respect to an assumed but fixed orbit not only decreases the cost, but it further reduces the effects of model biases on the results as opposed to a network solution. Analogous results and conclusions are obtained for the estimates of the coordinates of the pole.

Pablis, E. C.↗

NASA NTRS1985

Stability of interfaces with mesh refinement

A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.

Berger, M. J.↗

NASA NTRS1988

GENIE - Generation of computational geometry-grids for internal-external flow configurations

Progress realized in the development of a master geometry-grid generation code GENIE is presented. The grid refinement process is enhanced by developing strategies to utilize bezier curves/surfaces and splines along with weighted transfinite interpolation technique and by formulating new forcing function for the elliptic solver based on the minimization of a non-orthogonality functional. A two step grid adaptation procedure is developed by optimally blending adaptive weightings with weighted transfinite interpolation technique. Examples of 2D-3D grids are provided to illustrate the success of these methods.

Soni, B. K.↗

NASA NTRS2012

Uncertainty Due to Unsteady Fluid/Structure Interaction for the Ares I Vehicle Traversing the Transonic Regime

Rapid reduced-order numerical models are being investigated as candidates to simulate the dynamics of a flexible launch vehicle during atmospheric ascent. There has also been the extension of these new approaches to include gust response. These methods are used to perform aeroelastic and gust response analyses at isolated Mach numbers. Such models require a method to time march through a succession of ascent Mach numbers. An approach is presented for interpolating reduced-order models of the unsteady aerodynamics at successive Mach numbers. The transonic Mach number range is considered here since launch vehicles can suffer the highest dynamic loads through this range. Realistic simulations of the flexible vehicle behavior as it traverses this Mach number range are presented. The response of the vehicle due to gusts is computed. Uncertainties in root mean square and maximum bending moment and crew module accelerations are presented due to assumed probability distributions in design parameters, ascent flight conditions, gusts. The primary focus is on the uncertainty introduced by modeling fidelity. It is found that an unsteady reduced order model produces larger excursions in the root mean square loading and accelerations than does a quasi-steady reduced order model.

Bartels, Robert E.↗

NASA NTRS2012

A Study of Global Cirrus Cloud Morphology with AIRS Cloud-clear Radiances (CCRs)

Version 6 (V6) AIRS cloud-clear radiances (CCR) are used to derive cloud-induced radiance (Tcir=Tb-CCR) at the infrared frequencies of weighting functions peaked in the middle troposphere. The significantly improved V 6 CCR product allows a more accurate estimation of the expected clear-sky radiance as if clouds are absent. In the case where strong cloud scattering is present, the CCR becomes unreliable, which is reflected by its estimated uncertainty, and interpolation is employed to replace this CCR value. We find that Tcir derived from this CCR method are much better than other methods and detect more clouds in the upper and lower troposphere as well as in the polar regions where cloud detection is particularly challenging. The cloud morphology derived from the V6 test month, as well as some artifacts, will be shown.

Wu, Dong L.↗

NASA NTRS1973

A new technique for calculating reentry base heating

The laminar base flow field of a two-dimensional reentry body has been studied by Telenin's method. The flow domain was divided into strips along the x-axis, and the flow variations were represented by Lagrange interpolation polynomials in the transformed vertical coordinate. The complete Navier-Stokes equations were used in the near wake region, and the boundary layer equations were applied elsewhere. The boundary conditions consisted of the flat plate thermal boundary layer in the forebody region and the near wake profile in the downstream region. The resulting two-point boundary value problem of 33 ordinary differential equations was then solved by the multiple shooting method. The detailed flow field and thermal environment in the base region are presented in the form of temperature contours, Mach number contours, velocity vectors, pressure distributions, and heat transfer coefficients on the base surface. The maximum heating rate was found on the centerline, and the two-dimensional stagnation point flow solution was adquate to estimate the maximum heating rate so long as the local Reynolds number could be obtained.

Meng, J. C. S.↗

DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Time-dependent wave-packet method for the complete determination of S-matrix elements for reactive molecular collisions in three dimensions

An alternative time-dependent wave-packet method for treating three-dimensional gas phase reactive atom-diatom collisions is presented. The method employs a nonreactive body-frame wave packet propagation procedure, made possible by judicious use of absorbing optical potentials, a novel scheme for interpolating the wave function from coordinates in one arrangement to those in another and the fact that the time-dependent Schroedinger equation is an initial-value problem. The last feature makes possible a computationally viable and accurate procedure for changing from one arrangement's coordinates to another. In addition, the method allows the determination of S-matrix elements over a wide range of energies from a single wave-packet propagation. The method is illustrated by carrying out detailed calculations of inelastic and reactive scattering in the H + H2 system using the Liu-Siegbahn-Truhlar-Horowitz potential surface.

Judson, Richard S.↗

NASA NTRS1991

Application of artificial neural networks in nonlinear analysis of trusses

A method is developed to incorporate neural network model based upon the Backpropagation algorithm for material response into nonlinear elastic truss analysis using the initial stiffness method. Different network configurations are developed to assess the accuracy of neural network modeling of nonlinear material response. In addition to this, a scheme based upon linear interpolation for material data, is also implemented for comparison purposes. It is found that neural network approach can yield very accurate results if used with care. For the type of problems under consideration, it offers a viable alternative to other material modeling methods.

Alam, J.↗

NASA NTRS1990

Propane spectral resolution enhancement by the maximum entropy method

The Burg algorithm for maximum entropy power spectral density estimation is applied to a time series of data obtained from a Michelson interferometer and compared with a standard FFT estimate for resolution capability. The propane transmittance spectrum was estimated by use of the FFT with a 2 to the 18th data sample interferogram, giving a maximum unapodized resolution of 0.06/cm. This estimate was then interpolated by zero filling an additional 2 to the 18th points, and the final resolution was taken to be 0.06/cm. Comparison of the maximum entropy method (MEM) estimate with the FFT was made over a 45/cm region of the spectrum for several increasing record lengths of interferogram data beginning at 2 to the 10th. It is found that over this region the MEM estimate with 2 to the 16th data samples is in close agreement with the FFT estimate using 2 to the 18th samples.

Bonavito, N. L.↗

NASA NTRS2021

An Efficient and Accurate Algorithm for Computing Grid-Averaged Solar Fluxes for Horizontally Inhomogeneous Clouds

A computationally efficient method is presented to account for the horizontal cloud inhomogeneity by using a radiatively equivalent plane parallel homogeneous (PPH) cloud. The algorithm can accurately match the calculations of the reference (rPPH) independent column approximation (ICA) results, but use only the same computational time required for a single plane parallel computation. The effective optical depth of this synthetic sPPH cloud is derived by exactly matching the direct transmission to that of the inhomogeneous ICA cloud. The ffective9 scattering asymmetry factor is found from a pre-calculated albedo inverse look-up-table that is allowed to vary over the range from -1.0 to 1.0. In the special cases of conservative scattering and total absorption, the synthetic method is exactly equivalent to the ICA, with only a small bias (about 0.2% in flux) relative to ICA due to imperfect interpolation in using the look-up tables. In principle, the ICA albedo can be approximated accurately regardless of cloud inhomogeneity. For a more complete comparison, the broadband shortwave albedo and transmission calculated from the synthetic sPPH cloud and averaged over all incident directions, have the RMS biases of 0.26% and 0.76%, respectively, for inhomogeneous clouds over a wide variation of particle size. The advantages of the synthetic PPH method are that (1) it is not required that all the cloud subcolumns have uniform microphysical characteristic, (2) it is applicable to any 1D radiative transfer scheme, and (3) it can handle arbitrary cloud optical depth distributions and an arbitrary number of cloud subcolumns with uniform computational efficiency.

cloud inhomogeneity↗