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At least 739 records · Page 41
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NASA NTRS1976

A tensor formulation of the equation of transfer for spherically symmetric flows

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

Haisch, B. M.↗
NASA NTRS1976

Technique for atmospheric rate chemistry calculations

The possibility that predictions of atmospheric photochemistry/transport models are sensitive to uncertainties in reaction rates and other inputs stresses the need for rapid numerical integration schemes in rate photochemistry problems. Reducing the computational burden has a major merit in facilitating sensitivity studies to assess the effect of uncertainties on predicted ozone diminutions from NOx (NO + NO2) in the exhaust plume of SST engines. The paper discusses the validity of an algorithmic approach to integration of rate chemistry problems in combustion, developed by Rubel and Baronti for an approximate calculation of the production rate of the i-th chemical species involved. An analysis of two projected SST engines confirms the validity of the proposed algorithm. Because of the relative arithmetical simplicity, it may be easier to treat diffusion rate chemistry calculations using the Rubel and Baronti approximation than would be possible by other approaches.

Matloff, G. L.↗
NASA NTRS1977

Thermal stress analysis of a graded zirconia/metal gas path seal system for aircraft gas turbine engines

A ceramic/metallic aircraft gas turbine outer gas path seal designed to enable improved engine performance is studied. Flexible numerical analysis schemes suitable for the determination of transient temperature profiles and thermal stress distributions in the seal are outlined. An estimation of the stresses to which a test seal is subjected during simulated engine deceleration from sea level takeoff to idle conditions is made. Experimental evidence has indicated that the surface layer of the seal is probably subjected to excessive tensile stresses during cyclic temperature loading. This assertion is supported by the analytical results presented. Brief consideration is given to means of mitigating this adverse stressing.

Taylor, C. M.↗
NASA NTRS1977

Ray trajectories in a torus: An application of MACSYMA to a complex numerical computation

The study of ray trajectories of plasma waves in a torodial geometry using MACSYMA is an example of how symbolic, numerical, and graphical facilities can be used in concert to accomplish a complex computational goal. Computational features of this study which are of particular significance include: the derivation of code (i.e. writing functions to generate program fragments), the use of array functions to simplify the specification of a numerical iteration scheme, and the graphical presentation of the results. Mathematically, this study originates in the solution of a linear inhomogeneous partial differential equation in 3 dimensions by the method of characteristics. While it is possible to describe this equation compactly by using vector notation, and by specifying the spatial variation of the coefficients in terms of intermediate parameters, the transformation of the equation into a form amenable to solution is very tedious. A MACSYMA program is presented for obtaining description of the rf field structure excited by a waveguide located at the edge of a toroidal plasma confinement device.

Kulp, J. L.↗
NASA NTRS1977

Reliability evaluation of hermetic dual in-line flat microcircuit packages

The relative strengths and weaknesses of 35 commonly used hermetic flat and dual in-line packages were determined and used to rank each of the packages according to a numerical weighting scheme for package attributes. The list of attributes included desirable features in five major areas: lead and lead seal, body construction, body materials, lid and lid seal, and marking. The metal flat pack and multilayer integral ceramic flat pack and DIP received the highest rankings, and the soft glass Cerdip and Cerpak types received the lowest rankings. Loss of package hermeticity due to lead and lid seal problems was found to be the predominant failure mode from the literature/data search. However, environmental test results showed that lead and lid seal failures due to thermal stressing was only a problem with the hard glass (Ceramic) body DIP utilizing a metal lid and/or bottom. Insufficient failure data were generated for the other package types tested to correlate test results with the package ranking.

Johnson, G. M.↗
NASA NTRS1978

On decentralized estimation

A multilevel scheme is proposed to construct decentralized estimators for large linear systems. The scheme is numerically attractive since only observability tests of low-order subsystems are required. Equally important is the fact that the constructed estimators are reliable under structural perturbations and can tolerate a wide range of nonlinearities in coupling among the subsystems.

Siljak, D. D.↗
NASA NTRS1979

Frost formation on an airfoil: A mathematical model 1

A computer model to predict the frost formation process on a flat plate was developed for application to most environmental conditions under which frost occurs. The model was analytically based on a generalized frost thermal conductivity expression, on frost density and thickness rate equations, and on modified heat and mass transfer coefficients designed to fit the available experimental data. The broad experimental ranges reflected by the extremes in ambient humidities, wall temperatures, and convective flow properties in the various publications which were examined served to severely test the flexibility of the model. An efficient numerical integration scheme was developed to solve for the frost surface temperature, density, and thickness under the changing environmental conditions. The comparison of results with experimental data was very encouraging.

Dietenberger, M.↗
NASA NTRS1979

Supercritical wing design using numerical optimization and comparisons with experiment

A numerical minimization scheme is used in conjunction with two-dimensional and three-dimensional inviscid transonic flow analysis codes to provide procedures for wing leading edge aerodynamic design. The procedures are demonstrated in the design of a new leading edge to improve C-141 cruise performance. For the high aspect ratio moderately swept C-141 wing, the 2-D procedure is shown to yield results which are in close agreement with those obtained using the 3-D technique. Although the 2-D approach uses much less computation time than the 3-D technique, the latter requires fewer manhours than the former. Comparisons of predicted and wind tunnel measured performance improvements are presented which verify the design procedures.

Lores, M. E.↗
NASA NTRS1979

Design of quiet efficient propellers

A numerical computation scheme has been developed to determine the sound generated by propellers. A comparison of these calculations to the noise data taken in the flight test of a propeller driven aircraft shows good agreement. The method is then applied in a parametric study of fixed pitch propellers designed to reduce noise. All these techniques reduce noise while maintaining shaft speed so that the method presented here may be used in a retrofit option for the general aviation fleet.

Succi, G. P.↗
NASA NTRS1980

Numerical methods for large-scale time-dependent partial differential equations

The factors that influence the choice of a numerical solution scheme for large-scale time-dependent partial differential equations are examined with emphasis on the treatment of boundaries. Consideration is given to standard boundary treatments, moving boundaries, and artificial boundaries simulating an infinite domain. Implicit methods and applications to specific problems are discussed with special attention to shocks and steady state solutions.

Turkel, E.↗
NASA NTRS1981

A variational approach to the question of temporal stability of equilibrium models of solar prominences. I - The formal theory

A Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences is presented. Seven quantities are derived which, by analogy to the concepts of energy, momentum, and angular momentum, are conserved under conditions corresponding to ignorable coordinates of classical mechanics. It is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigenfrequencies for the perturbation equations when numerical techniques are used. The method is capable of handling complicated spatial dependences and has internal criteria for assessing the accuracy of any given numerical convergence scheme.

Lerche, I.↗
NASA NTRS1980

Conceptual design study for an advanced cab and visual system, volume 1

A conceptual design study was conducted to define requirements for an advanced cab and visual system. The rotorcraft system integration simulator is for engineering studies in the area of mission associated vehicle handling qualities. Principally a technology survey and assessment of existing and proposed simulator visual display systems, image generation systems, modular cab designs, and simulator control station designs were performed and are discussed. State of the art survey data were used to synthesize a set of preliminary visual display system concepts of which five candidate display configurations were selected for further evaluation. Basic display concepts incorporated in these configurations included: real image projection, using either periscopes, fiber optic bundles, or scanned laser optics; and virtual imaging with helmet mounted displays. These display concepts were integrated in the study with a simulator cab concept employing a modular base for aircraft controls, crew seating, and instrumentation (or other) displays. A simple concept to induce vibration in the various modules was developed and is described. Results of evaluations and trade offs related to the candidate system concepts are given, along with a suggested weighting scheme for numerically comparing visual system performance characteristics.

Rue, R. J.↗
NASA NTRS1983

Nonparametric solution of the Euler equations for steady flow

A theory is presented for formulating well-posed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that time-independent solutions of the Euler equations can be used to provide limits to solutions of the Navier-Stokes equations. A sample is worked out in terms of the motion of vortices inside a circle.

Garabedian, P. R.↗
NASA NTRS1985

Overset grids in compressible flow

Numerical experiments have been performed to investigate the importance of boundary data handling with overset grids in computational fluid dynamics. Experience in using embedded grid techniques in compressible flow has shown that shock waves which cross grid boundaries become ill defined and convergence is generally degraded. Numerical boundary schemes were studied to investigate the cause of these problems and a viable solution was generated using the method of characteristics to define a boundary scheme. The model test problem investigated consisted of a detached shock wave on a 2-dimensional Mach 2 blunt, cylindrical body.

Eberhardt, S.↗
NASA NTRS1985

Extension of Ostwald Ripening Theory

The objective is to develop models based on the mean field approximation of Ostwald ripening to describe the growth of second phase droplets or crystallites. The models will include time variations in nucleation rate, control of saturation through addition of solute, precipitating agents, changes in temperature, and various surface kinetic effects. Numerical integration schemes have been developed and tested against the asymptotic solution of Liftshitz, Slyozov and Wagner (LSW). A second attractor (in addition to the LSW distribution) has been found and, contrary to the LSW theory, the final distribution is dependent on the initial distribution. A series of microgravity experiments is being planned to test this and other results from this work.

Baird, J.↗
NASA NTRS1987

Calculating Theromodynamic And Transport Properties Of Fluids

Computer program incorporates van der Waals equation and correction tables. FLUID program developed to calculate thermodynamic and transport properties of pure fluids in both liquid and gas phases. Properties calculated by use of simple gas model, empirical corrections, and efficient numerical interpolation scheme. Produces results that agree very well with measured values. Much faster than older, more complex programs developed for same purpose.

Proctor, Margaret P.↗