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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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A review of various methods of calculating turbulent chemically reacting flow such as the Green Function, Navier-Stokes equation, and others is presented. Nonequilibrium degrees of freedom were employed to study the mixing behavior of a multiscale turbulence field. Classical and modern theories are discussed.
A number of recent works are reviewed concerning the generation and emission of gravitational waves. It is shown that at high frequencies, the generation of gravitational radiation is a local phenomenon. Two examples are described illustrating this generation when a high-energy particle collides against the space-time curvature. One, after Matzner and Nutku, uses a method of virtual photons; the other, after Chrzanowski and Misner, is based on the W.K.B. approximation, corresponding to geometric optics, for the inhomogeneous wave equation. This method uses a factorized integral representation of the Green function which is valid asymptotically to infinity in space.
The general method for analyzing steady subsonic potential aerodynamic flow around a lifting body having arbitrary shape is presented. By using the Green function method, an integral representation for the potential is obtained. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface of the body. Hence if the point P approaches the surface of the body, the representation reduces to an integral equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings. However, numerical results obtained for a rectangular wing in subsonic flow show that these problems do not appear even for thickness ratio tau = .001. Comparison with existing results shows that the proposed method is at least as fast and accurate as the lifting surface theories.
Plasmon and exciton superconductivity mechanisms are discussed. Superconductivity in a three layer metal semiconductor metal and insulator semimetal insulator sandwich structure was described in terms of the temperature dependent Green function of the longitudinal (Coulomb) field. The dependences of the superconducting transition temperature on structure parameters were obtained. In a semiconducting film, as a result of interactions of degenerate free carriers with excitons, superconductivity exists only in a certain range of parameter values, and the corresponding critical temperature is much lower than in the plasmon mechanism of superconductivity.
The acoustic loading in a complex planar network of ducts is determined by a method in which Green function surface elements are used. The network consists of straight ducts, elbows and branched ducts. A transfer matrix technique is developed in which each duct is treated separately and the matrix of the influence coefficients is transformed to tri-diagonal form allowing efficient inversion.
Potential and surface deformation Love numbers for internal loading have been calculated in order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces. These quantities depend on the depth and harmonic degree of loading, and can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Constructing a series of spherically symmetric, self-gravitating flow models for a variety of radial Newtonian viscosity variations and flow configurations, and calculating relaxation times for spherically symmetric viscous earth models, it is demonstrated that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound; this is much less time than the time scale for significant change in the convective flow pattern.
MNDO (modified neglect of diatomic overlap) calculations have been carried out for substitutional oxygen and sulfur impurities in silicon. The calculations of the gap levels reveal a reversal of trend with atomic ionization energies in agreement with self-consistent Green function results, and analysis of the MNDO charge distribution supports the view that the electronegativity difference between oxygen and sulfur gives rise to this shallower energy level.
An algorithm is presented for determining the minimum curvature surface passing through a set of nonuniformly spaced data points. The curve is generated as a linear combination of Green functions for the biharmonic operator at each data point, with the amplitudes of the functions adjusted so that the interpolating surfaces passes through each point. The function passing through the points can be regarded as a spline to which point forces are applied, defining the minimum curvature between the points. The technique was used to combine the along track slopes of the GEOS-3 and Seasat altimeter data into a consistent geoid height map of the Caribbean area, covering 0.5 million data points in the process. Sample images are provided and new topographic features that are revealed are discussed.
The design of magnets inside closed, cylindrical, superconducting shields is discussed. The Green function is given for the magnetic vector potential for cylindrically symmetric currents inside such a shield. The magnetic field everywhere inside the shield can be obtained from this function, which includes the effects of the induced shield currents exactly. The field is given for a thin solenoid as an example and the convergence of the series solution for this case is discussed. The shield can significantly reduce the strength and improve the homogeneity of a magnet. The improvement in homogeneity is of particular importance in the design of correction coils. These effects, and the maximum field on the shield, are examined for a typical solenoid. The results given are also useful, although not exact, for long shields with one or two open ends.
Convergence conditions of image integration in the exact image method of field calculation have been investigated, and the method is extended to include more general media than previously considered. It is demonstrated that the integral is well behaved and the method works best when the field is calculated in a medium with less loss. If the medium has more loss, it is shown that the image line may enter the improper half-space and still produce valid results. Means of correctly selecting the integration path branch for the case of crossing branch cuts of the Green function in complex integration planes are proposed.
The enhancement of the computational efficiency of the body of revolution (BOR) scattering problem is discused with a view to making it practical for solving large-body problems. The problem of EM scattering by a perfectly conducting BOR is considered, although the methods can be extended to multilayered dielectric bodies as well. Typically, the generation of the elements of the moment method matrix consumes a major portion of the computational time. It is shown how this time can be significantly reduced by manipulating the expression for the matrix elements to permit efficient FFT computation. A technique for extracting the singularity of the Green function that appears within the integrands of the matrix diagonal is also presented, further enhancing the usefulness of the FFT. The computation time can thus be improved by at least an order of magnitude for large bodies in comparison to that for previous algorithms.
The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.
The removal energies of constituent atoms from various unreconstructed semiconductor surfaces are calculated using a Green function method. An efficient difference-equation approach within the second-neighbor tight-binding model is employed. For a compound AB, binding energies for the A and B atoms on the (111), (-1 -1 -1), (100), and (110) surfaces are calculated. Analyses are made of the energy to remove an atom from the nearly full surface and from the nearly empty surface. Results are presented for Si, GaAs, CdTe, and HgTe; and the surface sublimation energies are found to depend on surface coverage and do not display a simple linear relationship to the number of bonds broken, as is often assumed in modeling growth by MBE.
Analytical expressions for temperature and laser beam deflection in multilayer medium is derived using Green function techniques. The approach is based on calculation of the normal component of heat fluxes across the boundaries, from which either the beam deflections or the temperature anywhere in space can be found. A general expression for the measured signals for the case of four-quadrant detection is also presented and compared with previous calculations of detector response for finite probe beams.
This report summarizes the result of research done under NASA NAG3-882 Nonlinear Mechanics of Composites with Periodic Microstructure. The effort involved the development of non-finite element methods to calculate local stresses around fibers in composite materials. The theory was developed and some promising numerical results were obtained. It is expected that when this approach is fully developed, it will provide an important tool for calculating local stresses and averaged constitutive behavior in composites. NASA currently has a major contractual effort (NAS3-24691) to bring the approach developed under this grant to application readiness. The report has three sections. One, the general theory that appeared as a NASA TM, a second section that gives greater details about the theory connecting Greens functions and Fourier series approaches, and a final section shows numerical results.
Conformal arrays are popular antennas for aircraft and missile platforms due to their inherent low weight and drag properties. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such non-planar antennas. The finite element-boundary integral method is extended to scattering and radiation by cavity-backed structures in an infinite, metallic cylinder. In particular, the formulation specifics such as weight functions, dyadic Green's function, implementation details, and particular difficulties inherent to cylindrical structures are discussed. Special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements. Both scattering and radiation parameters are computed and validated as much as possible.
Conformal arrays are popular antennas for aircraft, spacecraft, and land vehicle platforms due to their inherent low weight and drag properties. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such non-planar antennas. The finite element-boundary integral method is extended to scattering by cavity-backed structures in an infinite, metallic cylinder. In particular, the formulation specifics such as weight functions, dyadic Green's function, implementation details and particular difficulties inherent to cylindrical structures are discussed. Special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements. Scattering results are presented and validated as much as possible.
A simple model was developed to calculate the electronic transport parameters in disordered semiconductors in strong scattered regime. The calculation is based on a Green function solution to Kubo equation for the energy-dependent conductivity. This solution together with a rigorous calculation of the temperature-dependent chemical potential allows the determination of the dc conductivity and the thermopower. For wide-gap semiconductors with single defect bands, these transport properties are investigated as a function of defect concentration, defect energy, Fermi level, and temperature. Under certain conditions the calculated conductivity is quite similar to the measured conductivity in liquid 2-6 semiconductors in that two distinct temperature regimes are found. Under different conditions the conductivity is found to decrease with temperature; this result agrees with measurements in amorphous Si. Finally the calculated thermopower can be positive or negative and may change sign with temperature or defect concentration.