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Results for “Green's function methods”

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 NTRS1976

A kinetic-theory approach to turbulent chemically reacting flows

The paper examines the mathematical and physical foundations for the kinetic theory of reactive turbulent flows, discussing the differences and relation between the kinetic and averaged equations, and comparing some solutions of the kinetic equations obtained by the Green's function method with those obtained by the approximate bimodal method. The kinetic method described consists essentially in constructing the probability density functions of the chemical species on the basis of solutions of the Langevin stochastic equation for the influence of eddies on the behavior of fluid elements. When the kinetic equations are solved for the structure of the diffusion flame established in a shear layer by the bimodal method, discontinuities in gradients of the mean concentrations at the two flame edges appear. This is a consequence of the bimodal approximation of all distribution functions by two dissimilar half-Maxwellian functions, which is a very crude approximation. These discontinuities do not appear when the solutions are constructed by the Green's function method described here.

Chung, P. M.↗
NASA NTRS1977

Unsteady subsonic and supersonic potential aerodynamics for complex configurations

A recently developed general theory for unsteady compressible potential fluid dynamics for complex-configuration aircraft is reviewed. The method is based on a combination of the following techniques: Green's function method (to transform the differential equation into an integral differential-delay equation), finite element method (to transform the equation into a set of differential-delay equations in time), and the Laplace transform method (to transform the differential-delay equations into algebraic equations).

Morino, L.↗
NASA NTRS1982

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

The SOUSSA (steady, oscillatory, and unsteady subsonic and supersonic aerodynamics) program is the computational implementation of a general potential flow analysis (by the Green's function method) that can generate pressure distributions on complete aircraft having arbitrary shapes, motions and deformations. Some applications of the initial release version of this program to several wings in steady and oscillatory motion, including flutter are presented. The results are validated by comparisons with other calculations and experiments. Experiences in using the program as well as some recent improvements are described.

Yates, E. C., Jr.↗
NASA NTRS2023

Radiative interaction of atmosphere and surface: write up with elements of code

In passive satellite remote sensing of the Earth, separation of the path radiance (atmosphere-only contribution) from the surface reflection remains a “significant challenge”. Recent literature names it among the gaps in radiative transfer (RT) topics that “require continued research in the near future”. The challenge comes from multiple reflections (bouncing) between the atmosphere and surface – radiative interaction. In this paper we use a known RT technique, the matrix-operator method (MOM), and a new modification of the monochromatic vector RT (vRT) code IPOL (Intensity and POLarization) to simulate the interaction of a plane-parallel atmosphere and a few widely used surface reflection models. Following the idea of the Green’s function method, IPOL no longer takes the surface model parameters on input. Instead, it provides the path radiance, and the atmospheric reflection and transmission matrices as output. Despite many RT codes use the MOM formalism, this output does not seem common. The surface reflection matrix is computed externally. Therefore, this paper extends the Green’s function atmospheric correction technique to the case of polarized light. Aiming clarity rather than performance, we explain in Python the structure of the surface matrices for the isotropic (Lambertian), directional unpolarized, and polarized ocean reflection models. We then combine these surface matrices and the precomputed IPOL output to get numerically accurate signal at the top of atmosphere (TOA) and test it vs. published benchmarks. Then, for each benchmark scenario we show how to get the surface from the TOA signal, i.e. perform the RT-based atmospheric correction.

radiative transfer↗
NASA NTRS1996

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↗
NASA NTRS2009

Chemical Source Inversion using Assimilated Constituent Observations in an Idealized Two-dimensional System

We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.

Tangborn, Andrew↗
NASA NTRS1973

Unsteady compressible potential flow around lifting bodies - General theory.

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green's function method, an integral representation for the velocity potential is obtained for both supersonic and subsonic flow. This representation reduces properly to the lifting surface theories as well as to other classical mathematical formulas. 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 integrodifferential equation relating the potential and its normal derivative on the surface of the body.

Morino, L.↗
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

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Chrzanowski, P. L.↗
NASA NTRS1976

A new unified approach for analyzing wing-body-tail configurations with control surfaces

A general theory for steady and unsteady, subsonic and supersonic potential aerodynamics for complex configurations is presented. Special attention is given to the theoretical formulation and the corresponding numerical implementation for coplanar interfering surfaces. Applying the Green's function method to the equation of the velocity potential and discretizing the spatial problem by using the finite-element technique, yields a set of differential-delay equations in time relating the potential to the normal wash. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t less than or equal to 0 (steady state) and of small perturbations around the steady state for time t greater than 0; the solution is obtained in the Laplace domain. From the potential, the aerodynamic pressure and the generalized forces are evaluated. The program SOUSSA (Steady, Oscillatory and Unsteady Subsonic and Supersonic Aerodynamics) is briefly described. Numerical results obtained with SOUSSA are presented.

Tseng, K.↗
NASA NTRS1977

Aerodynamic interference effects on tilting proprotor aircraft

The Green's function method was used to study tilting proprotor aircraft aerodynamics with particular application to the problem of the mutual interference of the wing-fuselage-tail-rotor wake configuration. While the formulation is valid for fully unsteady rotor aerodynamics, attention was directed to steady state aerodynamics, which was achieved by replacing the rotor with the actuator disk approximation. The use of an actuator disk analysis introduced a mathematical singularity into the formulation; this problem was studied and resolved. The pressure distribution, lift, and pitching moment were obtained for an XV-15 wing-fuselage-tail rotor configuration at various flight conditions. For the flight configurations explored, the effects of the rotor wake interference on the XV-15 tilt rotor aircraft yielded a reduction in the total lift and an increase in the nose-down pitching moment. This method provides an analytical capability that is simple to apply and can be used to investigate fuselage-tail rotor wake interference as well as to explore other rotor design problem areas.

Soohoo, P.↗
NASA NTRS1979

A simplified computer program for the prediction of the linear stability behavior of liquid propellant combustors

A program for predicting the linear stability of liquid propellant rocket engines is presented. The underlying model assumptions and analytical steps necessary for understanding the program and its input and output are also given. The rocket engine is modeled as a right circular cylinder with an injector with a concentrated combustion zone, a nozzle, finite mean flow, and an acoustic admittance, or the sensitive time lag theory. The resulting partial differential equations are combined into two governing integral equations by the use of the Green's function method. These equations are solved using a successive approximation technique for the small amplitude (linear) case. The computational method used as well as the various user options available are discussed. Finally, a flow diagram, sample input and output for a typical application and a complete program listing for program MODULE are presented.

Mitchell, C. E.↗
NASA NTRS1982

Acoustic propagation in a rigid torus

The acoustic propagation in a rigid torus is analyzed using a Green's function method. Three types of surface elements are developed; a flat quadrilateral element used in modeling polygonal cavities, a curved conical element appropriate for surfaces with one curvature, and a toroidal element developed for such doubly curved surfaces as the torus. Curved elements are necessary since the acoustic pressure is sensitive to slope discontinuities between consecutive surface elements especially near cavity resonances. The acoustic characteristics of the torus are compared to those of a bend of square cross section for a frequency range that includes the transverse acoustic resonance. Two equivalences between the different sections are tested; the first conserves curvature and cross-sectional dimension while the second matches transverse resonance and duct volume. The second equivalence accurately matches the acoustic characteristics of the torus up to the cutoff frequency corresponding to a mode with two circumferential waves.

El-Raheb, M.↗
NASA NTRS1989

Green's function solution to heat transfer of a transparent gas through a tube

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

Frankel, J. I.↗
NASA NTRS1998

Transport of Light Ions in Matter

A recent set of light ion experiments are analyzed using the Green's function method of solving the Boltzmann equation for ions of high charge and energy (the GRNTRN transport code) and the NUCFRG2 fragmentation database generator code. Although the NUCFRG2 code reasonably represents the fragmentation of heavy ions, the effects of light ion fragmentation requires a more detailed nuclear model including shell structure and short range correlations appearing as tightly bound clusters in the light ion nucleus. The most recent NTJCFRG2 code is augmented with a quasielastic alpha knockout model and semiempirical adjustments (up to 30 percent in charge removal) in the fragmentation process allowing reasonable agreement with the experiments to be obtained. A final resolution of the appropriate cross sections must await the full development of a coupled channel reaction model in which shell structure and clustering can be accurately evaluated.

Wilson, J. W.↗
NASA NTRS2002

Influence of Scattering on Ballistic Nanotransistor Design

Importance of this work: (1) This is the first work to model electron-phonon scattering within a quantum mechanical approach to nanotransistors. The simulations use the non equilibrium Green's function method. (2) A simple equation which captures the importance of scattering as a function of the spatial location from source to drain is presented. This equation helps interpret the numerical simulations. (3) We show that the resistance per unit length in the source side is much larger than in the drain side. Thus making scattering in the source side of the device much more important than scattering in the drain side. Numerical estimates of ballisticity for 10nm channel length devices in the presence of of electron-phonon scattering are given. Based on these calculations, we propose that to achieve a larger on-current in nanotransistors, it is crucial to keep the highly doped source extension region extremely small, even if this is at the cost of making the highly doped drain extension region longer.

Anantram, M. P.↗
NASA NTRS2003

Where is scattering important in nanotransistors?

This viewgraph presentation provides an overview of scattering in nanotransistors. Topics covered include: scattering mechanisms, devices used and series resistance. The authors conclude: (1) the influence of electron-photon scattering on the on-current of dual gate MOSFET's using the non-equilibrium Green's function method and (2) the influence of the drain extension region can no longer be modeled as a series resistance.

Anantram, M. P.↗