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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 595 records · Page 33
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NASA NTRS1980

Spectral methods for problems in complex geometries

The properties of spectral methods are surveyed and their extension to solve problems in complex geometries is developed. A new iteration procedure is introduced to solve efficiently the full matrix equations resulting from spectral approximations to nonconstant coefficient boundary-value problems in complex geometries. It is shown that the work required to solve these spectral equations exceeds that of solving the lowest-order finite-difference approximation to the same problem by only O(N log N).

Orszag, S. A.↗
NASA NTRS1980

On the feasibility of quantitative ultrasonic determination of fracture toughness: A literature review

The three main topics covered are: (1) fracture toughness and microstructure, (2) quantitative ultrasonic and microstructure; and (3) scattering and related mathematical methods. Literature in these areas is reviewed to give insight to the search of a theoretical foundation for quantitative ultrasonic measurement of fracture toughness. The literature review shows that fracture toughness is inherently related to the microstructure and in particular, it depends upon the spacing of inclusions or second particles and the aspect ratio of second phase particles. There are indications that ultrasonic velocity attenuation measurements can be used to determine fracture toughness. The leads to a review of the mathematical models available in solving boundary value problems related to microstructural factors that govern facture toughness and wave motion. A framework towards the theoretical study for the quantitative determination of fracture toughness is described and suggestions for future research are proposed.

Fu, L. S.↗
NASA NTRS1980

Numerical grid generation techniques

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Source record↗
NASA NTRS1980

Generation of C-type cascade grids for viscous flow computation

A rapid procedure for generating C-type cascade grids suitable for viscous flow computations in turbomachinery blade rows is presented. The resulting mesh is periodic from one blade passage to the next, nearly orthogonal, and continuous across the wake downstream of a blade. The procedure employs a pair of conformal mappings that take the exterior of the cascade into the interior of an infinite strip with curved boundaries. The final transformation to a rectangular computational domain is accomplished numerically. The boundary values are obtained from a panel solution of an integral equation and the interior values by a rapid ADI solution of Laplace's equation. Examples of C-type grids are presented for both compressor and turbine blades and the extension of the procedure to three dimensions is briefly outlined.

Sockol, P. M.↗
NASA NTRS1981

An extended classical solution of the droplet growth problem

Problems of applying the classical kinetic theory to the growth of small droplets from vapor are examined. A solution for the droplet growth equation is derived which is based on the assumption of a diffusive field extending to the drop surface. The method accounts for partial thermal and mass accommodation at the interface and the kinetic limit to the mass and heat fluxes, and it avoids introducing the artifact of a discontinuity in the thermal and vapor field near the droplet. Consideration of the environmental fields in spherical geometry utilizing directional fluxes yields boundary values in terms of known parameters and a new Laplace transform integral.

Anderson, B. J.↗
NASA NTRS1981

Effect of Surface Roughness on Hydrodynamic Bearings

A theoretical analysis on the performance of hydrodynamic oil bearings is made considering surface roughness effect. The hydrodynamic as well as asperity contact load is found. The contact pressure was calculated with the assumption that the surface height distribution was Gaussian. The average Reynolds equation of partially lubricated surface was used to calculate hydrodynamic load. An analytical expression for average gap was found and was introduced to modify the average Reynolds equation. The resulting boundary value problem was then solved numerically by finite difference methods using the method of successive over relaxation. The pressure distribution and hydrodynamic load capacity of plane slider and journal bearings were calculated for various design data. The effects of attitude and roughness of surface on the bearing performance were shown. The results are compared with similar available solution of rough surface bearings. It is shown that: (1) the contribution of contact load is not significant; and (2) the hydrodynamic and contact load increase with surface roughness.

Majumdar, B. C.↗
NASA NTRS1981

On the polarity of cyclostrophic flow in planetary atmospheres

Fluids which are completely inviscid in the mathematical sense do not exist. Thus, the concepts of gradient flow and cyclostrophic balance are interpreted as approximate solutions of a boundary value problem for small but finite viscosity. Large scale phenomena such as the superrotation of Venus and cyclones are effectively bounded by the rigidly rotating planetary surface. This polarizes the circulation and excludes so-called anomalous motions from the flow regime. With scale phenomena such as dust devils, both directions are observed which is attributed to the stochastic nature of wind systems surrounding the disturbance.

Mayr, H. G.↗
NASA NTRS1981

Analysis of capacitive heat exchangers, part 1

Governing equations are developed for a simple capacitive heat exchanger. This type of heat exchanger consists of hot spherical particles falling through an ascending cold gas stream. The assumptions made in deriving the continuity, momentum and energy equations are clearly stated. The analysis yields a system of first order, ordinary, nonlinear equations which form a complex boundary value problem. The method of solution is presented together with a comparison between the performance of capacitive heat exchangers and conventional counter flow ones.

Schonfeld, D.↗
NASA NTRS1980

Some features of inverted-V events as seen from simulated double layers

Results from a numerical simulation of a double layer show some features similar to those of inverted-V events. The strong heating of thermal and precipitating electrons is observed along with extremely low frequency fluctuations found during inverted-V events. It is suggested that after the acceleration of auroral electrons by the double layer, the precipitating free electrons are heated by the nonlinear effects of the electron beam plasma instability. Fluctuations and pulsations of auroral electron fluxes during auroral events are caused by a relaxation type of oscillation. The finite extent of one dimensional plasma is simulated by solving the Vlasov and Poisson equations as an initial and boundary value problem.

Singh, N.↗
NASA NTRS1980

Vertical slender jets

The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface tension effects are neglected. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from orifices in various shapes including an ellipse, a rectangle, and an equilateral triangle. Computational results are presented illustrating the propagation of discontinuities and the formation of thin sheets of fluid.

Geer, J. F.↗
NASA NTRS1981

Construction of composite three dimensional grids from subregion grids generated by elliptic systems

A technique is presented for constructing a boundary-conforming grid throughout a general three-dimensional flow region as a composite of subregion grids. Each subregion grid is generated numerically by solving a nonlinear system of elliptic equations. The boundary values represent nodal points in a quasi-two-dimensional grid that covers the curved surface bounding the subregion, and are generated numerically by a modified elliptic system. A primary feature of the technique is that the composite three-dimensional grid remains both continuous and smooth across the surface of juncture between any two adjoining subregions. Sample results are given for a wing-body combination.

Thomas, P. D.↗
NASA NTRS1981

Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades

A linear unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, is being developed to predict the aerodynamic response to blade vibrations in the fan, compressor or turbine stages of modern jet engines. In previous work numerical solutions were restricted to cascades of sharp-edged blades aligned with the mean flow. Under the present effort the solution procedure has been extended to treat blades with rounded or blunt edges. As part of this effort an analytical model-problem study has been conducted to clarify the behavior of first-order perturbation solutions in the vicinity of airfoil edges. Further, a numerical approximation using concepts from singular perturbation theory has been developed to resolve the unsteady boundary value problem for cascades of blunt leading-edged blades. Numerical results for NACA 0012 cascades, including detailed results in the vicinity of a blade leading edge, are presented and evaluated.

Verdon, J. M.↗
NASA NTRS1980

The control and estimation of large space structures

A shape control or estimation problem for a large space structure can be modeled by a partial differential equation which represents changes in shape with respect to space and time, together with spatially discrete forcing functions or observations which represent the placement of actuators or sensors at discrete points along the structure. The use of Green's functions to convert boundary value problems into integral equations provides a convenient treatment of this mixture of continuous and discrete mathematics. Control and estimation algorithms are developed for the one-dimensional static beam to illustrate this technique.

Weeks, C.↗
NASA NTRS1981

Shape determination and control for large space structures

An integral operator approach is used to derive solutions to static shape determination and control problems associated with large space structures. Problem assumptions include a linear self-adjoint system model, observations and control forces at discrete points, and performance criteria for the comparison of estimates or control forms. Results are illustrated by simulations in the one dimensional case with a flexible beam model, and in the multidimensional case with a finite model of a large space antenna. Modal expansions for terms in the solution algorithms are presented, using modes from the static or associated dynamic mode. These expansions provide approximated solutions in the event that a used form analytical solution to the system boundary value problem is not available.

Weeks, C. J.↗
NASA NTRS1982

Solidification of a binary mixture

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Antar, B. N.↗
NASA NTRS1982

Surface tension and contact angles: Molecular origins and associated microstructure

Gradient theory converts the molecular theory of inhomogeneous fluid into nonlinear boundary value problems for density and stress distributions in fluid interfaces, contact line regions, nuclei and microdroplets, and other fluid microstructures. The relationship between the basic patterns of fluid phase behavior and the occurrence and stability of fluid microstructures was clearly established by the theory. All the inputs of the theory have molecular expressions which are computable from simple models. On another level, the theory becomes a phenomenological framework in which the equation of state of homogeneous fluid and sets of influence parameters of inhomogeneous fluids are the inputs and the structures, stress tensions and contact angles of menisci are the outputs. These outputs, which find applications in the science and technology of drops and bubbles, are discussed.

Davis, H. T.↗
NASA NTRS1982

The mechanics of fatigue in composite laminates

A status report is presented for the development of the mechanics of fatigue in composite materials. A concensus is noted on the need to construct mechanics treatments on the basis of precisely defined damage states which are both characteristic of the material and independent of as many extensive variables, such as load history, as possible. This approach is in keeping with the use of a single crack as the characteristic damage state in homogeneous materials, which has provided a well defined and precise boundary value problem that can be used in the description and prediction of damaged material response. The utility of stress redistribution concepts in determining residual strength, stiffness, and life in composite laminates is also recognized.

Reifsnider, K. L.↗
NASA NTRS1982

Statistical analysis of piloted simulation of real time trajectory optimization algorithms

A simulation of time-optimal intercept algorithms for on-board computation of control commands is described. The effects of three different display modes and two different computation modes on the pilots' ability to intercept a moving target in minimum time were tested. Both computation modes employed singular perturbation theory to help simplify the two-point boundary value problem associated with trajectory optimization. Target intercept time was affected by both the display and computation modes chosen, but the display mode chosen was the only significant influence on the miss distance.

Price, D. B.↗