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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Approximate methods for finding CO2 15-micron band transmission in planetary atmospheres

Physical band models that use simplifying assumptions about the structure of the CO2 15-micron band are described and compared with the accurate line-by-line model of Fels and Schwarzkopf (1981). The methods have application to the models of the atmospheres of Venus, earth, and Mars. The narrow-band methods include a general random model and techniques employing the Malkmus (1967) line-strength distribution, and the accuracy of these models at low pressure is found to be sensitive to the line-strength distribution and the line shape. When combined with a simple Voigt parameterization, the more efficient approximate methods represented by an exponential wideband model are found to be almost as accurate as the expensive narrow-band models. Empirical logarithmic wideband models used in climate-modeling studies are found to be very efficient, but of limited range of validity.

Crisp, David↗
NASA NTRS1959

Evaluation of Several Approximate Methods for Calculating the Symmetrical Bending-Moment Response of Flexible Airplanes to Isotropic Atmospheric Turbulence

Several approximate procedures for calculating the bending-moment response of flexible airplanes to continuous isotropic turbulence are presented and evaluated. The modal methods (the mode-displacement and force-summation methods) and a matrix method (segmented-wing method) are considered. These approximate procedures are applied to a simplified airplane for which an exact solution to the equation of motion can be obtained. The simplified airplane consists of a uniform beam with a concentrated fuselage mass at the center. Airplane motions are limited to vertical rigid-body translation and symmetrical wing bending deflections. Output power spectra of wing bending moments based on the exact transfer-function solutions are used as a basis for the evaluation of the approximate methods. It is shown that the force-summation and the matrix methods give satisfactory accuracy and that the mode-displacement method gives unsatisfactory accuracy.

Bennett, Floyd V.↗
NASA NTRS1977

Validity of approximate methods in molecular scattering. III - Effective potential and coupled states approximations for differential and gas kinetic cross sections

Two dimensionality-reducing approximations, the j sub z-conserving coupled states (sometimes called the centrifugal decoupling) method and the effective potential method, were applied to collision calculations of He with CO and with HCl. The coupled states method was found to be sensitive to the interpretation of the centrifugal angular momentum quantum number in the body-fixed frame, but the choice leading to the original McGuire-Kouri expression for the scattering amplitude - and to the simplest formulas - proved to be quite successful in reproducing differential and gas kinetic cross sections. The computationally cheaper effective potential method was much less accurate.

Monchick, L.↗
NASA NTRS1985

A review of some approximate methods used in aerodynamic heating analyses

It is pointed out that preliminary design and optimization studies for new aerospace vehicles require techniques which can calculate aerodynamic heating rates accurately and efficiently. The method employed to calculate the flow field depends to a large extent on the shape of the vehicle, Mach number, Reynolds number, and Knudsen number. In the case of the aero-assisted orbital transfer vehicle (AOTV), a substantial portion of the flight will be in the transitional regime between continuum and free molecule flow. The present paper discusses some approximate methods which have been used to calculate heating rates on high-speed vehicles. Attention is given to the stagnation point and leading edges, the downstream region, the axisymmetric analog, laminar and turbulent heating rates, transition heating rates, gas models, and three-dimensional applications.

Dejarnette, F. R.↗
NASA NTRS1984

Discrete approximation methods for parameter identification in delay systems

Approximation schemes for parameter identification problems in which the governing state equation is a linear functional differential equation of retarded type are constructed. The basis of the schemes is the replacement of the parameter identification problem having an infinite dimensional state equation by a sequence of approximating parameter identification problems in which the states are given by finite dimensional discrete difference equations. The difference equations are constructed using linear semigroup theory and rational function approximations to the exponential. Sufficient conditions are given for the convergence of solutions to the approximating problems, which can be obtained using conventional methods, to solutions to the original parameter identification problem. Finite difference and spline based schemes using Paderational function approximations to the exponential are constructed, and shown to satisfy the sufficient conditions for convergence. A discussion and analysis of numerical results obtained through the application of the schemes to several examples is included.

Rosen, I. G.↗
NASA NTRS1979

Approximation methods for combined thermal/structural design

Two approximation concepts for combined thermal/structural design are evaluated. The first concept is an approximate thermal analysis based on the first derivatives of structural temperatures with respect to design variables. Two commonly used first-order Taylor series expansions are examined. The direct and reciprocal expansions are special members of a general family of approximations, and for some conditions other members of that family of approximations are more accurate. Several examples are used to compare the accuracy of the different expansions. The second approximation concept is the use of critical time points for combined thermal and stress analyses of structures with transient loading conditions. Significant time savings are realized by identifying critical time points and performing the stress analysis for those points only. The design of an insulated panel which is exposed to transient heating conditions is discussed.

Haftka, R. T.↗
NASA NTRS1977

The application of the Routh approximation method to turbofan engine models

The Routh approximation technique is applied in the frequency domain to a 16th order state variable turbofan engine model. The results obtained motivate the extension of the frequency domain formulation of the Routh method to the time domain to handle the state variable formulation directly. The time domain formulation is derived and a new characterization, which specifies all possible Routh similarity transformations, is given. This characterization is computed by the solution of two eigenvalue-eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described and some results are given. Additional computational problems are discussed including an optimization procedure which can improve the approximation accuracy by taking advantage of the transformation characterization.

Merrill, W. C.↗
NASA NTRS1951

Approximate method of integration of laminar boundary layer in incompressible fluid

A method is given for the approximate solution of the equations of the two-dimensional laminar boundary layer in an incompressible fluid. The method is based on the use of a system of equations of successive moments that is easily solved for simple supplementary assumptions. The solution obtained is given in closed form by simple formulas and is claimed to be no less accurate than the complicated solutions previously obtained, which were based on the use of special classes of flows.

BOUNDARY LAYER - WING SECTIONS↗
NASA NTRS1977

The application of the Routh approximation method to turbofan engine models

The Routh approximation technique is applied in the frequency domain to a 16th order state variable turbofan engine model. The results obtained motivate the extension of the frequency domain formulation of the Routh method to the time domain to handle the state variable formulation directly. The time domain formulation is derived, and a characterization, which specifies all possible Routh similarity transformations, is given. The characterization is computed by the solution of two eigenvalue eigenvector problems. The application of the time domain Routh technique to the state variable engine model is described, and some results are given.

Merrill, W. C.↗
NASA NTRS1990

An approximate method for calculating three-dimensional inviscid hypersonic flow fields

An approximate solution technique was developed for 3-D inviscid, hypersonic flows. The method employs Maslen's explicit pressure equation in addition to the assumption of approximate stream surfaces in the shock layer. This approximation represents a simplification to Maslen's asymmetric method. The present method presents a tractable procedure for computing the inviscid flow over 3-D surfaces at angle of attack. The solution procedure involves iteratively changing the shock shape in the subsonic-transonic region until the correct body shape is obtained. Beyond this region, the shock surface is determined using a marching procedure. Results are presented for a spherically blunted cone, paraboloid, and elliptic cone at angle of attack. The calculated surface pressures are compared with experimental data and finite difference solutions of the Euler equations. Shock shapes and profiles of pressure are also examined. Comparisons indicate the method adequately predicts shock layer properties on blunt bodies in hypersonic flow. The speed of the calculations makes the procedure attractive for engineering design applications.

Riley, Christopher J.↗
DOE OSTI2021

Natively Periodic Fast Multipole Method: Approximating the Optimal Green’s Function

The fast multipole method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green's function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green's function for such a method that results in the numerical solution that converges to the equivalent particle-mesh (PM) solution in the limit of sufficiently high order of multipoles. A discrete functional equation for the optimal Green's function can be derived, but is not practically useful as methods for its solution are not known. Instead, this paper presents an approximation for the optimal Green's function that is accurate to better than 10 -3 in ${L}_{\mathrm{MAX}}$ norm and 10 -4 in L 2 norm for practically useful multipole counts. Such an approximately optimal Green's function offers a practical way for implementing the FMM with periodic boundary conditions natively, without the need to compute lattice sums or to rely on hybrid FMM-PM approaches.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1989

An approximate methods approach to probabilistic structural analysis

A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.

Mcclung, R. C.↗
NASA NTRS2003

Heats of Segregation of BCC Metals Using Ab Initio and Quantum Approximate Methods

Many multicomponent alloys exhibit surface segregation, in which the composition at or near a surface may be substantially different from that of the bulk. A number of phenomenological explanations for this tendency have been suggested, involving, among other things, differences among the components' surface energies, molar volumes, and heats of solution. From a theoretical standpoint, the complexity of the problem has precluded a simple, unified explanation, thus preventing the development of computational tools that would enable the identification of the driving mechanisms for segregation. In that context, we investigate the problem of surface segregation in a variety of bcc metal alloys by computing dilute-limit heats of segregation using both the quantum-approximate energy method of Bozzolo, Ferrante and Smith (BFS), and all-electron density functional theory. In addition, the composition dependence of the heats of segregation is investigated using a BFS-based Monte Carlo procedure, and, for selected cases of interest, density functional calculations. Results are discussed in the context of a simple picture that describes segregation behavior as the result of a competition between size mismatch and alloying effects

Good, Brian↗
NASA NTRS1991

Application of a two-point exponential approximation method in optimizing rotorcraft airframe structures

The Fadel (1990) two-point exponential approximation technique for rotorcraft airframe structural optimization is presently examined by comparing its results with the well established linear and hybrid first-order methods. Attention is given to both the elastic-line and FEM models of an AH-1G airframe. The Direct Matrix Abstraction Programming Language is used to compute sensitivity derivatives and motivate the CONMIN optimizer to produce the design change.

Sareen, Ashish K.↗
DOE OSTI2023

Systems and methods for approximating musculoskeletal dynamics

An approximation method and system are provided for more quickly controlling a prosthetic or other device by reducing computational processing time in a muscle model that can be used to control the prosthetic. For a given muscle, the approximation method can quickly compute polynomial structures for a muscle length and for each associated moment arms, which may be used to generate a torque for a joint position of a physics model. The physics model, in turn, produces a next joint position and velocity data for driving a prosthetic. The approximation method expands the polynomial structures as long as expansion is possible and sufficiently beneficial. The computations can be performed quickly by expanding the polynomial structures in a way that constrains the muscle length polynomial to the moment arm polynomial structures, and vice versa.

Sobinov, Anton↗
NASA NTRS1984

Approximation methods for inverse problems involving the vibration of beams with tip bodies

Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.

Rosen, I. G.↗
NASA NTRS2003

Atomistic Modeling of Nanostructures via the BFS Quantum Approximate Method

Ideally, computational modeling techniques for nanoscopic physics would be able to perform free of limitations on the type and number of elements, while providing comparable accuracy when dealing with bulk or surface problems. Computational efficiency is also desirable, if not mandatory, for properly dealing with the complexity of typical nano-strucured systems. A quantum approximate technique, the BFS method for alloys, which attempts to meet these demands, is introduced for the calculation of the energetics of nanostructures. The versatility of the technique is demonstrated through analysis of diverse systems, including multi-phase precipitation in a five element Ni-Al-Ti-Cr-Cu alloy and the formation of mixed composition Co-Cu islands on a metallic Cu(III) substrate.

Bozzolo, Guillermo↗