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At least 829 records · Page 46
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NASA NTRS1974

Development of solution techniques for nonlinear structural analysis

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Vos, R. G.↗
NASA NTRS1974

Numerical solution for unsteady sonic flow over thin wings

A numerical solution precedure of a simplified unsteady transonic equation which is fast, reasonably accurate, and takes into account many of the effects of the steady flow field is described. The numeric solution of this equation is accurate and is accomplished on an IBM 360/65 computer. Arbitrary planform shape is accommodated and variable local Mach number effects from the steady flow are easily handled.

Kimble, K. R.↗
NASA NTRS1975

Numerical solution of the hypersonic viscous-shock-layer equations for laminar, transitional, and turbulent flows of a perfect gas over blunt axially symmetric bodies

The viscous shock layer equations applicable to hypersonic laminar, transitional, and turbulent flows of a perfect gas over two-dimensional plane or axially symmetric blunt bodies are presented. The equations are solved by means of an implicit finite difference scheme, and the results are compared with a turbulent boundary layer analysis. The agreement between the two solution procedures is satisfactory for the region of flow where streamline swallowing effects are negligible. For the downstream regions, where streamline swallowing effects are present, the expected differences in the two solution procedures are evident.

Anderson, E. C.↗
NASA NTRS1974

Optimum three-dimensional atmospheric entry from the analytical solution of Chapman's exact equations

The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position.

Busemann, A.↗
NASA NTRS1975

Solutions for discharge chamber sputtering and anode deposit spalling in small mercury ion thrusters

Proposed solutions to the problems of sputter erosion and sputtered material spalling in the discharge chamber of small mercury ion thrusters are presented. The accelerated life test evaluated three such proposed solutions: (1) the use of tantalum as a single low sputter yield material for the exposed surfaces of the discharge chamber components subject to sputtering, (2) the use of a severely roughened anode surface to improve the adhesion of the sputter-deposited coating, and (3) the use of a wire cloth anode surface in order to limit the size of any coating flakes which might spall from it. Because of the promising results obtained in the accelerated life test with anode surfaces roughened by grit-blasting, experiments were carried out to optimize the grit-blasting procedure. The experimental results and an optimal grit-blasting procedure are presented.

Power, J. L.↗
NASA NTRS1975

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Anderson, E. C.↗
NASA NTRS1975

High-order numerical solutions using cubic splines

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

Rubin, S. G.↗
NASA NTRS1974

Steady simple shear flow past a circular cylinder at moderate Reynolds numbers - A numerical solution

The two-dimensional steady flow of an incompressible viscous fluid past a circular cylinder, placed symmetrically in a simple shear field, has been studied for both the stationary and the freely rotating case by solving numerically the Navier-Stokes equations for values of the Reynolds number R in the range from 0.047 to 70. At R = 0.047, the results obtained are in substantial agreement with the analytic small-R perturbation solution given by Robertson and Acrivos (1970). Inertia effects were found, however, to play a significant role even at R = 1, and hence the calculated flow pattern for R greater than or equal to 1 differs significantly from that of the creeping-flow solution. Specifically, for the freely rotating case, the region of closed streamlines decreases rapidly in extent with increasing R, two symmetrically placed wakes are formed on either side of the cylinder, and the dimensionless rotational speed of the freely suspended cylinder decreases as the reciprocal of the square root of R.

Kossack, C. A.↗
NASA NTRS1975

Analytic solution for low thrust out of ecliptic mission design

Description of an analytic trajectory solution for low thrust out of ecliptic mission design based on the two-variable asymptotic expansion technique. A practical steering program utilizing normal thrusting symmetrical about the nodes is assumed. A two-term expansion yields an essentially exact solution of the problem which is in a form suitable for evaluation on small desk-top computers. It is shown that for a circular base orbit at 1 AU, a 15-kw solar electric system with a specific impulse of 3000 sec is capable of delivering an 1100-kg net payload to a heliographic latitude of about 63 deg.

Flandro, G. A.↗
NASA NTRS1975

Numerical solutions for inviscid supersonic corner flows

Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for compressive-compressive and expansive-compressive corner flows are obtained. The governing equations are written in strong conservation-law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number (Re greater than 2,500,000 ft) experimental data. The results clearly show that the wave structure in the corner is dominated by the inviscid field.

Shankar, V. S. V.↗
NASA NTRS1975

Numerical solutions for supersonic corner flow

Analytical solutions for inviscid supersonic corner flows are virtually nonexistent due to the complexity of the interference geometry. In view of this, numerical solutions for swept-compressive and swept-expansive corner flows are obtained. The governing equations are written in strong conservation-law form and are solved iteratively in nonorthogonal conical coordinates by use of a second-order, shock-capturing, finite-difference technique. The computed wave structure and surface pressure distributions are compared with high Reynolds number experimental data and show very good agreement. The results clearly show that supersonic corner flow at reasonably high Reynolds numbers including the effect of sweep is dominated by the inviscid field.

Shankar, V.↗
NASA NTRS1974

Microbial metabolism and dynamic changes in the electrical conductivity of soil solutions - A method for detecting extraterrestrial life

Experiments are reported which show that measuring metabolic activity in soil solutions by means of dynamic changes in electrical conductivity, water-soluble Ca, or water-soluble Mg is a feasible life detection method. The addition of 0.5% glucose solutions to 12 different air-dried soils always resulted in increases in all three of these parameters. The kinetics and magnitude of these changes for at least two and usually all three of the parameters over a 14-day period were clearly distinguishable from the changes in heat-sterilized controls or unsterilized controls without added glucose. In general, maximal values were achieved more rapidly under aerobic than under anaerobic incubation.

Silverman, M. P.↗
NASA NTRS1974

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

The results of a determination of the coordinates of about 70 tracking stations are presented. The data were deived with the aid of dynamical techniques from precise reduced optical and laser observations of geodetic satellites. It is attempted to establish a reasonable accuracy estimate through a comparison of the data with other independent solutions. A brief description is given of the independent solutions used as a source of comparison.

Marsh, J. G.↗
NASA NTRS1975

Approximate solutions of radiative transfer in dusty nebulae. I - Pure hydrogen nebulae

This is the first of a series of papers dealing with transfer of radiation in dusty nebulae. The formulae for the general problem are presented. This paper discusses nebulae containing dust and hydrogen. Approximate solutions, accurate to within 50 percent, are obtained for spherical nebulae containing purely absorbing dust. Less accurate solutions are presented for the general case of scattering and absorbing dust. The results are presented in a form convenient for calculating the required number of ionizing photons, the fractional ionization of hydrogen, and the fractions of ionizing photons absorbed by dust and gas in terms of size, hydrogen density, dust albedo, and optical depth. Explicit relations between these quantities are obtained for uniform nebulae. Simple integrals are presented for calculating the above quantities for spherically symmetric nebulae with nonuniform gas and dust distribution.

Petrosian, V.↗
NASA NTRS1975

Viscous flow solutions with a cubic spline approximation

A cubic spline approximation is used for the solution of several problems in fluid mechanics. This procedure provides a high degree of accuracy even with a nonuniform mesh, and leads to a more accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several typical integration schemes are presented. For two-dimensional flows a spline-alternating-direction-implicit (SADI) method is evaluated. The spline procedure is assessed and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.↗
NASA NTRS1975

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-

Rubin, S. G.↗
NASA NTRS1975

Some properties of extremal solutions of zero-sum differential games

Necessary conditions for infinite-time linear-quadratic two-player differential games with perfect state information are examined in the light of Willems' work on the algebraic Riccati equation. Necessary conditions for the nonzero-sum game do not always reduce precisely to those of the zero-sum game, when the weighting parameters of the cost index are taken as those of a zero-sum game. Formulation of zero-sum game problems in extended L2-spaces reveals the existence of nonstabilizing but infimal controls, and explicit frequency-domain conditions for existence of solutions and stabilizing solutions are established through the algebraic Riccati equation (ARE).

Johnson, T. L.↗