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At least 649 records · Page 36
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NASA NTRS1974

Surface electrical properties experiment. Part 2: Theory of radio-frequency interferometry in geophysical subsurface probing

The radiation fields due to a horizontal electric dipole laid on the surface of a stratified medium were calculated using a geometrical optics approximation, a modal approach, and direct numerical integration. The solutions were obtained from the reflection coefficient formulation and written in integral forms. The calculated interference patterns are compared in terms of the usefulness of the methods used to obtain them. Scattering effects are also discussed and all numerical results for anisotropic and isotropic cases are presented.

Kong, J. A.↗
NASA NTRS1974

Quantum mechanical streamlines. I - Square potential barrier

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

Hirschfelder, J. O.↗
NASA NTRS1975

Numerical computation of viscous flows on the lee side of blunt shapes flying at supersonic speeds

A numerical method for solving the parabolic approximation to the steady-state compressible Navier-Stokes equations is examined. The approximation neglects only the streamwise gradients of shear stress. An implicit finite difference method is used which advances the solution downstream from an initial data surface and determines the complete viscous-inviscid flow between the body and bow shock wave. It is necessary that the inviscid portion of the flow field be supersonic. Crossflow separation is determined as part of the solution. The method is applied to a 15 deg sphere-cone at 15 deg angle of attack, and the results are compared with an inviscid method-of-characteristics calculation.

Rakich, J. V.↗
NASA NTRS1976

Estimates of nitric oxide production for lifting spacecraft reentry

An approximate analysis to estimate the quantity of nitric oxide that could be formed in the wake of a reentering lifting spacecraft is reported. Three different approaches are undertaken: two simplified analytical models utilizing the sudden-freezing concept named the 'trailing-edge-freezing' and 'wake-freezing' approximations, and a computer calculation involving numerical integration of chemical rate equations. The three methods predict a maximum nitric oxide production equivalent to 6, 9.5 and 8% of the mass of the spacecraft, respectively. Thus, the amount of nitric oxide expected to be produced by future space activities is negligibly small compared with that produced by the natural processes.

Park, C.↗
NASA NTRS1976

Interactions of the plasma sheet with the lunar surface at the Apollo 14 site

Calculations of the magnetic shadow zones of lunar-based particle detectors are extended to include the effects of local remanent magnetic fields. At the Apollo 14 site, the local magnetic field is approximated as that of a dipole. Numerically calculated open and shadowed zones are shown to be in agreement with quiet-time plasma-sheet observations of the charged-particle lunar-environment experiment. An analysis of three storm-time observations indicates that magnetic shadowing can significantly alter the near-lunar-surface electrostatic potential distribution.

Reiff, P. H.↗
NASA NTRS1976

Sound propagation through nonuniform ducts

Methods of determining the transmission and attenuation of sound propagating in nonuniform ducts with and without mean flows are discussed. The approaches reviewed include purely numerical techniques, quasi-one-dimensional approximations, solutions for slowly varying cross sections, solutions for weak wall undulations, approximation of the duct by a series of stepped uniform cross sections, variational methods and solutions for the mode envelopes.

Nayfeh, A. H.↗
NASA NTRS1977

Spectra and angular distributions of atmospheric gamma rays from 0.3 to 10 MeV at lambda = 40 deg

Measurements of the spectral and angular distributions of atmospheric gamma sq cm rays in the energy range 0.3-10 MeV over Palestine, Texas, at residual depths of 2.5 and 70 g/sq cm are reported. In confirmation of the general features of a model prediction, the measurements show at 2.5 g/sq cm upward moving fluxes greater than the downward moving fluxes, the effect increasing with energy, and approximate isotropy at 70 g/sq cm. Numerous characteristic gamma-ray lines were observed, most prominently at 0.511, 1.6, 2.3, 4.4, and 6.1 MeV. Their intensities were also compared with model predictions. Observations were made with an actively shielded scintillator counter with two detectors, one of aperture 50 deg FWHM and the other of 120 deg FWHM. Above 1 MeV, contributions to the counting rate from photons penetrating the shield annulus and from neutron interactions were large; they were studied by means of a Monte Carlo code and are extensively discussed.

Ling, J. C.↗
NASA NTRS1979

Analysis and computation of viscous subsonic primary and secondary flows

A new approximate flow analysis, designed to enable numerical solution as an initial value problem, is developed for a wide class of viscous subsonic flows at high Reynolds number and in straight or smoothly curved three-dimensional flow geometries. The analysis is coordinate-independent and corrects an a priori known inviscid primary flow for viscous and thermal effects, secondary flows, total pressure distortion, internal flow blockage and pressure drop. Computed results include laminar solutions for three-dimensional boundary layer flow, fully viscous flow in circular arc ducts, and also flow in a curved duct shaped like a turbine blade passage.

Briley, W. R.↗
NASA NTRS1979

Accuracy of relative oceanic geoid computations

An error analysis based on a model which requires potential coefficients and gravity anomaly information for the computation of oceanic geoidal undulations is developed. The rigorous models are presented and abandoned owing to the numerical difficulties associated with them. An approximate error model is developed in the frequency domain through which an idea is obtained as to the size and behavior of the errors involved. The use of the method is demonstrated by obtaining data requirements for the realization of a 10-cm relative oceanic geoid. Various data sets could result in the desired accuracy. One such set, indicative of the strictness of the requirements, involves gravity profile spacings of approximately 3 km with observational noise not exceeding 0.5 mGal inside detailed data caps of 30 deg and potential coefficients of prescribed accuracy available to degree and order 70.

Christodoulidis, D. C.↗
NASA NTRS1980

Distance corrections for single- and dual-color lasers by ray tracing

The physical arc length difference between the red and blue beam of a dual-color laser generates an error term in determining Delta-n as well as n (the refractive index) and D (the line length). Numerical ray trace examples and theoretical approximations show that the resulting relative error Delta-D/D increases as D-squared. Error reduction by a factor of nearly 10 is possible by using the pressure, temperature, and humidity of both endpoints to calculate n. The present study results from a desire to improve the precision of monitoring the local and regional position of the Lunar Laser Ranging Observatory atop Haleakala, Maui, Hawaii; the monitoring of the earth's crustal deformation and strain is a primary concern of the study.

Berg, E.↗
NASA NTRS1981

A PANSONIC Navier-Stokes solver

A finite-difference formulation of the full Navier-Stokes equations which demonstrates a capability to economically solve two-dimensional problems has been developed. The basic algorithm was derived from the full, Reynolds-averaged, conservative, Navier-Stokes equations expressed in curvilinear coordinates. Eddy viscosity was determined by the Baldwin and Lomax algebraic turbulence model. This non-iterative, second-order accurate, implicit, numerical algorithm is based on the approximate factorization finite-difference scheme of Beam and Warming. Results indicate a facility for solving subsonic, transonic, and supersonic (hence PANSONIC) flows about arbitrary airfoils for a wide range of Reynolds numbers, Mach numbers, and angles of attack. Current computations demonstrate that vectorized implementations of this algorithm can solve steady-state, two-dimensional problems in five to ten minutes of computer time.

Cooper, G. K.↗
NASA NTRS1983

Unsteady laminar boundary-layer calculations on oscillating configurations including backflow. Part 1: Flat plate, oscillating in its own plane

A finite difference method has been developed to calculate the unsteady boundary layer over an oscillating flat plate. Low- and high frequency approximations were used for comparison with numerical results. Special emphasis was placed on the behavior of the flow and on the numerical calculation procedure as soon as reversed flow has occurred over part of the oscillation cycle. The numerical method displayed neither problems nor singular behavior at the beginning of or within the reversed flow region. Calculations, however, came to a limit where the back-flow region reached the plate's leading edge in the case of high oscillation amplitudes. It is assumed that this limit is caused by the special behavior of the flow at the plate's leading edge where the boundary layer equations are not valid.

Geissler, W.↗
NASA NTRS1983

Three-dimensional Euler solutions for long-duct nacelles

A three-dimensional Euler-equation computational technique has been developed to solve for the transonic flow past flow-through nacelles. The technique employs an approximately-factored alternating-direction implicit numerical algorithm and a radiation treatment of the outflow boundary. Studies are presented which show that the radiation treatment gives better numerical convergence than the condition of specifying the pressure at the outflow boundary. Calculations made with the technique are presented for a long-duct turbofan engine nacelle at a Mach number of 0.80 and angles of attack of 0 deg and 4 deg. Good agreement is shown between the computational results and wind-tunnel data. Problem areas are identified and recommendations are made for further numerical studies.

Compton, W. B., III↗
NASA NTRS1984

A tentative unified sea model for scattering and emission

This work is an attempt to relate active and passive observations of the sea surface to each other, considering that more information can be obtained from a set of instruments when they are not just considered as a juxtaposition of separate and independent boxes, but as a single complex instrument. A careful review of several approaches to the solution of the scattering problem for a random rough surface has been performed. Inherent simplifications, and inconsistencies, are pointed out. To reduce the computation time to reasonable values, an approximate model is selected and some numerical results will be presented in order to illustrate the benefit that can be gained by a unified approach.

Guissard, A.↗
NASA NTRS1984

Error analysis and correction of discrete solutions from finite element codes

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Thurston, G. A.↗
NASA NTRS1981

On the relation between upwind-differencing schemes of Godunov, Engquist-Osher and Roe

The upwind differencing first order schemes of Godunov, Engquist-Osher and Roe are discussed on the basis of the inviscid Burgers equations. The differences between the schemes are interpreted as differences between the approximate Riemann solutions on which their numerical flux functions are based. Special attention is given to the proper formulation of these schemes when a source term is present. Second order two step schemes, based on the numerical flux functions of the first order schemes are also described. The schemes are compared in a numerical experiment, and recommendations on their use are included.

Vanleer, B.↗
NASA NTRS1985

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗
NASA NTRS1987

Volume interchange factors for hypersonic vehicle wake radiation

Volume interchange factors are shown to be convenient in modeling the radiative processes in the wake of a hypersonic vehicle. Use of the factors facilitates calculating not just the radiative heating rates on afterbody surfaces but also the radiative de-excitation rates from stimulated emission and re-excitation rates from absorption in rarefied nonequilibrium flows. Sample calculations of volume interchange factors are presented for volume configurations modeling wake elements, and the numerical results are compared to limiting approximations to clarify the operation of the emission, transmission, and absorption processes.

Edwards, D. K.↗