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At least 559 records · Page 31

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NASA NTRS1980

Computation of three-dimensional viscous supersonic flow in inlets

A new approach has been developed for the computation of the three-dimensional viscous supersonic flow with embedded subsonic regions adjacent to solid boundaries and is applied to a mixed-compression supersonic inlet typical of current designs. The approach uses a reduced form of the three-dimensional Navier-Stokes equations so that the resultant equations can be treated as an initial boundary value problem and thus be solved by non-iterative forward marching in space. The numerical procedure utilizes an efficient consistently-split linearized block implicit technique to solve the finite difference analogues to the set of governing partial differential equations.

Buggeln, R. C.↗

NASA NTRS1980

Interaction of ocean waves with a soft bottom

Soft muddy bottoms have significant effects on properties of water waves which propagate over them. The wave dispersion equation is modified and wave energy is dissipated by the coupling between the waves in water and those induced in the mud layer. These effects are theoretically determined by assuming a viscoelastic mud layer. A boundary-value problem is solved for the water-mud system with sinusoidal waves. The theoretical dissipation rates are compared favorably with field measurements.

Hsiao, S. V.↗

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.

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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 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.↗

NASA NTRS1983

Optimal large-angle maneuvers with vibration suppression

Some methods and applications which determine optimal maneuver controls are overviewed. The main aspects of optimal control theory are summarized and the essential ideas involved in a class of methods ('continuation' or 'homotopy' methods) which are useful in solving the resulting two-point boundary value problems are discussed. Several low dimensioned, nonlinear maneuvers of multiple rigid-body configurations using optimal momentum transfer are discussed. Several linear and nonlinear flexible-body maneuvers are then presented and include distributed controls, vibration suppression/arrest, and computational issues. Finally, the key problem areas in which future research appears most urgent are identified.

Turner, J. D.↗

NASA NTRS1982

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

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NASA NTRS1983

Analysis of coolant entrance boundary shape of porous region to control cooling along exit boundary

A cooled porous region has a plane surface exposed to a specified spatially varying heat flux. The coolant leaves the region through this surface, and it is desired to control the flow distribution to maintain a specified uniform surface temperature. This is accomplished by having the coolant entrance surface shaped to provide in the region the necessary variation of path length and, hence, flow resistance. The surface shape at the coolant entrance is found by solving a Cauchy boundary value problem. An exact solution is obtained that will deal with a wide variety of heating distributions for both two- and three-dimensional shapes.

Siegel, R.↗

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 NTRS1983

MHD thermal instabilities in cool inhomogeneous atmospheres

The formation of a coronal state in a stellar atmosphere is investigated. A numerical code is used to study the effects of atmospheric gradients and finite loop dimension on the scale of unstable perturbations, solving for oscillatory perturbations as eigenfunctions of a boundary value problem. The atmosphere is considered as initially isothermal, with density and pressure having scale heights fixed by the hydrostatic equations. Joule mode instability is found to be an efficient mechanism for current filamentation and subsequent heating in initially cool atmospheres. This instability is mainly effective at the top of magnetic loops and is not suppressed by thermal conduction.

Bodo, G.↗

NASA NTRS1982

Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

Hamrock, B. J.↗

NASA NTRS1983

Spinning mode acoustic radiation from the flight inlet

A mathematical model was developed for spinning mode acoustic radiation from a thick wall duct without flow. This model is based on a series of experiments (with and without flow). A nearly pure azimuthal spinning mode was isolated and then reflection coefficients and far field pressure (amplitude and phase) were measured. In our model the governing boundary value problem for the Helmholtz equation is first converted into an integral equation for the unknown acoustic pressure over a disk, S1, near the mouth of the duct and over the exterior surface, S2, of the duct. Assuming a pure azimuthal mode excitation, the azimuthal dependence is integrated out which yields an integral equation over the generator C1 of S1 and the generator C2 of S2. The sound pressure on C1 was approximated by a truncated modal expansion of the interior acoustic pressure. Piecewise linear spline approximation on C2 was used.

Moss, W. F.↗