Results for “Green function” — Page 17

NASA NTRS1994

Nonperturbative methods in HZE propagation

An analytical solution to the perturbative multiple collision series of a fragmenting HZE ion beam has limited usefulness since the first collision term has several hundred contributions, the second collision term has tens of thousands of contributions, and each successive collision term progresses to unwieldy computational proportions. Our previous work has revealed the multiple collision terms in the straight-ahead approximation to be simple products of a spatially dependent factor times a linear energy-dependent factor of limited domain and unit normalization. The properties of these forms allow the development of the nonperturbative summation of the series to all orders assuming energy-independent nuclear cross sections as matrix products of a scaled Green's function described herein. This nonperturbative Green's function with multiple scattering correction factors compares well with experiments using 670 MeV/u neon-20 ion beams in thick water targets.

Non-NASA Center↗

NASA NTRS2011

The Prediction of Broadband Shock-Associated Noise Including Propagation Effects

An acoustic analogy is developed based on the Euler equations for broadband shock- associated noise (BBSAN) that directly incorporates the vector Green's function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) as the mean flow. The vector Green's function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation. An adjoint vector Green's function solver is implemented to determine the vector Green's function based on a locally parallel mean flow at streamwise locations of the SRANS solution. However, the developed acoustic analogy could easily be based on any adjoint vector Green's function solver, such as one that makes no assumptions about the mean flow. The newly developed acoustic analogy can be simplified to one that uses the Green's function associated with the Helmholtz equation, which is consistent with the formulation of Morris and Miller (AIAAJ 2010). A large number of predictions are generated using three different nozzles over a wide range of fully expanded Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise labs. In addition, two models for the so-called 'fine-scale' mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include the propagation effects, especially in the upstream direction of the jet.

Miller, Steven↗

NASA NTRS2012

Prediction of Broadband Shock-Associated Noise Including Propagation Effects Originating NASA

An acoustic analogy is developed based on the Euler equations for broadband shock-associated noise (BBSAN) that directly incorporates the vector Green s function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) to describe the mean flow. The vector Green s function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation rate. An adjoint vector Green s function solver is implemented to determine the vector Green s function based on a locally parallel mean flow at different streamwise locations. The newly developed acoustic analogy can be simplified to one that uses the Green s function associated with the Helmholtz equation, which is consistent with a previous formulation by the authors. A large number of predictions are generated using three different nozzles over a wide range of fully-expanded jet Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise experimental facilities. In addition, two models for the so-called fine-scale mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include propagation effects.

Miller, Steven↗

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 NTRS2004

Modeling of Turbulence Generated Noise in Jets

A numerically calculated Green's function is used to predict jet noise spectrum and its far-field directivity. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. In this paper, contributions from the so-called self- and shear-noise source terms will be discussed. A Reynolds-averaged Navier-Stokes solution yields the required mean flow as well as time- and length scales of a noise-generating turbulent eddy. A non-compact source, with exponential temporal and spatial functions, is used to describe the turbulence velocity correlation tensors. It is shown that while an exact non-causal Green's function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at moderate Mach numbers, at high subsonic and supersonic acoustic Mach numbers the polar directivity of radiated sound is not entirely captured by this Green's function. Results presented for Mach 0.5 and 0.9 isothermal jets, as well as a Mach 0.8 hot jet conclude that near the peak radiation angle a different source/Green's function convolution integral may be required in order to capture the peak observed directivity of jet noise.

Khavaran, Abbas↗

NASA NTRS2005

Prediction of Turbulence-Generated Noise in Unheated Jets: JeNo Technical Manual (Version 1.0) - Part 1

The model-based approach, used by the JeNo code to predict jet noise spectral directivity, is described. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. A Reynolds-averaged Navier-Stokes (RANS) solution yields the required mean flow for the solution of the propagation Green s function in a locally parallel flow. The RANS solution also produces time- and length-scales needed to model the non-compact source, the turbulent velocity correlation tensor, with exponential temporal and spatial functions. It is shown that while an exact non-causal Green s function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at low to moderate Mach numbers, the polar directivity of radiated sound is not entirely captured by this Green s function at high subsonic and supersonic acoustic Mach numbers. Results presented for unheated jets in the Mach number range of 0.51 to 1.8 suggest that near the peak radiation angle of high-speed jets, a different source/Green s function convolution integral may be required in order to capture the peak observed directivity of jet noise. A sample Mach 0.90 heated jet is also discussed that highlights the requirements for a comprehensive jet noise prediction model.

Khavaran, Abbas↗

DOE OSTI2020

Atomistic modeling of energy band alignment in CdTe(1 0 0) and CdTe(1 1 1) surfaces

An atomic-scale perspective of energy band alignment in CdTe surfaces has not been spatially studied despite the major role surfaces play in forming interfaces within CdTe-based thin film photovoltaic devices. Atomistic modeling based on density functional theory coupled with surface Green’s function is used for calculating energy band alignment of CdTe surfaces. The CdTe(1 0 0) ((1×1) and c(2×2) reconstruction) and CdTe(1 1 1) ((1×1) and (2×2) reconstruction) facets without and with surface relaxation provide insightful band bending characteristics that influence charge carrier transport. Results show that unrelaxed (1×1) CdTe(1 0 0) and CdTe(1 1 1) surfaces bend the valence band downward with surface polarity dictating the surface potential magnitude. The reconstructed CdTe(1 0 0) c(2×2) and CdTe(1 1 1) (2×2) surfaces result in favorable surface electronic features in relation to their unreconstructed variants. In addition, the structurally relaxed CdTe(1 1 1) surfaces develop an internal energy cusp potential that may enhance hole charge transport toward the back of CdTe solar cell devices. In conclusion, energy band alignments calculated within the study lead to a detailed understanding of how CdTe surfaces may affect CdTe-based thin film photovoltaic applications.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Pre-equilibrium evolution of conserved charges with initial conditions in the ICCING Monte Carlo event generator

Heavy-ion collisions can be well described through relativistic viscous hydrodynamics, but questions still remain when hydrodynamics is applicable because the initial state may begin very far from equilibrium. Thus, a pre-equilibrium evolution phase is used to bridge the gap between the initial state and hydrodynamics. KøMPøST is one such pre-equilibrium model that propagates the energy-momentum tensor by decomposing it into the background and fluctuations around that background, whose evolution is captured by Green's functions. We extend this formalism to include conserved charges and calculate the corresponding nonequilibrium Green's functions in the relaxation-time approximation. The ICCING algorithm initializes conserved charges in the initial state by sampling $g$ → $q$$\overline{q}$ splitting probabilities and is, thus, perfectly positioned to implement Green's functions for charge propagation. As a result, we show that this method alters the initial-state charge geometries and is applicable in central to mid-central collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1992

Scattering from dielectric structures above impedance surfaces and resistive sheets

Interest in understanding of electromagnetic interaction with rough surfaces has prompted the study of scattering from typical dielectric humps over impedance surfaces. It is shown that the Green's function of the problem for a resistive sheet resembles that of the impedance surface. Hence both problems are considered here. A numerical solution for the scattered field of a two-dimensional dielectric object, possibly inhomogeneous, with arbitrary cross section above the impedance surface or resistive sheet is sought. First the Green's function of the problem is derived based on the exact image theory. This form of the Green's function is amenable to numerical computation. Then the induced polarization currents are calculated by casting the integral equations into a matrix equation via the method of moments. Numerical problems in calculation of the Green's function when both source and observation points are close to the surface are discussed. Comparison of numerical results with a perturbation solution shows excellent agreement between the two methods.

Sarabandi, Kamal↗

DOE OSTI2020

Method of Green’s Potentials for Elliptic PDEs in Domains with Random Apertures

Problems with topological uncertainties appear in many fields ranging from nano-device engineering to the design of bridges. In many of such problems, a part of the domains boundaries is subjected to random perturbations making inefficient conventional schemes that rely on discretization of the whole domain. Here, we study elliptic PDEs in domains with boundaries comprised of a deterministic part and random apertures, and apply the method of modified potentials with Green’s kernels defined on the deterministic part of the domain. This approach allows to reduce the dimension of the original differential problem by reformulating it as a boundary integral equation posed on the random apertures only. The multilevel Monte Carlo method is then applied to this modified integral equation and its optimal ϵ -2 asymptotical complexity is shown. Finally, we provide the qualitative analysis of the proposed technique and support it with numerical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The Effects of Atmospheric Models on the Estimation of Infrasonic Source Functions at the Source Physics Experiment

We invert infrasound signals for an equivalent seismoacoustic source function using different atmospheric models to produce the necessary Green’s functions. The infrasound signals were produced by a series of underground chemical explosions as part of the Source Physics Experiment (SPE). In a previous study, we inverted the infrasound data using so-called predictive atmospheric models, which were based on historic, regional-scaled, publicly available weather observations interpolated onto a 3D grid. For the work presented here, we invert the same infrasound data, but using atmospheric models based on weather data collected in a time window that includes the approximate time of the explosion experiments, which we term postdictive models. We build two versions of the postdictive models for each SPE event: one that is based solely on the regional scaled observations, and one that is based on both regional scaled observations combined with on-site observations obtained by a weather sonde released at the time of the SPE. We then invert the observed data set three times, once for each atmospheric model type. We find that the estimated seismoacoustic source functions are relatively similar in waveform shape regardless of which atmospheric model that we used to construct the Green’s functions. However, we find that the amplitude of the estimated source functions is systematically dependent on the atmospheric model type: using the predictive atmospheric models to invert the data generally yields estimated source functions that are larger in amplitude than those estimated using the postdictive models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1975

The generation of gravitational waves. I - Weak-field sources

This paper derives and summarizes a 'plug-in-and-grind' formalism for calculating the gravitational waves emitted by any system with weak internal gravitational fields. If the internal fields have negligible influence on the system's motions, the formalism reduces to standard 'linearized theory'. Independent of the effects of gravity on the motions, the formalism reduces to the standard 'quadrupole-moment formalism' if the motions are slow and internal stresses are weak. In the general case, the formalism expresses the radiation in terms of a retarded Green's function for slightly curved spacetime and breaks the Green's function integral into five easily understood pieces: direct radiation, produced directly by the motions of the source; whump radiation, produced by the 'gravitational stresses' of the source; transition radiation, produced by a time-changing time delay ('Shapiro effect') in the propagation of the nonradiative 1/r field of the source; focusing radiation, produced when one portion of the source focuses, in a time-dependent way, the nonradiative field of another portion of the source; and tail radiation, produced by 'back-scatter' of the nonradiative field in regions of focusing.

Thorne, K. S.↗

NASA NTRS2000

Electromagnetic Field Penetration Studies

A numerical method is presented to determine electromagnetic shielding effectiveness of rectangular enclosure with apertures on its wall used for input and output connections, control panels, visual-access windows, ventilation panels, etc. Expressing EM fields in terms of cavity Green's function inside the enclosure and the free space Green's function outside the enclosure, integral equations with aperture tangential electric fields as unknown variables are obtained by enforcing the continuity of tangential electric and magnetic fields across the apertures. Using the Method of Moments, the integral equations are solved for unknown aperture fields. From these aperture fields, the EM field inside a rectangular enclosure due to external electromagnetic sources are determined. Numerical results on electric field shielding of a rectangular cavity with a thin rectangular slot obtained using the present method are compared with the results obtained using simple transmission line technique for code validation. The present technique is applied to determine field penetration inside a Boeing-757 by approximating its passenger cabin as a rectangular cavity filled with a homogeneous medium and its passenger windows by rectangular apertures. Preliminary results for, two windows, one on each side of fuselage were considered. Numerical results for Boeing-757 at frequencies 26 MHz, 171-175 MHz, and 428-432 MHz are presented.

Deshpande, M.D.↗

DOE OSTI2020

NESSi : The N on- E quilibrium S ystems S imulation package

The nonequilibrium dynamics of correlated many-particle systems is of interest in connection with pump–probe experiments on molecular systems and solids, as well as theoretical investigations of transport properties and relaxation processes. Nonequilibrium Green’s functions are a powerful tool to study interaction effects in quantum many-particle systems out of equilibrium, and to extract physically relevant information for the interpretation of experiments. Here, we present the open-source software package NESSi (The Non-Equilibrium Systems Simulation package) which allows to perform many-body dynamics simulations based on Green’s functions on the L-shaped Kadanoff–Baym contour. NESSi contains the library libcntr which implements tools for basic operations on these nonequilibrium Green’s functions, for constructing Feynman diagrams, and for the solution of integral and integro-differential equations involving contour Green’s functions. The library employs a discretization of the Kadanoff–Baym contour into time points and a high-order implementation of integration routines. The total integrated error scales up to $\mathcal{O}(N^{-7})$, which is important since the numerical effort increases at least cubically with the simulation time. A distributed-memory parallelization over reciprocal space allows large-scale simulations of lattice systems. We provide a collection of example programs ranging from dynamics in simple two-level systems to problems relevant in contemporary condensed matter physics, including Hubbard clusters and Hubbard or Holstein lattice models. The libcntr library is the basis of a follow-up software package for nonequilibrium dynamical mean-field theory calculations based on strong-coupling perturbative impurity solvers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Accurate numerical, integral methods for computing drift-kinetic Trubnikov-Rosenbluth potentials

A novel numerical method is employed to compute the integral form of the axi-symmetric Trubnikov-Rosenbluth potentials. Two methods for quadrature in pitch-angle are described and their convergence properties are studied. Careful attention is given to quadrature over a singular Green's function. Here it is shown that an infinite series representation of the Green's function can be used more efficiently than its closed form involving complete elliptic integrals. Then a collocation method in speed, with its associated quadrature scheme, is laid out and its convergence properties are studied. Using the proposed scheme, accurate low-order moments of the field collision operator are obtained using relatively few velocity space degrees of freedom. The scheme is showcased by solving for the equilibrium, axi-symmetric bootstrap current in tokamaks. A C 0 Gauss-Lobatto-Legendre finite element pitch-angle basis with vertex nodes at the trapped/passing boundary is shown, in the context of the integral methods used, to be much more efficient than the more common Legendre polynomial expansion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Aircraft↗