Search NASA⌕ Search

SEARCH · Search NASA

Results for “extrapolate”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Noise of the 10-bladed 60 deg swept SR-5 propeller in a wind tunnel

Noise generated by supersonic helical tip speed propellers is a possible cabin environment problem for future airplanes powered by these propellers. Noise characteristics of one of these propellers, designated SR-5, are presented. A matrix of tests was conducted to provide as much acoustic information as possible. During aerodynamic testing it was discovered that the propeller had an aeroelastic instability which prevented testing the propeller at its design advance ratio of 4.08 at axial Mach numbers over 0.7. Plots of the variation of the maximum blade passage tone with helical tip Mach number indicate that, at higher helical tip Mach numbers, the propeller operated on sharply increasing portion of the noise curve; therefore, extrapolations to the design condition would not be accurate. A possible extrapolation indicated that SR-5 at its design point should be quieter than SR-3 at its design point. Directivity plots at the higher helical tip Mach numbers indicate a lobed directivity pattern as was observed previously on the SR-3 propeller.

Dittmar, J. H.↗
NASA NTRS1983

Subsonic panel method for designing wing surfaces from pressure distribution

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Bristow, D. R.↗
NASA NTRS1982

Electron impact cross sections for the 2,2P state excitation of lithium

Electron impact excitation of the 2p 2P state of Li was studied at 10, 20, 60, 100, 150 and 200 eV. Relative differential cross sections in the angular range 3-120 deg were measured and then normalized to the absolute scale by using the optical f value. Integral and momentum transfer cross sections were obtained by extrapolating the differential cross sections to 0 deg and to 180 deg. The question of normalizing electron-metal-atom collision cross sections in general was examined and the method of normalization to optical f values in particular was investigated in detail. It has been concluded that the extrapolation of the apparent generalized oscillator strength (obtained from the measured differential cross sections) to the zero momentum transfer limit with an expression using even powers of the momentum transfer and normalization of the limit to the optical f value yields reliable absolute cross sections.

Vuskovic, L.↗
NASA NTRS1983

Reliability of constricted double-heterojunction AlGaAs diode lasers

Constricted double-heterojunction diode lasers have been life tested at 70 C heatsink temperature and 3-4 mW/facet in CW operation. A median life of 7800 h is obtained at 70 C, which extrapolates to 400,000 h median life at room temperature. The extrapolated mean time to failure at room temperature is in excess of 1,000,000 h. Single-longitudinal-mode CW operation is maintained after 10,000 h of accelerated aging at 70 C.

Botez, D.↗
NASA NTRS1983

Increase and seasonal cycles of nitrous oxide in the earth's atmosphere

It is determined that nitrous oxide (N2O) is increasing at about 0.9 ppb/yr in the northern hemisphere and at about 0.7 ppb/yr in the southern hemisphere, based on about 9000 ground-level measurements at Cape Meares, Oregon (45 deg N), and Cape Grim, Tasmania (42 deg S), spanning a three-year period. It is also shown that the N2O concentrations vary with season in the northern hemisphere, where the concentrations are 0.8 ppbv higher during April, May, and June compared to the rest of the year, and in the southern hemisphere where the concentrations are about 0.5 ppbv lower during March, April, and May compared to the rest of the year. An explanation of this increase as a sizeable anthropogenically-controlled land-based source is presented, based on an examination of the existing estimates of natural and anthropogenic sources of N2O. Mass-balance calculations are also presented which suggest that a natural land-based source, peaking in spring, would explain the main features of the observed seasonal cycle. A growth model is employed to extrapolate the observed increase of N2O into the future and the results are compared with exponential extrapolations.

Khalil, M. A. K.↗
NASA NTRS1983

Self-organization of the protocell was a forward process

Yockey's (1981) interpretation of information theory relative to concepts of self-organization in the origin of life is criticized on the ground that it assumes that each amino acid residue type in a given sequence is an unaided information carrier throughout evolution. It is argued that more than one amino acid residue can act as a unit information carrier, and that this was the case in prebiotic protein evolution. Forward-extrapolation should be used to study prebiotic evolution, not backward-extrapolation. Transposing the near-random internal order of modern proteins to primitive proteins, as Yockey has done, is an unsupported assumption and disagrees with the results of experimental models of the primordial type. Studies indicate that early primary information carriers in evolution were mixtures of free alpha amino acids which necessarily had the capability of sequencing themselves.

Fox, S. W.↗
NASA NTRS1983

An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams

An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.

Subrahmanyam, K. B.↗
NASA NTRS1983

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iteratively. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗
NASA NTRS1984

Development of MCAERO wing design panel method with interactive graphics module

A reliable and efficient iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical pressure distribution. The design process is initialized by using MCAERO (MCAIR 3-D Subsonic Potential Flow Analysis Code) to analyze a baseline configuration. A second program DMCAERO is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter by applying a first-order expansion to the baseline equations in MCAERO. This matrix is calculated only once but is used in each iteration cycle to calculate the geometry perturbation and to analyze the perturbed geometry. The potential on the new geometry is calculated by linear extrapolation from the baseline solution. This extrapolated potential is converted to velocity by numerical differentiation, and velocity is converted to pressure by using Bernoulli's equation. There is an interactive graphics option which allows the user to graphically display the results of the design process and to interactively change either the geometry or the prescribed pressure distribution.

Hawk, J. D.↗
NASA NTRS1985

SSME Turbopump Turbine Computations

A two-dimensional viscous code was developed to be used in the prediction of the flow in the SSME high-pressure turbopump blade passages. The rotor viscous code (RVC) employs a four-step Runge-Kutta scheme to solve the two-dimensional, thin-layer Navier-Stokes equations. The Baldwin-Lomax eddy-viscosity model is used for these turbulent flow calculations. A viable method was developed to use the relative exit conditions from an upstream blade row as the inlet conditions to the next blade row. The blade loading diagrams are compared with the meridional values obtained from an in-house quasithree-dimensional inviscid code. Periodic boundary conditions are imposed on a body-fitted C-grid computed by using the GRAPE GRids about Airfoils using Poisson's Equation (GRAPE) code. Total pressure, total temperature, and flow angle are specified at the inlet. The upstream-running Riemann invariant is extrapolated from the interior. Static pressure is specified at the exit such that mass flow is conserved from blade row to blade row, and the conservative variables are extrapolated from the interior. For viscous flows the noslip condition is imposed at the wall. The normal momentum equation gives the pressure at the wall. The density at the wall is obtained from the wall total temperature.

Jorgenson, P. G. E.↗
NASA NTRS1985

Scaling laws for testing of high lift airfoils under heavy rainfall

The results of studies regarding the effect of rainfall about aircraft are briefly reviewed. It is found that performance penalties on airfoils have been identified in subscale tests. For this reason, it is of great importance that scaling laws be dveloped to aid in the extrapolation of these data to fullscale. The present investigation represents an attempt to develop scaling laws for testing subscale airfoils under heavy rain conditions. Attention is given to rain statistics, airfoil operation in heavy rain, scaling laws, thermodynamics of condensation and/or evaporation, rainfall and airfoil scaling, aspects of splash back, film thickness, rivulets, and flap slot blockage. It is concluded that the extrapolation of airfoil performance data taken at subscale under simulated heavy rain conditions to fullscale must be undertaken with caution.

Bilanin, A. J.↗
NASA NTRS1985

An absolute photometric system at 10 and 20 microns

Two new direct calibrations at 10 and 20 microns are presented in which terrestrial flux standards are referred to infrared standard stars. These measurements give both good agreement and higher accuracy when compared with previous direct calibrations. As a result, the absolute calibrations at 10 and 20 microns have now been determined with accuracies of 3 and 8 percent, respectively. A variety of absolute calibrations based on extrapolation of stellar spectra from the visible to 10 microns are reviewed. Current atmospheric models of A-type stars underestimate their fluxes by about 10 percent at 10 microns, whereas models of solar-type stars agree well with the direct calibrations. The calibration at 20 microns can probably be determined to about 5 percent by extrapolation from the more accurate result at 10 microns. The photometric system at 10 and 20 microns is updated to reflect the new absolute calibration, to base its zero point directly on the colors of A0 stars, and to improve the accuracy in the comparison of the standard stars.

Rieke, G. H.↗
NASA NTRS1985

Convergence acceleration of iterative solutions of Euler equations for transonic flow computations

In this paper, two acceleration techniques for Euler calculations are investigated. The first technique is an extrapolation procedure based on the Power Method; it is applicable when the iterative matrix has dominant eigenvalues. Both real and complex conjugate roots are allowed. The second technique is a generalization of the Minimal Residual Method, where the extrapolation step consists of a weighted combination of the corrections at different iteration levels and the weights are chosen to minimize the Lz norm of the residual. Numerical results, using Jameson's Runge-Kutta Multigrid Code, are presented. The extra computational work to apply either technique is negligible and the extra storage is not a problem on current supercomputers.

Hafez, M.↗
NASA NTRS1986

Creep properties of PWC-11 base metal and weldments as affected by heat treatment

In a preliminary study using single specimens for each condition, PWC-11 (a niobium-base alloy with a nominal composition of Nb-1%Zr-0.1%C) was creep tested at 1350 K and 40 MPa. Base metal specimens and specimens with transverse electron beam welds were tested with and without a 1000 hr, 1350 K aging treatment prior to testing. In the annealed condition (1 hr at 1755 K + 2 hr at 1475 K), the base metal exhibited superior creep strength compared to the nonaged condition, reaching 1 percent strain in 3480 hr. A 1000 hr, 1350 K aging treatment prior to creep testing had a severe detrimental effect on creep strength of the base metal and transverse electron beam weldments, reducing the time to attain 1 percent strain by an order of magnitude. Extrapolated temperature compensated creep rates indicate that the present heat of PWC-11 may be four times as creep resistant as similarly tested Nb-1%Zr. The extrapolated stress to achieve 1 percent creep strain in 7 yr at 1350 K is 2.7 MPa for annealed Nb-1%Zr and 12 MPa for annealed and aged PWC-11 base metal with and without a transverse electron beam weld.

Titran, R. H.↗
NASA NTRS1985

On stellar X-ray emission

Stellar X-ray astronomy represents an entirely new astronomical discipline which has emerged during the past five years. It lies at the crossroads of solar physics, stellar physics, and general astrophysics. The present review is concerned with the main physical problems which arise in connection with a study of the stellar X-ray data. A central issue is the extent to which the extrapolation from solar physics is justified and the definition (if possible) of the limits to such extrapolation. The observational properties of X-ray emission from stars are considered along with the solar analogy and the modeling of X-ray emission from late-type stars, the modeling of X-ray emission from early-type stars, the physics of stellar X-ray emission, stellar X-ray emission in the more general astrophysical context, and future prospects.

Rosner, R.↗
NASA NTRS1986

Acceleration of convergence of vector sequences

A general approach to the construction of convergence acceleration methods for vector sequence is proposed. Using this approach, one can generate some known methods, such as the minimal polynomial extrapolation, the reduced rank extrapolation, and the topological epsilon algorithm, and also some new ones. Some of the new methods are easier to implement than the known methods and are observed to have similar numerical properties. The convergence analysis of these new methods is carried out, and it is shown that they are especially suitable for accelerating the convergence of vector sequences that are obtained when one solves linear systems of equations iterative. A stability analysis is also given, and numerical examples are provided. The convergence and stability properties of the topological epsilon algorithm are likewise given.

Sidi, A.↗
NASA NTRS1986

Transformation of two and three-dimensional regions by elliptic systems

Efforts in transferring computational work from the LRC computer to the IRIS Graphics Workstation at MSU are reported and the computation of a conservative solution of a simple hyperbolic equation on an overlapping grid is discussed. Several conclusions concerning computations on overlapping grids are apparent. Problems only occur when there is a major difference in grid spacing on the individual component grids. In the case of hyperbolic equations, it is necessary that both interpolation and extrapolation be applied at the grid boundaries. When interpolated values are used at outflow boundary points, excessive oscillations in the numerical solution may be the result. The same conclusions would be valid for more complicated systems of hyperbolic equations such as the Euler equations for inviscid flow. Some of the solution values would be extrapolated at the overlap boundary, the exact number depending on the number of characteristics pointing out of the overlap region. It is also possible that similar boundary conditions may be needed for some parabolic equations such as high Reynolds number viscous flow equations. Efforts were also expended on the development of three-dimensional conservative interpolation procedures. Finally, the investigation of grid smoothing procedures were initiated during this reporting period. It was decided that the first grid smoothing algorithms will be based on the concepts of variational grid generation.

Mastin, C. W.↗