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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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NASA NTRS1974

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Hwang, Y. M.↗
NASA NTRSDate not supplied

Predictions of the Azimuthal Variation of the Noise from Chevron Jets using an Acoustic Analogy

An existing acoustic analogy formulation is used to make predictions of the turbulent mixing noise from a series of chevron jets tested at NASA Glenn Research Center. Reynolds-averaged Navier-Stokes solutions are used as input to provide the mean flow and turbulence quantities needed to compute the Green’s function and parameterize the source model. The Green’s function for the non-axisymmetric mean flows generated by these nozzles is computed using a second-order finite volume method. A slightly modified version of an existing source model originally developed for round jets is used to assess its capability in these non-axisymmetric flows. Prediction results are compared with experimental data for a range of azimuthal orders of the nozzle geometry and flow speeds. The results show that the RANS-based acoustic analogy prediction method is able to capture the observed azimuthal variation of the sound field fairly well at relatively low jet exit velocities. At higher speeds, the prediction method still captures the observed trends in azimuthal directivity but not the absolute levels, particularly at higher frequencies. Areas for potential improvement of the method are suggested.

Jet Noise↗
NASA NTRSDate not supplied

Predictions of the Azimuthal Variation of the Noise from Chevron Jets using an Acoustic Analogy

An existing acoustic analogy formulation is used to make predictions of the turbulent mixing noise from a series of chevron jets tested at NASA Glenn Research Center. Reynolds-averaged Navier-Stokes solutions are used as input to provide the mean flow and turbulence quantities needed to compute the Green’s function and parameterize the source model. The Green’s function for the non-axisymmetric mean flows generated by these nozzles is computed using a second-order finite volume method. A slightly modified version of an existing source model originally developed for round jets is used to assess its capability in these non-axisymmetric flows. Prediction results are compared with experimental data for a range of azimuthal orders of the nozzle geometry and flow speeds. The results show that the RANS-based acoustic analogy prediction method is able to capture the observed azimuthal variation of the sound field fairly well at relatively low jet exit velocities. At higher speeds, the prediction method still captures the observed trends in azimuthal directivity but not the absolute levels, particularly at higher frequencies. Areas for potential improvement of the method are suggested.

Jet Noise↗
NASA NTRS1985

Time-dependent radiation transport in a one-dimensional medium

An analytic solution of the time-dependent radiation transport problem in a one-dimensional, stationary and homogeneous medium of finite thickness is presented. The solution is found by the method of images, and is compared with an eigenfunction expansion. Previous conjectures about the structure of such an expansion are clarified. The Green's function of this problem is also expanded in scattering orders.

Nagel, W.↗
NASA NTRS2004

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Barth, Timothy↗
NASA NTRS1985

A General-applications Direct Global Matrix Algorithm for Rapid Seismo-acoustic Wavefield Computations

A new matrix method for rapid wave propagation modeling in generalized stratified media, which has recently been applied to numerical simulations in diverse areas of underwater acoustics, solid earth seismology, and nondestructive ultrasonic scattering is explained and illustrated. A portion of recent efforts jointly undertaken at NATOSACLANT and NORDA Numerical Modeling groups in developing, implementing, and testing a new fast general-applications wave propagation algorithm, SAFARI, formulated at SACLANT is summarized. The present general-applications SAFARI program uses a Direct Global Matrix Approach to multilayer Green's function calculation. A rapid and unconditionally stable solution is readily obtained via simple Gaussian ellimination on the resulting sparsely banded block system, precisely analogous to that arising in the Finite Element Method. The resulting gains in accuracy and computational speed allow consideration of much larger multilayered air/ocean/Earth/engineering material media models, for many more source-receiver configurations than previously possible. The validity and versatility of the SAFARI-DGM method is demonstrated by reviewing three practical examples of engineering interest, drawn from ocean acoustics, engineering seismology and ultrasonic scattering.

Schmidt, H.↗
NASA NTRS1994

Scattering by cavity-backed antennas on a circular cylinder

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.

Kempel, Leo C.↗
NASA NTRS1993

Development of deterministic transport methods for low energy neutrons for shielding in space

Transport of low energy neutrons associated with the galactic cosmic ray cascade is analyzed in this dissertation. A benchmark quality analytical algorithm is demonstrated for use with BRYNTRN, a computer program written by the High Energy Physics Division of NASA Langley Research Center, which is used to design and analyze shielding against the radiation created by the cascade. BRYNTRN uses numerical methods to solve the integral transport equations for baryons with the straight-ahead approximation, and numerical and empirical methods to generate the interaction probabilities. The straight-ahead approximation is adequate for charged particles, but not for neutrons. As NASA Langley improves BRYNTRN to include low energy neutrons, a benchmark quality solution is needed for comparison. The neutron transport algorithm demonstrated in this dissertation uses the closed-form Green's function solution to the galactic cosmic ray cascade transport equations to generate a source of neutrons. A basis function expansion for finite heterogeneous and semi-infinite homogeneous slabs with multiple energy groups and isotropic scattering is used to generate neutron fluxes resulting from the cascade. This method, called the FN method, is used to solve the neutral particle linear Boltzmann transport equation. As a demonstration of the algorithm coded in the programs MGSLAB and MGSEMI, neutron and ion fluxes are shown for a beam of fluorine ions at 1000 MeV per nucleon incident on semi-infinite and finite aluminum slabs. Also, to demonstrate that the shielding effectiveness against the radiation from the galactic cosmic ray cascade is not directly proportional to shield thickness, a graph of transmitted total neutron scalar flux versus slab thickness is shown. A simple model based on the nuclear liquid drop assumption is used to generate cross sections for the galactic cosmic ray cascade. The ENDF/B V database is used to generate the total and scattering cross sections for neutrons in aluminum. As an external verification, the results from MGSLAB and MGSEMI were compared to ANISN/PC, a routinely used neutron transport code, showing excellent agreement. In an application to an aluminum shield, the FN method seems to generate reasonable results.

Ganapol, Barry↗
NASA NTRS2007

Using EIGER for Antenna Design and Analysis

EIGER (Electromagnetic Interactions GenERalized) is a frequency-domain electromagnetics software package that is built upon a flexible framework, designed using object-oriented techniques. The analysis methods used include moment method solutions of integral equations, finite element solutions of partial differential equations, and combinations thereof. The framework design permits new analysis techniques (boundary conditions, Green#s functions, etc.) to be added to the software suite with a sensible effort. The code has been designed to execute (in serial or parallel) on a wide variety of platforms from Intel-based PCs and Unix-based workstations. Recently, new potential integration scheme s that avoid singularity extraction techniques have been added for integral equation analysis. These new integration schemes are required for facilitating the use of higher-order elements and basis functions. Higher-order elements are better able to model geometrical curvature using fewer elements than when using linear elements. Higher-order basis functions are beneficial for simulating structures with rapidly varying fields or currents. Results presented here will demonstrate curren t and future capabilities of EIGER with respect to analysis of installed antenna system performance in support of NASA#s mission of exploration. Examples include antenna coupling within an enclosed environment and antenna analysis on electrically large manned space vehicles.

Champagne, Nathan J.↗
NASA NTRS1985

Improving the Accuracy of the Boundary Integral Method Based on the Helmholtz Integral

Several recent papers in the literature have been based on various forms of the Helmholtz integral to compute the radiation fields of vibrating bodies. The surface integral form is given. The symbols of P,R micron, rho,G,R,V, and S micron are acoustic pressure, source coordinate, angular frequency, fluid density, Green function, field coordinate, surface velocity and body surface respectively. A discretized form of the surface integral is also given. Solutions to the surface integral are complicated with the singularity of the Green function at R=R micron and with the uniqueness problem at interior eigen frequencies of the enclosed space. The use of the interior integral circumvents the singularity problem since the field points are chosen in the interior space of the vibrating body where a zero pressure condition exists. The interior integral form is given. The method to improve the accuracy is detailed. Examples of the method is presented for a variety of radiators.

Koopmann, G. H.↗
NASA NTRS2005

Constraining Oceanic Sources and Sinks of CO2 by Inverse Modeling: A First Step Toward Assimilation of In Situ and Remote Data

The primary goal of this collaborative project, lead by Nicholas Gruber at UCLA, is to better quantify the air-sea fluxes of pre-industrial and anthropogenic carbon dioxide CO2 for the global ocean with a newly developed inverse method. The method involves using ocean general circulation models (OGCMs) to characterize the subsurface distribution of tracers injected for different regions of the ocean surface. By linearly combining a series of these basis (or Greens) functions, one should be able to recreate any arbitrary ocean tracer field. In our case, we are using the global database of ocean dissolved inorganic carbon (DIC) from the WOCE/JGOFS global CO2 survey from the 1990s. The observed DIC field has been partitioned into pre-industrial and anthropogenic components using the empirical C* technique. We then solve for an optimal combination of the regional basis functions that best match the two sets observations in a least-squares sense with singular value decomposition. This in turn provides solutions for the regional air-sea CO2 fluxes (pre-industrial and anthropogenic) that are independent of more traditional estimates derived from surface water disequilibria in the partial pressure of CO2 and wind speed gas exchange parameterizations. We are apply the method to a suite of nine different OGCMs to test the robustness of the derived surface fluxes fields to differences in ocean circulation. Together with a collegue Keith Lindsay at NCAR, S. Doney's role in this project was to create the appropriate steady-state and temporally evolving basis functions from the NCAR CSM-1 ocean circulation model. Because of a slow start across the project in defining a common set of experimental protocols, we requested and were given a one year, no cost extension. Both the steady-state and temporally evolving basis functions were delivered to the UCLA group for further analysis. Additional information is included in the original extended abstract.

Doney, Scott↗
NASA NTRS1974

Useful extremum principle for the variational calculation of matrix elements

Variational principles are considered for the approximate evaluation of the diagonal matrix elements of an arbitrary known linear Hermitian operator. A method is derived that is immediately applicable to the variational determination of both the off-diagonal and diagonal matrix elements of normal and modified Green's functions.

Gerjuoy, E.↗
NASA NTRS1976

Evidence of the beam pattern concept of subsonic jet noise emission

The methods and results are described of an approach toward positively identifying the apparent location and strength of the sound source in a subsonic jet. The Green's function technique is applied to regenerate the three-dimensional distribution of the acoustic far field from measured data on a two-dimensional plane. The apparent sound-source location is also determined by using geometrical ray acoustics. The results revealed a number of features of the subsonic jet noise mechanisms; they show that the apparent sound source is highly localized within the jet flow and that the spontaneous noise emission from such a compact source volume is in the fashion of a narrow beam with random directions. These observable properties of the sound field offer the basis for a beam pattern concept of subsonic jet noise radiation. A powerful and accurate technique of aerodynamic noise measurement is verified. This technique is expected to have important applications in the development of jet noise reduction technology.

Pao, S. P.↗
NASA NTRS1982

Input impedance and mutual coupling of rectangular microstrip antennas

A moment method solution to the problem of input impedance and mutual coupling of rectangular microstrip antenna elements is presented. The formulation uses the grounded dielectric slab Green's function to account rigorously for the presence of the substrate and surface waves. Both entire basis (EB) and piecewise sinusoidal (PWS) expansion modes are used, and their relative advantages are noted. Calculations of input impedance and mutual coupling are compared with measured data and other calculations.

Pozar, D. M.↗
NASA NTRS1993

Radiation and scattering by cavity-backed antennas on a circular cylinder

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.

Kempel, Leo C.↗
NASA NTRS1982

Subsonic aerodynamic and flutter characteristics of several wings calculated by the SOUSSA P1.1 panel method

Several applications of the steady, oscillatory, and unsteady subsonic and supersonic aerodynamics (SOUSSA) computer program to wings with steady and oscillatory motion, including flutter, are discussed. The program employs a generalized Green's function to the full, time-dependent potential-flow equation to obtain an integral equation for the velocity potential at any point in a flow, even points on a body or whole bodies in a flow. Aerodynamic calculations are provided for two rectangular wings, a clipped-tip delta wing, and two swept wings with and without a fuselage. The number and distribution of the finite element panels are varied in order to demonstrate the convergence of the results. The results are shown to be close to those of lifting-surface theory, and further applications with bodies having deformities, arbitrary shapes, motions, and deformations are indicated.

Yates, E. C., Jr.↗
NASA NTRS2007

A Fast Method of Deriving the Kirchhoff Formula for Moving Surfaces

The Kirchhoff formula for a moving surface is very useful in many wave propagation problems, particularly in the prediction of noise from rotating machinery. Several publications in the last two decades have presented derivations of the Kirchhoff formula for moving surfaces in both time and frequency domains. Here we present a method originally developed by Farassat and Myers in time domain that is both simple and direct. It is based on generalized function theory and the useful concept of imbedding the problem in the unbounded three-dimensional space. We derive an inhomogeneous wave equation with the source terms that involve Dirac delta functions with their supports on the moving data surface. This wave equation is then solved using the simple free space Green's function of the wave equation resulting in the Kirchhoff formula. The algebraic manipulations are minimal and simple. We do not need the Green's theorem in four dimensions and there is no ambiguity in the interpretation of any terms in the final formulas. Furthermore, this method also gives the simplest derivation of the classical Kirchhoff formula which has a fairly lengthy derivation in physics and applied mathematics books. The Farassat-Myers method can be used easily in frequency domain.

Farassat, F.↗
NASA NTRS1983

Impedance properties of circular microstrip antenna

A moment method solution to the input impedance of a circular microstrip antenna excited by either a microstrip feed or a coaxial probe is presented. Using the exact dyadic Green's function and the Fourier transform the problem is formulated in terms of Richmond's reaction integral equation from which the unknown patch current can be solved for. The patch current is expanded in terms of regular surface patch modes and an attachment mode (for probe excited case) which insures continuity of the current at probe/patch junction, proper polarization and p-dependance of patch current in the vicinity of the probe. The input impedance of a circular microstrip antenna is computed and compared with earlier results. Effect of attachment mode on the input impedance is also discussed.

Deshpande, M. D.↗