Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Helicopter rotor loads using a matched asymptotic expansion technique

The theoretical basis and computational feasibility of the Van Holten method, and its performance and range of validity by comparison with experiment and other approximate methods was examined. It is found that within the restrictions of incompressible, potential flow and the assumption of small disturbances, the method does lead to a valid description of the flow. However, the method begins to break down under conditions favoring nonlinear effects such as wake distortion and blade/rotor interaction.

Pierce, G. A.↗
NASA NTRS1993

Nongray gas analyses for reflecting walls utilizing a flux technique

A flux formulation for a planar slab of molecular gas radiation bounded by diffuse reflecting walls is developed. While this formulation is limited to the planar geometry, it is useful for studying approximations necessary in modeling nongray radiative heat transfer. The governing equations are derived by considering the history of multiple reflections between the walls. Accurate solutions are obtained by explicitly accounting for a finite number of reflections and approximating the spectral effects of the remaining reflections. Four approximate methods are presented and compared using a single absorption band of H2O. All four methods reduce to an identical zeroth-order formulation, which accounts for all reflections approximately but does handle nonreflected radiation correctly. A single absorption band of CO2 is also considered using the best-behaved approximation for higher orders. A zeroth-order formulation is sufficient to predict the radiative transfer accurately for many cases considered. For highly reflecting walls, higher order solutions are necessary for better accuracy. Including all the important bands of H2O, the radiative source distributions are also obtained for two different temperature and concentration profiles.

Menart, J. A.↗
NASA NTRS1971

Investigation of thermal protection systems effects on viscid and inviscid flow fields for manned entry systems

Procedures and methods for predicting aerothermodynamic heating to delta orbiter shuttle vehicles were reviewed. A number of approximate methods were found to be adequate for large scale parameter studies, but are considered inadequate for final design calculations. It is recommended that final design calculations be based on a computer code which accounts for nonequilibrium chemistry, streamline spreading, entropy swallowing, and turbulence. It is further recommended that this code be developed with the intent that it can be directly coupled with an exact inviscid flow field calculation when the latter becomes available. A nonsimilar, equilibrium chemistry computer code (BLIMP) was used to evaluate the effects of entropy swallowing, turbulence, and various three dimensional approximations. These solutions were compared with available wind tunnel data. It was found study that, for wind tunnel conditions, the effect of entropy swallowing and three dimensionality are small for laminar boundary layers but entropy swallowing causes a significant increase in turbulent heat transfer. However, it is noted that even small effects (say, 10-20%) may be important for the shuttle reusability concept.

Bartlett, E. P.↗
NASA NTRS2008

Accuracy of Gradient Reconstruction on Grids with High Aspect Ratio

Gradient approximation methods commonly used in unstructured-grid finite-volume schemes intended for solutions of high Reynolds number flow equations are studied comprehensively. The accuracy of gradients within cells and within faces is evaluated systematically for both node-centered and cell-centered formulations. Computational and analytical evaluations are made on a series of high-aspect-ratio grids with different primal elements, including quadrilateral, triangular, and mixed element grids, with and without random perturbations to the mesh. Both rectangular and cylindrical geometries are considered; the latter serves to study the effects of geometric curvature. The study shows that the accuracy of gradient reconstruction on high-aspect-ratio grids is determined by a combination of the grid and the solution. The contributors to the error are identified and approaches to reduce errors are given, including the addition of higher-order terms in the direction of larger mesh spacing. A parameter GAMMA characterizing accuracy on curved high-aspect-ratio grids is discussed and an approximate-mapped-least-square method using a commonly-available distance function is presented; the method provides accurate gradient reconstruction on general grids. The study is intended to be a reference guide accompanying the construction of accurate and efficient methods for high Reynolds number applications

Thomas, James↗
NASA NTRS1980

Theoretical mean colors for RR Lyrae variables

A hydrodynamically pulsating 0.6 solar mass model of a typical RR Lyrae variable was studied with a radiation transport-hydrodynamic computer program to predict theoretical T sub 3 and colors at many phases and to find the proper methods for getting mean colors and the consequent mean effective temperatures. The variable Eddington radiation approximation method was used with gray and with multifrequency absorption coefficients to represent the radiation flow in the outer optically thin layers. Comparison between observed and computed B-V colors indicate that these low Z population 2 models are reasonably accurate using King 1A composition opacities. The well known Oke, Giver, and Searle relation between B-V and T sub e reproduced. Mean colors were found by four different averaging methods. The method that gives a mean color and the mean T sub e closest to the nonpulsating model was the separate intensity means of B and V.

Davis, C. G.↗
NASA NTRS1994

A rapid radiative transfer model for reflection of solar radiation

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Xiang, X.↗
NASA NTRS1972

Adjoint variational methods in nonconservative stability problems.

A general nonself-adjoint eigenvalue problem is examined and it is shown that the commonly employed approximate methods, such as the Galerkin procedure, the method of weighted residuals and the least square technique lack variational descriptions. When used in their previously known forms they do not yield stationary eigenvalues and eigenfunctions. With the help of an adjoint system, however, several analogous variational descriptions may be developed and it is shown in the present study that by properly restating the method of least squares, stationary eigenvalues may be obtained. Several properties of the adjoint eigenvalue problem, known only for a restricted group, are shown to exist for the more general class selected for study.

Prasad, S. N.↗
NASA NTRS1987

Aerodynamic sensitivities from subsonic, sonic and supersonic unsteady, nonplanar lifting-surface theory

The technique of implicit differentiation has been used in combination with linearized lifting-surface theory to derive analytical expressions for aerodynamic sensitivities (i.e., rates of change of lifting pressures with respect to general changes in aircraft geometry, including planform variations) for steady or oscillating planar or nonplanar lifting surfaces in subsonic, sonic, or supersonic flow. The geometric perturbation is defined in terms of a single variable, and the user need only provide simple expressions or similar means for defining the continuous or discontinuous global or local perturbation of interest. Example expressions are given for perturbations of the sweep, taper, and aspect ratio of a wing with trapezoidal semispan planform. In addition to direct computational use, the analytical method presented here should provide benchmark criteria for assessing the accuracy of aerodynamic sensitivities obtained by approximate methods such as finite geometry perturbation and differencing. The present process appears to be readily adaptable to more general surface-panel methods.

Yates, E. Carson, Jr.↗
NASA NTRS1944

The conformal transformation of an airfoil into a straight line and its application to the inverse problem of airfoil theory

A method of conformal transformation is developed that maps an airfoil into a straight line, the line being chosen as the extended chord line of the airfoil. The mapping is accomplished by operating directly with the airfoil ordinates. The absence of any preliminary transformation is found to shorten the work substantially over that of previous methods. Use is made of the superposition of solutions to obtain a rigorous counterpart of the approximate methods of thin-airfoils theory. The method is applied to the solution of the direct and inverse problems for arbitrary airfoils and pressure distributions. Numerical examples are given. Applications to more general types of regions, in particular to biplanes and to cascades of airfoils, are indicated. (author)

Mutterperl, William↗
NASA NTRS1950

Application of radial-equilibrium condition to axial-flow compressor and turbine design

Basic general equations governing the three-dimensional compressible flow of gas through a compressor or turbine are given in terms of total enthalpy, entropy, and velocity components of the gas. Two methods of solution are obtained for the simplified, steady axially symmetric flow; one involves the use of a number of successive planes normal to the axis of the machine and short distances apart, and the other involves only three stations for a stage in which an appropriate radial-flow path is used. Methods of calculation for the limiting cases of zero and infinite blade aspect ratios and an approximate method of calculation for finite blade aspect ratio are also given. In these methods, the blade loading and the shape of the annular passage wall may be arbitrarily specified.

Wu, Chung-Hua↗
NASA NTRS2015

Predicting the Mineral Composition of Dust Aerosols: Model Evaluation and Identification of Key Processes with Observations - Part 2

A global compilation of nearly sixty measurement studies is used to evaluate two methods of simulating the mineral composition of dust aerosols in an Earth system model. Both methods are based upon a Mean Mineralogical Table (MMT) that relates the soil mineral fractions to a global atlas of arid soil type. The Soil Mineral Fraction (SMF) method assumes that the aerosol mineral fractions match the fractions of the soil. The MMT is based upon soil measurements after wet sieving, a process that destroys aggregates of soil particles that would have been emitted from the original, undisturbed soil. The second method approximately reconstructs the emitted aggregates. This model is referred to as the Aerosol Mineral Fraction (AMF) method because the mineral fractions of the aerosols differ from those of the wet-sieved parent soil, partly due to reaggregation. The AMF method remedies some of the deficiencies of the SMF method in comparison to observations. Only the AMF method exhibits phyllosilicate mass at silt sizes, where they are abundant according to observations. In addition, the AMF quartz fraction of silt particles is in better agreement with measured values, in contrast to the overestimated SMF fraction. Measurements at distinct clay and silt particle sizes are shown to be more useful for evaluation of the models, in contrast to the sum over all particles sizes that is susceptible to compensating errors, as illustrated by the SMF experiment. Model errors suggest that allocation of the emitted silt fraction of each mineral into the corresponding transported size categories is an important remaining source of uncertainty. Evaluation of both models and the MMT is hindered by the limited number of size-resolved measurements of mineral content that sparsely sample aerosols from the major dust sources. The importance of climate processes dependent upon aerosol mineral composition shows the need for global and routine mineral measurements.

aerosols↗
NASA NTRS1945

A method for the calculation of external lift, moment, and pressure drag of slender open-nose bodies of revolution at supersonic speeds

An approximate method is presented for the calculation of the external lift, moment, and pressure drag of slender open-nose bodies of revolution of supersonic speeds. The lift, moment, and pressure drag of a typical ram-jet body shape are calculated at Mach numbers 1.45, 1.60, 1.75, and 3.00; and the lift and moment results are compared with available experimental data. The agreement of the calculated lift and moment data with the experimental data is excellent. The pressure-drag comparison was not presented because of the uncertainty of the amount of skin-friction drag present in the experimental results.

Brown, Clinton E↗
NASA NTRS1977

Review of radiative transfer methods in scattering atmospheres

The radiative transfer in a scattering plane-parallel atmosphere is discussed, considering the exact analytical, the computational and the approximate methods. Some results of numerical comparisons are given. Finally, the difficulties of realistic atmospheric models are emphasized.

Lenoble, J.↗
NASA NTRS1951

Method of successive approximations for the solution of certain problems in aerodynamics

A method of successive approximations for the solution of problems in the fields of diffusion, boundary-layer flow, and heat-transfer is illustrated by solving problems in each of these fields. In most of the examples, the approximate solutions are compared with known accurate solutions and the agreement is shown to be good.

FLOW, TURBULENT - DIFFUSION↗
NASA NTRS1991

Combining global and local approximations

A method based on a linear approximation to a scaling factor, designated the 'global-local approximation' (GLA) method, is presented and shown capable of extending the range of usefulness of derivative-based approximations to a more refined model. The GLA approach refines the conventional scaling factor by means of a linearly varying, rather than constant, scaling factor. The capabilities of the method are demonstrated for a simple beam example with a crude and more refined FEM model.

Haftka, Raphael T.↗
NASA NTRS1985

Application of axisymmetric analogue for calculating heating in three-dimensional flows

A rapid, approximate method has been developed for calculating the heating rates on three-dimensional vehicles such as the Space Shuttle Orbiter and other advanced reentry configurations. The method is based on the axisymmetric analogue for three-dimensional boundary layers. It uses information obtained from a three-dimensional inviscid flowfield solution, such as HALIS, to calculate inviscid surface streamlines along which approximate heating rates are calculated independent of what happens along other streamlines. Three-dimensional effects are included through the metric coefficient that describes the divergence or convergence of streamlines. Boundary-layer edge properties are obtained from the inviscid flowfield solution by interpolating in the inviscid flowfield at a distance equal to the boundary-layer thickness away from the wall. This accounts, approximately, for the variable boundary-layer edge entropy. Using this method, heating calculations can be made along a typical streamline in a few seconds. This method has been used to accurately predict heating rates for simple shapes such as a spherically blunted cone and more complex shapes such as the Shuttle Orbiter for a variety of wind-tunnel and flight conditions. A unique feature of the method is its ability to accurately predict heating rates on the Shuttle Orbiter wing.

Hamilton, H. H.↗