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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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NASA NTRS1986

Three-Dimensional Turbomachine-Blade-Row Analysis Code

Computer program (MERNEW3D) developed that prepares bulk of input data set required for Denton three-dimensional inviscid turbomachine-blade-row analysis code. Denton input generated from minimum of geometry and flow-variable information by using cubic spline curve fits for interpolation and extrapolation. Curve-fitting procedures taken from previously developed and widely used NASA computer program (MERIDL), which performs meridional streamsurface analysis.

Glassman, A. J.↗
NASA NTRS1984

Some New Mathematical Methods for Variational Objective Analysis

New and/or improved variational methods for simultaneously combining forecast, heterogeneous observational data, a priori climatology, and physics to obtain improved estimates of the initial state of the atmosphere for the purpose of numerical weather prediction are developed. Cross validated spline methods are applied to atmospheric data for the purpose of improved description and analysis of atmospheric phenomena such as the tropopause and frontal boundary surfaces.

Wahba, G.↗
NASA NTRS1985

A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies

An approximation scheme is developed for the identification of hybrid systems describing the transverse vibrations of flexible beams with attached tip bodies. In particular, problems involving the estimation of functional parameters are considered. The identification problem is formulated as a least squares fit to data subject to the coupled system of partial and ordinary differential equations describing the transverse displacement of the beam and the motion of the tip bodies respectively. A cubic spline-based Galerkin method applied to the state equations in weak form and the discretization of the admissible parameter space yield a sequence of approximating finite dimensional identification problems. It is shown that each of the approximating problems admits a solution and that from the resulting sequence of optimal solutions a convergent subsequence can be extracted, the limit of which is a solution to the original identification problem. The approximating identification problems can be solved using standard techniques and readily available software.

Banks, H. T.↗
NASA NTRS1985

Gravity Field of Venus and Comparison with Earth

The acceleration (gravity) anomaly estimates by spacecraft tracking, determined from Doppler residuals, are components of the gravity field directed along the spacecraft Earth line of sight (LOS). These data constitute a set of vector components of a planet's gravity field, the specific component depending upon where the Earth happened to be at the time of each measurement, and they are at varying altitudes above the planet surface. From this data set the gravity field vector components were derived using the method of harmonic splines which imposes a smoothness criterion to select a gravity model compatible with the LOS data. Given the piecewise model it is now possible to upward and downward continue the field quantities desired with a few parameters unlike some other methods which must return to the full dataset for each desired calculation.

Bowin, C.↗
NASA NTRS1985

Plant Growth Biophysics: the Basis for Growth Asymmetry Induced by Gravity

The identification and quantification of the physical properties altered by gravity when plant stems grow upward was studied. Growth of the stem in vertical and horizontal positions was recorded by time lapse photography. A computer program that uses a cubic spline fitting algorithm was used to calculate the growth rate and curvature of the stem as a function of time. Plant stems were tested to ascertain whether cell osmotic pressure was altered by gravity. A technique for measuring the yielding properties of the cell wall was developed.

Cosgrove, D.↗
NASA NTRS1985

Approximation Techniques for Parameter Estimation and Feedback Control for Distributed Models of Large Flexible Structures

Approximation ideas that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems are discussed. Focusing on parameter estimation problems, the authors outline how one can obtain convergence results for cubic spline-based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration. Sample numerical findings are also presented.

Banks, H. T.↗
NASA NTRS1983

Computation of internal flows: Methods and applications; Proceedings of the Energy Sources Technology Conference, New Orleans, LA, February 12-16, 1984

The present conference covers computational method applications, viscous-inviscid interaction techniques, viscous flow computational methods, and design-related methods. Attention is given to viscous flows in turbomachinery cascades, forbidden signals and apparent Mach numbers in supersonic cascades, the flow field in an engine particle separator, two-dimensional separated channel flows, turbulent separating flows over a rearward-facing step, the semielliptic analysis of two-dimensional internal and compressible viscous flows, spline solutions of the incompressible Navier-Stokes equations in a mildly nonorthogonal coordinate system, the design of highly loaded blades with blockage in cascade, and a finite analytic method for unsteady, three-dimensional Navier-Stokes equations.

Sockol, P. M.↗
NASA NTRS1985

Gravity field of Venus at constant altitude and comparison with earth

The gravity field of Venus is characterized in gravity-anomaly and geoid-undulation maps produced by applying the harmonic-spline technique (Shure et al., 1982 and 1983; Parker and Shure, 1982) to Pioneer Venus Orbiter line-of-sight data. A positive correlation between Venusian topographic features and gravity anomalies is observed, in contrast to the noncorrelation seen on earth, and attributed to the thicker crust of Venus (70-80 vs 5-40 km for earth), crustal loading by recent volcanism, and possible regional elevation due to deep heating and thermal expansion.

Bowin, C.↗
NASA NTRS1985

Higher order methods for convection-diffusion problems

This paper applies C1 cubic Hermite polynomials embedded in an orthogonal collocation scheme to the spatial discretization of the unsteady nonlinear Burgers equation as a model of the equations of fluid mechanics. The temporal discretization is carried out by means of either a noniterative finite difference or an iterative finite difference procedure. Results of this method are compared with those of a second-order finite difference scheme and a splined-cubic Taylor's series scheme. Stability limits are derived and the matrix structure of the several schemes are compared.

Murphy, J. D.↗
NASA NTRS1985

Energy-modelled climb and climb-dash - The Kaiser technique

F. Kaiser's germinal 1944 report on his 'resultant-height' concept, now known as energy modelling, is reviewed. The data base for the Me. 262 jet fighter is recreated via spline-lattice representation of specific excess power. Minimum-time and 'distance'-climb trajectories are generated in an attempt to check Kaiser's results. Agreement is good for the minimum-time calculations but only qualitative agreement is obtained for the mysterious 'distance climbs' whose documentation is fragmentary. The character of optimal climb-dash trajectories in energy approximation is examined and illustrated.

Merritt, S. R.↗
NASA NTRS1985

A numerical method for approximating antenna surfaces defined by discrete surface points

A simple numerical method for the quadratic approximation of a discretely defined reflector surface is described. The numerical method was applied to interpolate the surface normal of a parabolic reflector surface from a grid of nine closest surface points to the point of incidence. After computing the surface normals, the geometrical optics and the aperture integration method using the discrete Fast Fourier Transform (FFT) were applied to compute the radiaton patterns for a symmetric and an offset antenna configurations. The computed patterns are compared to that of the analytic case and to the patterns generated from another numerical technique using the spline function approximation. In the paper, examples of computations are given. The accuracy of the numerical method is discussed.

Lee, R. Q.↗
NASA NTRS1986

STEP and STEPSPL: Computer programs for aerodynamic model structure determination and parameter estimation

The successful parametric modeling of the aerodynamics for an airplane operating at high angles of attack or sideslip is performed in two phases. First the aerodynamic model structure must be determined and second the associated aerodynamic parameters (stability and control derivatives) must be estimated for that model. The purpose of this paper is to document two versions of a stepwise regression computer program which were developed for the determination of airplane aerodynamic model structure and to provide two examples of their use on computer generated data. References are provided for the application of the programs to real flight data. The two computer programs that are the subject of this report, STEP and STEPSPL, are written in FORTRAN IV (ANSI l966) compatible with a CDC FTN4 compiler. Both programs are adaptations of a standard forward stepwise regression algorithm. The purpose of the adaptation is to facilitate the selection of a adequate mathematical model of the aerodynamic force and moment coefficients of an airplane from flight test data. The major difference between STEP and STEPSPL is in the basis for the model. The basis for the model in STEP is the standard polynomial Taylor's series expansion of the aerodynamic function about some steady-state trim condition. Program STEPSPL utilizes a set of spline basis functions.

Batterson, J. G.↗
NASA NTRS1986

Interactive algebraic grid-generation technique

An algebraic grid generation technique and use of an associated interactive computer program are described. The technique, called the two boundary technique, is based on Hermite cubic interpolation between two fixed, nonintersecting boundaries. The boundaries are referred to as the bottom and top, and they are defined by two ordered sets of points. Left and right side boundaries which intersect the bottom and top boundaries may also be specified by two ordered sets of points. when side boundaries are specified, linear blending functions are used to conform interior interpolation to the side boundaries. Spacing between physical grid coordinates is determined as a function of boundary data and uniformly space computational coordinates. Control functions relating computational coordinates to parametric intermediate variables that affect the distance between grid points are embedded in the interpolation formulas. A versatile control function technique with smooth-cubic-spline functions is presented. The technique works best in an interactive graphics environment where computational displays and user responses are quickly exchanged. An interactive computer program based on the technique and called TBGG (two boundary grid generation) is also described.

Smith, R. E.↗
NASA NTRS1986

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.↗
NASA NTRS1986

Estimation of discontinuous coefficients and boundary parameters for hyperbolic systems

The problem of estimating discontinuous coefficients, including locations of discontinuities, that occur in second order hyperbolic systems typical of those arising in I-D surface seismic problems is discussed. In addition, the problem of identifying unknown parameters that appear in boundary conditions for the system is treated. A spline-based approximation theory is presented, together with related convergence findings and representative numerical examples.

Lamm, P. K.↗
NASA NTRS1985

Proceedings of the Third Annual Symposium on Mathematical Pattern Recognition and Image Analysis

Topics addressed include: multivariate spline method; normal mixture analysis applied to remote sensing; image data analysis; classifications in spatially correlated environments; probability density functions; graphical nonparametric methods; subpixel registration analysis; hypothesis integration in image understanding systems; rectification of satellite scanner imagery; spatial variation in remotely sensed images; smooth multidimensional interpolation; and optimal frequency domain textural edge detection filters.

Guseman, L. F., Jr.↗
NASA NTRS1986

Legendre-tau approximations for functional differential equations

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

Ito, K.↗