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At least 127 records · Page 7

Application of the Green's function method for 2- and 3-dimensional steady transonic flows

A Time-Domain Green's function method for the nonlinear time-dependent three-dimensional aerodynamic potential equation is presented. The Green's theorem is being used to transform the partial differential equation into an integro-differential-delay equation. Finite-element and finite-difference methods are employed for the spatial and time discretizations to approximate the integral equation by a system of differential-delay equations. Solution may be obtained by solving for this nonlinear simultaneous system of equations in time. This paper discusses the application of the method to the Transonic Small Disturbance Equation and numerical results for lifting and nonlifting airfoils and wings in steady flows are presented.

Tseng, K.↗

High frequency green function for aerodynamic noise in moving media. I - General theory. II - Noise from a spreading jet

It is shown how a high frequency analysis can be made for general problems involving flow-generated noise. In the parallel shear flow problem treated by Balsa (1976) and Goldstein (1982), the equation governing sound propagation in the moving medium could be transformed into a wave equation for a stationary medium with an inhomogeneous index of refraction. It is noted that the procedure of Avila and Keller (1963) was then used to construct a high frequency Green function. This procedure involves matching a solution valid in an inner region around the point source to an outer, ray-acoustics solution. This same procedure is used here to construct the Green function for a source in an arbitrary mean flow. In view of the fact that there is no restriction to parallel flow, the governing equations cannot be transformed into a wave equation; the analysis therefore proceeds from the equations of motion themselves.

Durbin, P. A.↗

A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment

A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

A first-order time-domain Green's function approach to supersonic unsteady flow

A time-domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. The Green's function method is employed in order to convert the potential-flow differential equation into an integral one. This integral equation is then discretized, in space through standard finite-element technique, and in time through finite-difference, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. Consistent with the spatial linear (first-order) finite-element approximations, the potential and co-normalwash are assumed to vary linearly in time. The long range goal of our research is to develop a comprehensive theory for unsteady supersonic potential aerodynamics which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

Lens collimation and testing using a Twyman-Green interferometer with a self-pumped phase-conjugating mirror

Ordinarily Twyman-Green interferometers are employed testing optical elements. In a modification of the basic configuration, the ordinary mirror in the test arm is replaced with a self-pumped phase-conjugating mirror using a barium titanate crystal. It is shown that, with a redefinition of components, the new configuration permits retention and improvement of the optical element testing function while simultaneously serving as a sensitive test for collimation. The optical path difference resulting from the double pass in the original Twyman-Green interferometer approximately equals that of the single pass and phase conjugation in the modification.

Howes, W. L.↗

Estimates of green tensors for certain boundary value problems

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Solonnikov, V.↗

Broadband, Achromatic Twyman-Green Interferometer

Improved Twyman-Green interferometer used in wave-front testing optical components at wavelengths from 200 to 1,100 nm, without having to readjust focus when changing wavelength. Built to measure aberrations of light passing through optical filters. Collimating and imaging lenses of classical Twyman-Green configuration replaced by single spherical mirror. Field lens replaced by field mirror. Mirrors exhibit no axial chromatic aberration and made to reflect light efficiently over desired broad range of wavelengths.

Steimle, Lawrence J.↗

Apollo 15 green glass - Relationships between texture and composition

A suite of 365 Apollo 15 green-glass particles was analyzed by INAA and then described petrographically so that comparisons between composition and physical characteristics could be made. Nonuniform compositional distributions of crystalline and elongate particles were evident, although differences in the distribution of volatile-element coatings and extent of particle breakage were not as striking. A binomial evaluation of these textures on an intergroup basis supports the previously proposed hypothesis that the green-glass groups formed during discrete eruptive events because the groups that were defined compositionally also show significant differences in the average texture and structure of particles. Furthermore, in at least one case (Group D), intragroup differences in the distribution of vitrophyric and vitric particles were apparent. An extension of previous models for pyroclastic volcanism suggests that this feature may indicate that a systematic change in the composition of ejecta occurred as eruption progressed.

Steele, Alison M.↗

Green's function methods in heavy ion shielding

An analytic solution to the heavy ion transport in terms of Green's function is used to generate a highly efficient computer code for space applications. The efficiency of the computer code is accomplished by a nonperturbative technique extending Green's function over the solution domain. The computer code can also be applied to accelerator boundary conditions to allow code validation in laboratory experiments.

Wilson, John W.↗

The application of Green's theorem to the solution of boundary-value problems in linearized supersonic wing theory

Following the introduction of the linearized partial differential equation for nonsteady three-dimensional compressible flow, general methods of solution are given for the two and three-dimensional steady-state and two-dimensional unsteady-state equations. It is also pointed out that, in the absence of thickness effects, linear theory yields solutions consistent with the assumptions made when applied to lifting-surface problems for swept-back plan forms at sonic speeds. The solutions of the particular equations are determined in all cases by means of Green's theorem, and thus depend on the use of Green's equivalent layer of sources, sinks, and doublets. Improper integrals in the supersonic theory are treated by means of Hadamard's "finite part" technique.

Heaslet, Max A↗

Compositional heterogeneity within a dumbbell-shaped Apollo 15 green glass: Evidence for simultaneous eruption of different magmas

The Apollo 15 green glasses that occur most prominently in 15425, 15426, and 15427 consist of compositionally distinct groups. The six groups that have thus far been defined are thought to represent different batches of magma that were erupted as fire-fountains, probably at different times in lunar history; although isotopic analyses of representative glasses within some of these groups have not yet found any differences in age at the +/- 100 Ma precision. While the petrogenesis of these picritic magmas has been contentious, the discovery of a compositionally heterogeneous, dumbbell-shaped green glass raises additional questions and problems about their origin.

Delano, J. W.↗

A linear spectral matching technique for retrieving equivalent water thickness and biochemical constituents of green vegetation

Over the last decade, technological advances in airborne imaging spectrometers, having spectral resolution comparable with laboratory spectrometers, have made it possible to estimate biochemical constituents of vegetation canopies. Wessman estimated lignin concentration from data acquired with NASA's Airborne Imaging Spectrometer (AIS) over Blackhawk Island in Wisconsin. A stepwise linear regression technique was used to determine the single spectral channel or channels in the AIS data that best correlated with measured lignin contents using chemical methods. The regression technique does not take advantage of the spectral shape of the lignin reflectance feature as a diagnostic tool nor the increased discrimination among other leaf components with overlapping spectral features. A nonlinear least squares spectral matching technique was recently reported for deriving both the equivalent water thicknesses of surface vegetation and the amounts of water vapor in the atmosphere from contiguous spectra measured with the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS). The same technique was applied to a laboratory reflectance spectrum of fresh, green leaves. The result demonstrates that the fresh leaf spectrum in the 1.0-2.5 microns region consists of spectral components of dry leaves and the spectral component of liquid water. A linear least squares spectral matching technique for retrieving equivalent water thickness and biochemical components of green vegetation is described.

Gao, Bo-Cai↗

Primary studies of trace quantities of green vegetation in Mono Lake area using 1990 AVIRIS data

Our primary results in Jasper Ridge Biological Preserve indicate that high spectral resolution Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data may provide a substantial advantage in vegetation, based on the chlorophyll red edge feature from 700-780 nm. The chlorophyll red edge was detected for green vegetation cover as low as 4.8 percent. The objective of our studies in Mono Lake area is to continue the experiments performed in Jasper Ridge and to examine the persistence of red edge feature of trace quantities of green vegetation for different plant communities with non-uniform soil backgrounds.

Chen, Zhi-Kang↗

Origin of the Apollo 15 very low Ti green glass. A perspective from the compositional diversity in the very low Ti glasses

The very low Ti green glasses from the Apollo 15 site have intrigued scientists for over 20 years. Their primitive composition has been used to understand magmatic processes and the structure of the moon. The compositional variability observed in the Apollo 15 glass population has long been a point of debate. Initial studies did not recognize the compositional diversity in the glasses. Stolper et al. documented the major element variability and concluded it could not be produced by magmatic processes and therefore concluded that these glasses must be of impact origin. Subsequent studies confirmed a volcanic origin for the glass population and attempted to elucidate magmatic processes to account for its compositional variability. Models that have been proposed for these glasses include the following: (1) the crystallization of single or multiple phases (olivine, pyroxene, Fe metal, immiscible sulfide); (2) the incompatible behavior of Ni and Co during multiple phase crystallization at extremely low fO2; and (3) magma or source mixing. All of these models have problems. Type (1) models appear not to be consistent with recent trace element studies on the glasses; model (2) is dependent on the debatable incompatible behavior of Ni and Co, and, in models of type (3), the origin and nature of mixing models are somewhat unconstrained. This study compares the Apollo 15 green glasses with the very low Ti picritic glasses from other landing sites.

Shearer, C. K.↗

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗

Two-Flux Green's Function Analysis for Transient Spectral Radiation in a Composite

An analysis is developed for obtaining transient temperatures in a two-layer semitransparent composite with spectrally dependent properties. Each external boundary of the composite is subjected to radiation and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. This produces internal reflections at the boundaries and the internal interface; the reflections are assumed diffuse. Spectral results using the Green's function method are verified by comparing with numerical solutions using the exact radiative transfer equations. Transient temperature distributions are given to illustrate the effect of radiative heating on one side of a composite with external convective cooling. The protection of a material from incident radiation is illustrated by adding scattering to the layer adjacent to the radiative source.

Siegel, Robert↗

The Determination of the Large-Scale Circulation of the Pacific Ocean from Satellite Altimetry using Model Green's Functions

A Green's function method for obtaining an estimate of the ocean circulation using both a general circulation model and altimetric data is demonstrated. The fundamental assumption is that the model is so accurate that the differences between the observations and the model-estimated fields obey a linear dynamics. In the present case, the calculations are demonstrated for model/data differences occurring on very a large scale, where the linearization hypothesis appears to be a good one. A semi-automatic linearization of the Bryan/Cox general circulation model is effected by calculating the model response to a series of isolated (in both space and time) geostrophically balanced vortices. These resulting impulse responses or 'Green's functions' then provide the kernels for a linear inverse problem. The method is first demonstrated with a set of 'twin experiments' and then with real data spanning the entire model domain and a year of TOPEX/POSEIDON observations. Our present focus is on the estimate of the time-mean and annual cycle of the model. Residuals of the inversion/assimilation are largest in the western tropical Pacific, and are believed to reflect primarily geoid error. Vertical resolution diminishes with depth with 1 year of data. The model mean is modified such that the subtropical gyre is weakened by about 1 cm/s and the center of the gyre shifted southward by about 10 deg. Corrections to the flow field at the annual cycle suggest that the dynamical response is weak except in the tropics, where the estimated seasonal cycle of the low-latitude current system is of the order of 2 cm/s. The underestimation of observed fluctuations can be related to the inversion on the coarse spatial grid, which does not permit full resolution of the tropical physics. The methodology is easily extended to higher resolution, to use of spatially correlated errors, and to other data types.

Stammer, Detlef↗

Preparation and Dielectric Measurements of the Rare Earth Green Phases R2BaCuO(5-x) (R = Y, Sm, Gd, Dy, Ho, Er, Yb)

It has been demonstrated that R2BaCuO(5-x) (R = Y, Sm, Gd, Dy, Ho, Er, Yb) does not undergo significant densification unless the sintering temperatures are near the incongruent melting point or the sintering times are long. Good quality powders of Y2BaCuO(5-x) have been synthesized by using oxide raw materials or precursors such as acetates and nitrates. The acetates- and the nitrates-derived yttrium green phase resulted in finer particle sizes, acceptable dielectric properties and lower melting temperatures than those processed via oxide raw materials. The hot pressing technique has been employed to produce a dense R2BaCuO(5-x) (R=Y,Gd) substrate with satisfactory dielectric properties. Reactivity to reducing conditions, i.e. graphite die, limited the optimization of the properties. A high sensitivity to the annealing atmosphere has been demonstrated in Y2BaCuO,.,,. Oxygen treatment at 950 OC has been shown to improve the dielectric properties while treatment in nitrogen, at the same temperature, degraded desirable properties. A high sensitivity to the annealing atmosphere has been demonstrated in Y2BaCuO(5-x). Oxygen treatment at 950 C has been shown to improve the dielectric properties while treatment in nitrogen, at the same temperature, degraded desirable properties. The dielectric constants of the rare earth green phases R2BaCuO(5-x) were found to be low. Relaxation peaks were detected at low temperatures (T less than 150 K) and at high temperatures (150 less than T greater than 420 K). The dielectric losses and conductivities at 77 K were measured to be in the range of 10(exp -4) and 10(exp -12) (Omega-cm)(exp -1), respectively. Many parameters were found to exhibit dependencies on the rare earth cation sizes.

Gonzalez-Titman, Carlos↗