SEARCH · Engineering Papers

Results for “Green function”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 685 records · Page 38

All sources NASA NTRS DOE OSTI

NASA NTRS1972

Signal processing in a randomly time varying system.

Stochastic operators are applied to an analysis of some deterministic systems of signal transformation. The distribution of a random process at the output of a system is given through its distribution at the input and through a stochastic Green's function. A two-point correlation function is derived to obtain a solution to differential equations which contain coefficients, boundary conditions, or right-hand terms representing random processes.

Adomian, G.↗

NASA NTRS1973

Mars - Crustal structure inferred from Bouguer gravity anomalies.

Bouguer gravity has been computed for the equatorial region of Mars by differencing free air gravity and the gravity predicted from topographic variations. The free air gravity was generated from an eighth-order set of spherical harmonic coefficients. The gravity from topographic variations was generated by integrating a two-dimensional Green's function over each contour level. The Bouguer gravity indicates crustal inhomogeneities on Mars that are postulated to be variations in crustal thickness. The Tharsis ridge is a region of thick continental type crust. The gravity data, structural patterns, topography, and surface geology of this region lead to the interpretation of the Tharsis topographic high as a broad crustal upwarp possibly associated with local formation of lower-density crustal material and subsequent rise of a thicker crust. The Amazonis region is one of several basins of relatively thin crust, analogous to terrestrial ocean basins. The Libya and Hellas basins, which are probable impact features, are also underlain by thin crust and are possible regions of mantle upwelling.

Phillips, R. J.↗

NASA NTRS1973

An analysis of the unified and scalar additivity theories of spectral line broadening

The qualities of the unified and scalar theories proposed by various authors for describing the static and dynamic characteristics of a radiation perturber interaction are discussed. The regions of validity of these theories and the properties of the approximations applied by them are considered. New derivation procedures are proposed for the unified and scalar additivity theories of line broadening. These procedures do not require the use of an elaborate projection operator, of Green's function techniques in contrast to previous methods.

Smith, E. W.↗

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 NTRS1974

Elementary solutions of coupled model equations in the kinetic theory of gases

The method of elementary solutions is employed to solve two coupled integrodifferential equations sufficient for determining temperature-density effects in a linearized BGK model in the kinetic theory of gases. Full-range completeness and orthogonality theorems are proved for the developed normal modes and the infinite-medium Green's function is constructed as an illustration of the full-range formalism. The appropriate homogeneous matrix Riemann problem is discussed, and half-range completeness and orthogonality theorems are proved for a certain subset of the normal modes. The required existence and uniqueness theorems relevant to the H matrix, basic to the half-range analysis, are proved, and an accurate and efficient computational method is discussed. The half-space temperature-slip problem is solved analytically, and a highly accurate value of the temperature-slip coefficient is reported.

Kriese, J. T.↗

NASA NTRS1974

Finite-amplitude thermal convection in a spherical shell

The properties of finite-amplitude thermal convection for a Boussinesq fluid contained in a spherical shell are investigated. All nonlinear terms are retained in the equations, and both axisymmetric and nonaxisymmetric solutions are studied. The velocity is expanded in terms of poloidal and toroidal vectors. Spherical surface harmonics resolve the horizontal structure of the flow, but finite differences are used in the vertical. With a few modifications, the transform method developed by Orszag (1970) is used to calculate the nonlinear terms, while Green's function techniques are applied to the poloidal equation and diffusion terms.

Young, R. E.↗

NASA NTRS1975

Broadband noise generated by turbulent inflow to rotor or stator blades in an annular duct

The Green's function relating the radiated pressure field to the fluctuating forces on rotor or stator blades is developed in the presence of dissipation due to turbulent velocity fluctuations and sound speed fluctuations. The resonances in the output power spectrum which would occur at the cut-off frequencies in the absence of dissipation should be removed and smeared out by the incorporation of dissipation. Wave number dependence is developed for an effective eddy viscosity due to the aforementioned fluctuations in the background medium. The space-time correlation function for blade-normal velocity fluctuations on a single or on two different blades is developed in terms of the velocity correlation tensor for the inflow under the assumptions of isotropy and (Taylor) frozen behavior. The correlation function is then simplified under certain approximations and the behavior of the blade-force correlation function is inferred.

Lnae, F.↗

NASA NTRS1975

Suppression of nonlinear oscillations in combustors with partial length acoustic liners

An analytical model is formulated for a three-dimensional nonlinear stability problem in a rocket motor combustion chamber. The chamber is modeled as a right circular cylinder with a short (multi-orifice) nozzle, and an acoustic linear covering an arbitrary portion of the cylindrical periphery. The combustion is concentrated at the injector and the gas flow field is characterized by a mean Mach number. The unsteady combustion processes are formulated using the Crocco time lag model. The resulting equations are solved using a Green's function method combined with numerical evaluation techniques. The influence of acoustic liners on the nonlinear waveforms is predicted. Nonlinear stability limits and regions where triggering is possible are also predicted for both lined and unlined combustors in terms of the combustion parameters.

Espander, W. R.↗

NASA NTRS1974

Normal-mode approach to wave propagation in the turbulent atmosphere

Recent studies have used the superposition principle (extended Huygens-Fresnel principle) to characterize completely the statistics of a field that has propagated through a thick slab of turbulent air in terms of the statistics for spherical-wave sources. In this paper, we consider the normal-mode decomposition associated with this linear system propagation model. In particular, we use the statistics of the atmospheric impulse response (Green's function) to show that the atmospheric mode decomposition exhibits far-field and near-field regimes very similar to those of free-space propagation. The significance of these results for optical communication through the atmosphere is briefly discussed.

Shapiro, J. H.↗

NASA NTRS1975

On an integro-differential equation model for the study of the response of an acoustically coupled panel

The response of a clamped panel to supersonically convected turbulence is considered. A theoretical model in the form of an integro-differential equation is employed that takes into account the coupling between the panel motion and the surrounding acoustic medium. The kernels of the integrals, which represent induced pressures due to the panel motion, are Green's functions for sound radiations under various moving and stationary sources. An approximate analysis is made by following a finite-element Ritz-Galerkin procedure. Preliminary numerical results, in agreement with experimental findings, indicate that the acoustic damping is the controlling mechanism of the response.

Yen, D. H. Y.↗

NASA NTRS1975

Interaction between a circular inclusion and an arbitrarily oriented crack

The plane interaction problem for a circular elastic inclusion embedded in an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equations with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress-intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress-intensity factors are given.

Erdogan, F.↗

NASA NTRS1975

The scattering of electromagnetic pulses by a slit in a conducting screen

A direct method for calculating the impulse response of a slit in a conducting screen is presented which is derived specifically for the analysis of transient scattering by two-dimensional objects illuminated by a plane incident wave. The impulse response is obtained by assuming that the total response is composed of two sequences of diffracted waves. The solution is determined for the first two waves in one sequence by using Green's functions and the equivalence principle, for additional waves in the sequence by iteration, and for the other sequence by a transformation of coordinates. The cases of E-polarization and H-polarization are considered.

Ackerknecht, W. E., III↗

NASA NTRS1975

Vector potential and metric perturbations of a rotating black hole

The assumption of factorized Green's functions together with the inhomogeneous Teukolsky equations are used to derive analytic expressions for homogeneous metric (and vector potential) perturbations of a Kerr black hole. These homogeneous solutions are used to construct solutions to the perturbation equations when sources are present. What one finds are particularly simple formulas for the energy and angular momentum flux in the asymptotic regions at plus or minus infinity.-

Chrzanowski, P. L.↗

NASA NTRS1975

Derivation and application of the reciprocity relations for radiative transfer with internal illumination

A Green's function formulation is used to derive basic reciprocity relations for planar radiative transfer in a general medium with internal illumination. Reciprocity (or functional symmetry) allows an explicit and generalized development of the equivalence between source and probability functions. Assuming similar symmetry in three-dimensional space, a general relationship is derived between planar-source intensity and point-source total directional energy. These quantities are expressed in terms of standard (universal) functions associated with the planar medium, while all results are derived from the differential equation of radiative transfer.

Cogley, A. C.↗

NASA NTRS1975

Combustion instability with partial length acoustic liners

The development is discussed of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors with partial length acoustic liners, injector face baffles, and nonlinear combustion responses. Three primary objectives included: (1) extension of the Green's Function integral-iteration technique previously developed so that nonlinear three dimensional wave propagation effects could be included in stability predictions; (2) development of an analytical technique and a computer program for the prediction of the damping effects caused by injector face baffles; and (3) inclusion of a nonlinear, wave distortation dependent, combustion response model in the global stability analysis and determination of its effect on combustor stability.

Mitchell, C. 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 NTRS1975

Effect of flow on the acoustic resonances of an open-ended duct

The effect of flow on the acoustic resonances of an open-ended, hard-walled duct is analyzed. The flow produces acoustic losses both in the interior of the duct and at the ends. Unless the duct is very long, typically 100 times the diameter, the losses at the ends dominate. At flow Mach numbers in excess of 0.4 the losses are so large that axial duct resonances are almost completely suppressed. The plane-wave Green's function for the duct with flow is expressed in terms of the (experimentally determined) pressure reflection coefficients at the ends of the duct, and the flow dependence of the complex eigenfrequencies of the duct is obtained. Some observations concerning the noise produced by the flow in the duct are also reported.

Ingard, U.↗

NASA NTRS1976

Microwave remote sensing of a two-layer random medium

A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.

Tsang, L.↗