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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

The effects of solution treatment on the mechanical properties of age-hardened A-286 bar stock at elevated and cryogenic temperature

The mechanical properties are presented of solution treated and age hardened A-286 corrosion resistant steel bar stock. Material solution treated at 899 C or 982 C, each followed by an age hardening treatment of 718 C, was evaluated. Test specimens manufactured from 1.50 inch (3.81 cm) diameter bar stock were tested at temperatures from +649 C to -253 C. The test data indicated excellent tensile, yield, elongation and reduction-in-area properties at all testing temperatures for both solution treated and aged materials. Cryogenic temperature notched tensile, impact, and shear tests indicated excellent notch strength, ductility, and shear values. There was very little difference in the mechanical properties of the two solution treated and aged materials. The only exception was that the 962 C solution treated and aged material had superior stress rupture properties at 649 C.

Montano, J. W.↗
NASA NTRS1971

The effect of solute additions on the steady-state creep behavior of dispersion-strengthened aluminum.

The effect of solute additions on the steady-state creep behavior of coarse-grained dispersion-strengthened aluminum alloys was studied. Recrystallized dispersion-strengthened solid solutions were found to have stress and temperature sensitivities quite unlike those observed in single-phase solid solutions having the same composition and grain size. The addition of magnesium or copper to the matrix of a recrystallized dispersion-strengthened aluminum causes a decrease in the steady-state creep rate which is much smaller than that caused by similar amounts of solute in single-phase solid solutions. All alloys exhibited essentially a 4.0 power stress exponent in agreement with the model of Ansell and Weertman. The activation energy for steady-state creep in dispersion-strengthened Al-Mg alloys, as well as the stress dependence, was in agreement with the physical model of dislocation climb over the dispersed particles.

Reynolds, G. H.↗
NASA NTRS1971

Similarity and generalized finite-difference solutions of parabolic partial differential equations.

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Clausing, A. M.↗
NASA NTRS1972

Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

Stricklin, J. A.↗
NASA NTRS1972

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Garrett, L. B.↗
NASA NTRS1973

Simultaneous observation solutions for NASA-MOTS and SPEOPT station positions on the North American datum

Simultaneous observations of the GEOS-I and II flashing lamps by the NASA MOTS and SPEOPT cameras on the North American Datum (NAD) were analyzed using geometrical techniques to provide an adjustment of the station coordinates. Two separate adjustments were obtained. An optical data only solution was computed in which the solution scale was provided by the Rosman-Mojave distance obtained from a dynamic station solution. In a second adjustment, scaling was provided by processing simultaneous laser ranging data from Greenbelt and Wallops Island in a combined optical-laser solution. Comparisons of these results with previous GSFC dynamical solutions indicate an rms agreement on the order of 4 meters or better in each coordinate. Comparison with a detailed gravimetric geoid of North America yields agreement of 3 meters or better for mainland U.S. stations and 7 and 3 meters, respectively, for Bermuda and Puerto Rico.

Reece, J. S.↗
NASA NTRS1973

A global station coordinate solution based upon camera and laser data - GSFC 1973

Results for the geocentric coordinates of 72 globally distributed satellite tracking stations consisting of 58 cameras and 14 lasers are presented. The observational data for this solution consists of over 65,000 optical observations and more than 350 laser passes recorded during the National Geodetic Satellite Program, the 1968 Centre National d'Etudes Spatiales/Smithsonian Astrophysical Observatory (SAO) Program, and International Satellite Geodesy Experiment Program. Dynamic methods were used. The data were analyzed with the GSFC GEM and SAO 1969 Standard Earth Gravity Models. The recent value of GM = 398600.8 cu km/sec square derived at the Jet Propulsion Laboratory (JPL) gave the best results for this combination laser/optical solution. Solutions are made with the deep space solution of JPL (LS-25 solution) including results obtained at GSFC from Mariner-9 Unified B-Band tracking. Datum transformation parameters relating North America, Europe, South America, and Australia are given, enabling the positions of some 200 other tracking stations to be placed in the geocentric system.

Marsh, J. G.↗
NASA NTRS1973

An interative solution of an integral equation for radiative transfer by using variational technique

An effective iterative technique is introduced to solve a nonlinear integral equation frequently associated with radiative transfer problems. The problem is formulated in such a way that each step of an iterative sequence requires the solution of a linear integral equation. The advantage of a previously introduced variational technique which utilizes a stepwise constant trial function is exploited to cope with the nonlinear problem. The method is simple and straightforward. Rapid convergence is obtained by employing a linear interpolation of the iterative solutions. Using absorption coefficients of the Milne-Eddington type, which are applicable to some planetary atmospheric radiation problems. Solutions are found in terms of temperature and radiative flux. These solutions are presented numerically and show excellent agreement with other numerical solutions.

Yoshikawa, K. K.↗
NASA NTRS1973

Backlund transformation for solutions of the Korteweg-de Vries equation

We present a Backlund transformation operating on solutions of the Korteweg-de Vries equation. It provides a unifying approach to the theory of solitary waves (solutions). Recursive application of the transformation to any solution of the Korteweg-de Vries equation generates a hierarchy of solutions for which an algebraic recursion relation is obtained. Every such hierarchy (one of which is the known family of pure multisoliton solutions) thus admits a nonlinear superposition principle.

Wahlquist, H. D.↗
NASA NTRS1974

Solutions for laminar boundary layers with separation and reattachment

Numerical solutions of the laminar, incompressible boundary-layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified, and the pressure is deduced from the solution. A stream function/vorticity formulation of the boundary-layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite-difference equations, in which the flow direction is taken into account, are obtained by a successive column iteration scheme. Results are compared with Klineberg and Steger's (1974) separated boundary-layer calculations, and with Briley's (1971) solution of the Navier-Stokes equations for a separated region.

Carter, J. E.↗
NASA NTRS1975

Almost periodic solutions to difference equations

The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

Bayliss, A.↗
NASA NTRS1974

An improved solution of the simplified two-phase plume

An exact solution of the two-phase, gas-particle, solid propellant rocket exhaust plume flowfield is presented. The good agreement between the exact solution and the experimental data proves that the accuracy of the present technique is acceptable for, at least, preliminary design calculations. A good comparison between the plume impingement effects predicted by the exact solution and those by the best computer code available has also been found for various propellant formulations and rocket sizes. This shows that the present exact solution does describe the basic characteristics of the two-phase plume. In case of a parametric analysis for obtaining an optimum design, the present exact solution will be a more convenient tool than any one of the numerical techniques especially when many parameters are involved in the optimization study. Several typical results are shown herein and their physical significance is discussed.

Wang, S. Y.↗
NASA NTRS1974

The influence of the computational mesh on accuracy for initial value problems with discontinuous or nonunique solutions

Discontinuous, or weak, solutions of the wave equation, the inviscid form of Burgers equation, and the time-dependent, two-dimensional Euler equations are studied. A numerical method of second-order accuracy in two forms, differential and integral, is used to calculate the weak solutions of these equations for several initial value problems, including supersonic flow past a wedge, a double symmetric wedge, and a sphere. The effect of the computational mesh on the accuracy of computed weak solutions including shock waves and expansion phenomena is studied. Modifications to the finite-difference method are presented which aid in obtaining desired solutions for initial value problems in which the solutions are nonunique.

Maccormack, R. W.↗
NASA NTRS1975

Use of numerically generated body-fitted coordinate systems for solution of the Navier-Stokes equations

A procedure for numerical solution of the time-dependent, two-dimensional incompressible Navier-Stokes equations that can treat the unsteady laminar flow about bodies of arbitrary shape, such as two-dimensional airfoils, multiple airfoils, and submerged hydrofoils, as naturally as it can deal with the flow about simple bodies. The solution is based on a method of automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multiconnected region containing any number of arbitrarily shaped bodies. The curvilinear coordinates are generated as the solution of two elliptical partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other being specified along the boundaries. The solution compares excellently with the Blasius boundary layer solution for the flow past a semiinfinite flat plate.

Thompson, J. F.↗
NASA NTRS1975

Inverse solutions for laminar boundary-layer flows with separation and reattachment

Numerical solutions of the laminar, incompressible boundary layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity-stream-function formulation of the boundary layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary layer calculations, and with Briley's solution of Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward marching procedure for separated flows.

Carter, J. E.↗
NASA NTRS1976

Supersonic flow of chemically reacting gas-particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

A numerical solution for chemically reacting supersonic gas-particle flows in rocket nozzles and exhaust plumes was described. The gas-particle flow solution is fully coupled in that the effects of particle drag and heat transfer between the gas and particle phases are treated. Gas and particles exchange momentum via the drag exerted on the gas by the particles. Energy is exchanged between the phases via heat transfer (convection and/or radiation). Thermochemistry calculations (chemical equilibrium, frozen or chemical kinetics) were shown to be uncoupled from the flow solution and, as such, can be solved separately. The solution to the set of governing equations is obtained by utilizing the method of characteristics. The equations cast in characteristic form are shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The particle distribution is represented in the numerical solution by a finite distribution of particle sizes.

Penny, M. M.↗
NASA NTRS1976

Solution of linear systems by a singular perturbation technique

An approximate solution is obtained for a singularly perturbed system of initial valued, time invariant, linear differential equations with multiple boundary layers. Conditions are stated under which the approximate solution converges uniformly to the exact solution as the perturbation parameter tends to zero. The solution is obtained by the method of matched asymptotic expansions. Use of the results for obtaining approximate solutions of general linear systems is discussed. An example is considered to illustrate the method and it is shown that the formulas derived give a readily computed uniform approximation.

Ardema, M. D.↗
NASA NTRS1976

Turbulent viscous-shock-layer solutions with strong vorticity interaction

Numerical solutions of the viscous-shock-layer equations governing laminar and turbulent flows of a perfect gas and radiating and nonradiating mixtures of perfect gases in chemical equilibrium are presented for hypersonic flow over spherically blunted cones and hyperboloids. The results are compared with boundary-layer and inviscid flow-field solutions. The agreement with the inviscid flow field data is satisfactory. The agreement with boundary-layer solutions is good except in regions of strong vorticity interaction. In these flow regions, the viscous-shock-layer solutions appear to be more satisfactory than the boundary-layer solutions.

Anderson, E. C.↗