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NASA NTRS1983

Numerical computations on one-dimensional inverse scattering problems

An approximate method to determine the index of refraction of a dielectric obstacle is presented. For simplicity one dimensional models of electromagnetic scattering are treated. The governing equations yield a second order boundary value problem, in which the index of refraction appears as a functional parameter. The availability of reflection coefficients yield two additional boundary conditions. The index of refraction by a k-th order spline which can be written as a linear combination of B-splines is approximated. For N distinct reflection coefficients, the resulting N boundary value problems yield a system of N nonlinear equations in N unknowns which are the coefficients of the B-splines.

Dunn, M. H.↗

NASA NTRS1982

Transient and diffusion analysis of HgCdTe

Solute redistribution during directional solidification of HgCdTe is addressed. Both one-dimensional and two-dimensional models for solute redistribution are treated and model results compared to experiment. The central problem studied is the cause of radial inhomogeneities found in directionally solidified HgCdTe. A large scale gravity-driven interface instability, termed shape instability, is postulated to be the cause of radial inhomogeneities. Recommendations for future work, along with appropriate computer programs, are included.

Clayton, J. C.↗

NASA NTRS1984

Numerical computations on one-dimensional inverse scattering problems

Dunn, M. H.↗

NASA NTRS1984

A SAR correlation algorithm which accommodates large-range migration

This paper presents an algorithm for azimuth correlation of synthetic aperture radar (SAR) data with extraordinarily large-range migration which cannot be accommodated by the existing frequency domain interpolation approach used in current Seasat SAR processing. A mathematical model is provided for the SAR range-correlated point-target response both in the spatial and frequency domains. A simple and efficient processing algorithm derived from the exact two-dimensional correlation algorithm is given. This algorithm enables azimuth correlation by two cascaded one-dimensional correlation steps. The first step is to transform the range-correlated SAR data into the frequency domain in azimuth, followed by a newly developed range convolution filter to correct the range-dispersed spectrum of the range-correlated point-target response (RCPTR). The second step is the frequency-domain range migration correction approach for the azimuth compression. Simulation results provided here indicate that this processing algorithm yields a satisfactory compressed impulse response for SAR data with large-range migration whereas previous methods were subject to a broadening of the impulse response along range.

Jin, M. Y.↗

NASA NTRS1985

Coupled transient response of tiles bonded elastically to a finite flexible plate

Presented are several methods to study a system of tiles bonded elastically to a finite flexible plate responding to an impulse. First, a one-dimensional (1-D) approximation to the system is constructed using Timoshenko beam theory and transfer matrices. This simulates a strip one tile wide. Modal analysis determines the transient response to an impulse of short duration. Also presented are parametric studies of the effect of bond stiffness and the effect of stiffening from inplane stresses produced by large out-of-plane deflections. A two-dimensional (2-D) model is constructed from the eigenfunctions of the 1-D model in a Galerkin method using pairwise products of the 1-D modes as trial functions. Comparison of the two models establishes a factor applied to peak impulse pressure for results to agree.

El-Raheb, M.↗

NASA NTRS1986

Comparison of analytical and experimental performance of a wind-tunnel diffuser section

Wind tunnel diffuser performance is evaluated by comparing experimental data with analytical results predicted by an one-dimensional integration procedure with skin friction coefficient, a two-dimensional interactive boundary layer procedure for analyzing conical diffusers, and a two-dimensional, integral, compressible laminar and turbulent boundary layer code. Pressure, temperature, and velocity data for a 3.25 deg equivalent cone half-angle diffuser (37.3 in., 94.742 cm outlet diameter) was obtained from the one-tenth scale Altitude Wind Tunnel modeling program at the NASA Lewis Research Center. The comparison is performed at Mach numbers of 0.162 (Re = 3.097x19(6)), 0.326 (Re = 6.2737x19(6)), and 0.363 (Re = 7.0129x10(6)). The Reynolds numbers are all based on an inlet diffuser diameter of 32.4 in., 82.296 cm, and reasonable quantitative agreement was obtained between the experimental data and computational codes.

Shyne, R. J.↗

NASA NTRS1985

Evolution and interaction of interplanetary shocks

Whang's unsteady, one-dimensional, one-fluid MHD model is used to carry out a simulation study of the evolution of the solar wind based on two shock events over a distance of the order of 10 AU in the outer heliosphere. The study is based on the observation of two events, each observed by two or more spacecraft. The results show that the shock process, including the formation, collision, and merging of shocks, dominates the dynamical evolution of large-scale solar wind structures. In the outer heliosphere, the large-scale solar wind and magnetic field evolve into a much simpler structure, and MHD shocks are present as a principal component of the solar wind. The simulation results shed new light on the interaction and evolution of large interplanetary streams.

Whang, Y. C.↗

NASA NTRS1986

Electromagnetic ion beam instabilities - Comparison of oneand two-dimensional simulations

Numerical simulations of electromagnetic instabilities, driven by a cool tenuous ion beam propagating along an ambient magnetic field, have been conducted in one and two spatial dimensions. The calculations employ particle ions, fluid electrons, and a predictor corrector scheme for solving the electromagnetic field in two dimensions that is described in some detail. While the principal features of the one-dimensional calculations (which reproduce previous work) are retained, the two-dimensional simulations show some reduction of the overall level of the magnetic field fluctuations. Enhancement of the heating of the beam ions at the expense of the core ions also occurs in the case where the beam density is sufficiently large that the right-hand nonresonant instability dominates. Implications of the results for modeling of the ion foreshock and quasi-parallel shocks are discussed.

Winske, D.↗

NASA NTRS1986

The coalescence of two merged interaction regions between 6.2 and 9.5 AU - September 1979 event

A simulation study, based on an unsteady, one-dimensional, one-fluid MHD model, and using the plasma and magnetic field data from the Voyager 1 at 6.2 AU, was conducted on the evolution and interaction of solar wind structures to explain the two interaction regions observed by Voyager 1 within a large-scale interplanetary compound stream that was recorded at a heliocentric distance of 6.2 AU. A strong forward shock F(D) with a speed of 960 km/s was present at the front of the second interaction region, and two reverse shocks, R1 and R2, were at the end of the first interaction region. The model shows that the forward shock passed through the two reverse shocks and into the first interaction region, becoming weaker in each of these interactions. The reverse shocks coalesced to form a stronger reverse shock R; thus, the shock signature changed from R1-R2-F(D) to F(D)-R between 6.2 and 9.5 AU. The major stream structures at 9.5 AU predicted by the simulation model agree well with those directly observed from Pioneer 11.

Whang, Y. C.↗

NASA NTRS1987

The plasma environment during particle beam injection into space plasmas. I - Electron beams. II - Charge-neutral beams

A realistic electrostatic simulation model is used to investigate the plasma environment in the near vicinity of a spacecraft during the injection of electon beams from the spacecraft. The model is described, and the cases of injection into vacuum and into a low-density plasma are addressed. The relationship of the two-dimensional results to the purely field-aligned one-dimensional simulations is discussed. The dependence of the results on the ambient plasma density is investigated. Then, the properties of a charge-neutral beam and the plasma response are examined for the case where the beam has nonzero velocity components parallel and perpendicular to the magnetic field. The parameters used in the simulation are described, and the properties of the beam injection into the vacuum and in the case where a plasma is present are given.

Pritchett, P. L.↗

NASA NTRS1987

A scanning modulation collimator observation of the high-energy X-ray source in the Crab Nebula

Two-dimensional maps of the 22-64 keV emission from the Crab Nebula with an angular resolution of 15 arcsec has been synthesized. The maps are generated by application of a maximum entropy method operating on a series of one-dimensional scans obtained with a balloon-borne modulation collimator telescope. The two-dimensional size, shape and orientation of the hard X-ray nebula relative to the pulsar have been measured for the first time. The implications of these results for models of electron transport in the Crab are discussed, and the geometry of the observed X-ray nebula is related to other features of the Crab Nebula system.

Pelling, R. M.↗

NASA NTRS1987

Faceting and roughening in quasicrystals

The question whether quasi-crystal shapes should be faceted is studied in a simple model of quasi-crystalline order. At T = 0, the model is proved to yield a completely faceted equilibrium shape in both two and three dimensions. At T greater than 0, an interface model is derived for a two-dimensional Penrose tiling. By mapping it onto a one-dimensional quasi-periodic Schroedinger equation, it is shown that the roughness exponent varies continuously with T at low T.

Garg, Anupam↗

NASA NTRS1988

Overview of numerical codes developed for predicted electrothermal deicing of aircraft blades

An overview of the deicing computer codes that have been developed at the University of Toledo under sponsorship of the NASA-Lewis Research Center is presented. These codes simulate the transient heat conduction and phase change occurring in an electrothermal deicier pad that has an arbitrary accreted ice shape on its surface. The codes are one-dimensional rectangular, two-dimensional rectangular, and two-dimensional with a coordinate transformation to model the true blade geometry. All modifications relating to the thermal physics of the deicing problem that have been incorporated into the codes will be discussed. Recent results of reformulating the codes using different numerical methods to increase program efficiency are described. In particular, this reformulation has enabled a more comprehensive two-dimensional code to run in much less CPU time than the original version. The code predictions are compared with experimental data obtained in the NASA-Lewis Icing Research Tunnel with a UH1H blade fitted with a B. F. Goodrich electrothermal deicer pad. Both continuous and cyclic heater firing cases are considered. The major objective in this comparison is to illustrate which codes give acceptable results in different regions of the airfoil for different heater firing sequences.

Keith, Theo G.↗

NASA NTRS1988

Velocity-coupled flow oscillations in a simulated solid-propellant rocket environment

A comprehensive numerical analysis has been carried out to study the unsteady flowfields in a simulated rocket-motor environment. The model is based on the time-dependent compressible Navier-Stokes equations with a two-equation turbulence closure scheme. Various important aspects of the coupling between acoustic oscillations and mean flowfields, including flow reversal, modification of transport properties, etc., are addressed. Results indicate that multi-dimensional effects play important roles in determining local flow structures and wave characteristics. In much of the domain, acoustic velocity nodal points are observed in the near-wall region. The classical one-dimensional theory fails to describe several important mechanisms associated with velocity-induced flow instabilities.

Yang, Vigor↗

NASA NTRS1987

Time-dependent approximation schemes for some problems of parameter estimation in distributed systems

A parameter estimation method that can be used to estimate functional parameters in delay differential equations and moving boundary problems is discussed. In either problem, the original model equation (which is infinite-dimensional) is approximated by a system of ordinary differential equations that can be solved numerically in an efficient way. The approximation scheme is based on time-dependent spline elements. For the delay equation with time-varying delay, convergence results are presented that indicate the estimates obtained using the approximating system. Numerical test examples converge in some sense to a best-fit parameter for the original system are included by means of which time-varying and state-dependent delays and a time-varying diffusion coefficient in a one-phase, one-dimensional Stefan problem are estimated.

Murphy, K. A.↗

NASA NTRS1988

Development of a thermal and structural analysis procedure for cooled radial turbines

A procedure for computing the rotor temperature and stress distributions in a cooled radial turbine is considered. Existing codes for modeling the external mainstream flow and the internal cooling flow are used to compute boundary conditions for the heat transfer and stress analyses. An inviscid, quasi three-dimensional code computes the external free stream velocity. The external velocity is then used in a boundary layer analysis to compute the external heat transfer coefficients. Coolant temperatures are computed by a viscous one-dimensional internal flow code for the momentum and energy equation. These boundary conditions are input to a three-dimensional heat conduction code for calculation of rotor temperatures. The rotor stress distribution may be determined for the given thermal, pressure and centrifugal loading. The procedure is applied to a cooled radial turbine which will be tested at the NASA Lewis Research Center. Representative results from this case are included.

Kumar, Ganesh N.↗

NASA NTRS1989

Analysis of internal ablation for the thermal control of aerospace vehicles

A new method of thermal protection for transatmospheric vehicles is introduced. The method involves the combination of radiation, ablation and transpiration cooling. By placing an ablating material behind a fixed-shape, porous outer shield, the effectiveness of transpiration cooling is made possible while retaining the simplicity of a passive mechanism. A simplified one-dimensional approach is used to derive the governing equations. Reduction of these equations to non-dimensional form yields two parameters which characterize the thermal protection effectiveness of the shield and ablator combination for a given trajectory. The non-dimensional equations are solved numerically for a sample trajectory corresponding to glide re-entry. Four typical ablators are tested and compared with results obtained by using the thermal properties of water. For the present level of analysis, the numerical computations adequately support the analytical model.

Camberos, Jose A.↗

NASA NTRS1989

Dimensionality of high temperature superconductivity in oxides

Many models have been proposed to account for the high temperature superconductivity observed in oxide systems. Almost all of these models proposed are based on the uncoupled low dimensional carrier Cu-O layers of the oxides. Results of several experiments are presented and discussed. They suggest that the high temperature superconductivity observed cannot be strictly two- or one-dimensional, and that the environment between the Cu-O layers and the interlayer coupling play an important role in the occurrence of such high temperature superconductivity. A comment on the very short coherence length reported is also made.

Chu, C. W.↗