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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

The Prediction and Analysis of Jet Flows and Scattered Turbulent Mixing Noise About Flight Vehicle Airframes

Jet flows interacting with nearby surfaces exhibit a complex behavior in which acoustic and aerodynamic characteristics are altered. The physical understanding and prediction of these characteristics are essential to designing future low noise aircraft. A new approach is created for predicting scattered jet mixing noise that utilizes an acoustic analogy and steady Reynolds-averaged Navier-Stokes solutions. A tailored Green's function accounts for the propagation of mixing noise about the air-frame and is calculated numerically using a newly developed ray tracing method. The steady aerodynamic statistics, associated unsteady sound source, and acoustic intensity are examined as jet conditions are varied about a large at plate. A non-dimensional number is proposed to estimate the effect of the aerodynamic noise source relative to jet operating condition and airframe position. The steady Reynolds-averaged Navier-Stokes solutions, acoustic analogy, tailored Green's function, non- dimensional number, and predicted noise are validated with a wide variety of measurements. The combination of the developed theory, ray tracing method, and careful implementation in a stand-alone computer program result in an approach that is more first principles oriented than alternatives, computationally efficient, and captures the relevant physics of fluid-structure interaction.

Miller, Steven A.↗
NASA NTRS2015

The Prediction of Scattered Broadband Shock-Associated Noise

A mathematical model is developed for the prediction of scattered broadband shock-associated noise. Model arguments are dependent on the vector Green's function of the linearized Euler equations, steady Reynolds-averaged Navier-Stokes solutions, and the two-point cross-correlation of the equivalent source. The equivalent source is dependent on steady Reynolds-averaged Navier-Stokes solutions of the jet flow, that capture the nozzle geometry and airframe surface. Contours of the time-averaged streamwise velocity component and turbulent kinetic energy are examined with varying airframe position relative to the nozzle exit. Propagation effects are incorporated by approximating the vector Green's function of the linearized Euler equations. This approximation involves the use of ray theory and an assumption that broadband shock-associated noise is relatively unaffected by the refraction of the jet shear layer. A non-dimensional parameter is proposed that quantifies the changes of the broadband shock-associated noise source with varying jet operating condition and airframe position. Scattered broadband shock-associated noise possesses a second set of broadband lobes that are due to the effect of scattering. Presented predictions demonstrate relatively good agreement compared to a wide variety of measurements.

Miller, Steven A. E.↗
NASA NTRS2017

Cyclotron Resonant Scattering Feature Simulations II. Description of the CRSF Simulation Process

Context. Cyclotron resonant scattering features (CRSFs) are formed by scattering of X-ray photons o_ quantized plasma electrons in the strong magnetic field (of the order 1012 G) close to the surface of an accreting X-ray pulsar. Due to the complex scattering cross-sections, the line profiles of CRSFs cannot be described by an analytic expression. Numerical methods, such as Monte Carlo (MC) simulations of the scattering processes, are required in order to predict precise line shapes for a given physical setup, which can be compared to observations to gain information about the underlying physics in these systems.Aims. A versatile simulation code is needed for the generation of synthetic cyclotron lines. Sophisticated geometries should be investigatable by making their simulation possible for the first time.Methods. The simulation utilizes the mean free path tables described in the first paper of this series for the fast interpolation of propagation lengths. The code is parallelized to make the very time-consuming simulations possible on convenient time scales. Furthermore, it can generate responses to monoenergetic photon injections, producing Green's functions, which can be used later to generate spectra for arbitrary continua.Results. We develop a new simulation code to generate synthetic cyclotron lines for complex scenarios, allowing for unprecedented physical interpretation of the observed data. An associated XSPEC model implementation is used to fit synthetic line profiles to NuSTAR data of Cep X-4. The code has been developed with the main goal of overcoming previous geometrical constraints in MC simulations of CRSFs. By applying this code also to more simple, classic geometries used in previous works, we furthermore address issues of code verification and cross-comparison of various models. The XSPEC model and the Green's function tables are available online (see link in footnote, page 1).

Schwarm, F.-W.↗
NASA NTRS1988

A theory for the radiation of magnetohydrodynamic surface waves and body waves into the solar corona

The Green's function for the slab coronal hole is obtained explicitly. The Fourier integral representation for the radiated field inside and outside the coronal hole waveguide is obtained. The radiated field outside the coronal hole is calculated using the method of steepest descents. It is shown that the radiated field can be written as the sum of two contributions: (1) a contribution from the integral along the steepest descent path and (2) a contribution from all the poles of the integrand between the path of the original integral and the steepest descent path. The free oscillations of the waveguide can be associated with the pole contributions in the steepest descent representation for the Green's function. These pole contributions are essentially generalized surface waves with a maximum amplitude near the interface which separates the plasma inside the coronal hole from the surrounding background corona. The path contribution to the integral is essentially the power radiated in body waves.

Davila, Joseph M.↗
NASA NTRS1980

Note on the eigensolution of a homogeneous equation with semi-infinite domain

The 'variation-iteration' method using Green's functions to find the eigenvalues and the corresponding eigenfunctions of a homogeneous Fredholm integral equation is employed for the stability analysis of fluid hydromechanics problems with a semiinfinite (infinite) domain of application. The objective of the study is to develop a suitable numerical approach to the solution of such equations in order to better understand the full set of equations for 'real-world' flow models. The study involves a search for a suitable value of the length of the domain which is a fair finite approximation to infinity, which makes the eigensolution an approximation dependent on the length of the interval chosen. In the examples investigated y = 1 = a seems to be the best approximation of infinity; for y greater than unity this method fails due to the polynomial nature of Green's functions.

Wadia, A. R.↗
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 NTRS2013

Towards a Comprehensive Model of Jet Noise Using an Acoustic Analogy and Steady RANS Solutions

An acoustic analogy is developed to predict the noise from jet flows. It contains two source models that independently predict the noise from turbulence and shock wave shear layer interactions. The acoustic analogy is based on the Euler equations and separates the sources from propagation. Propagation effects are taken into account by calculating the vector Green's function of the linearized Euler equations. The sources are modeled following the work of Tam and Auriault, Morris and Boluriaan, and Morris and Miller. A statistical model of the two-point cross-correlation of the velocity fluctuations is used to describe the turbulence. The acoustic analogy attempts to take into account the correct scaling of the sources for a wide range of nozzle pressure and temperature ratios. It does not make assumptions regarding fine- or large-scale turbulent noise sources, self- or shear-noise, or convective amplification. The acoustic analogy is partially informed by three-dimensional steady Reynolds-Averaged Navier-Stokes solutions that include the nozzle geometry. The predictions are compared with experiments of jets operating subsonically through supersonically and at unheated and heated temperatures. Predictions generally capture the scaling of both mixing noise and BBSAN for the conditions examined, but some discrepancies remain that are due to the accuracy of the steady RANS turbulence model closure, the equivalent sources, and the use of a simplified vector Green's function solver of the linearized Euler equations.

Miller, Steven A. E.↗
NASA NTRS1983

The relationship between surface topography, gravity anomalies, and temperature structure of convection

Consideration is given to the relationship between the temperature structure of mantle convection and the resulting surface topography and gravity anomalies, which are used in its investigation. Integral expressions relating the three variables as a function of wavelength are obtained with the use of Green's function solutions to the equations of motion for the case of constant-viscosity convection in a plane layer subject to a uniform gravitational field. The influence of the boundary conditions, particularly at large wavelengths, is pointed out, and surface topographies and gravity produced by convection are illustrated for a number of simple temperature distributions. It is shown that the upper thermal boundary layer plays an important role in determining the surface observables, while temperatures near the bottom of the layer affect mainly that boundary. This result is consistent with an explanation of geoid anomalies over mid-ocean swells in terms of convection beneath the lithosphere.

Parsons, B.↗
NASA NTRS1988

The effect of a hot, spherical scattering cloud on quasi-periodic oscillation behavior

A Monte Carlo technique is used to investigate the effects of a hot electron scattering cloud surrounding a time-dependent X-ray source. Results are presented for the time-averaged emergent energy spectra and the mean residence time in the cloud as a function of energy. Moreover, after Fourier transforming the scattering Green's function, it is shown how the cloud affects both the observed power spectrum of a time-dependent source and the cross spectrum (Fourier transform of a cross correlation between energy bands). It is found that the power spectra intrinsic to the source are related to those observed by a relatively simple frequency-dependent multiplicative factor (a transmission function). The cloud can severely attenuate high frequencies in the power spectra, depending on optical depth, and, at lower frequencies, the transmission function has roughly a Lorentzian shape. It is also found that if the intrinsic energy spectrum is constant in time, the phase of the cross spectrum is determined entirely by scattering. Finally, the implications of the results for studies of the X-ray quasi-periodic oscillators are discussed.

Bussard, R. W.↗
NASA NTRS1995

Coseismic fault slip associated with the 1992 M(sub w) 6.1 Joshua Tree, California, earthquake: Implications for the Joshua Tree-Landers earthquake sequence

Coseismic surface deformation associated with the M(sub w) 6.1, April 23, 1992, Joshua Tree earthquake is well represented by estimates of geodetic monument displacements at 20 locations independently derived from Global Positioning System and trilateration measurements. The rms signal to noise ratio for these inferred displacements is 1.8 with near-fault displacement estimates exceeding 40 mm. In order to determine the long-wavelength distribution of slip over the plane of rupture, a Tikhonov regularization operator is applied to these estimates which minimizes stress variability subject to purely right-lateral slip and zero surface slip constraints. The resulting slip distribution yields a geodetic moment estimate of 1.7 x 10(exp 18) N m with corresponding maximum slip around 0.8 m and compares well with independent and complementary information including seismic moment and source time function estimates and main shock and aftershock locations. From empirical Green's functions analyses, a rupture duration of 5 s is obtained which implies a rupture radius of 6-8 km. Most of the inferred slip lies to the north of the hypocenter, consistent with northward rupture propagation. Stress drop estimates are in the range of 2-4 MPa. In addition, predicted Coulomb stress increases correlate remarkably well with the distribution of aftershock hypocenters; most of the aftershocks occur in areas for which the mainshock rupture produced stress increases larger than about 0.1 MPa. In contrast, predicted stress changes are near zero at the hypocenter of the M(sub w) 7.3, June 28, 1992, Landers earthquake which nucleated about 20 km beyond the northernmost edge of the Joshua Tree rupture. Based on aftershock migrations and the predicted static stress field, we speculate that redistribution of Joshua Tree-induced stress perturbations played a role in the spatio-temporal development of the earth sequence culminating in the Landers event.

Bennett, Richard A.↗
NASA NTRS1982

Perturbation corrections to Koopmans' theorem. V - A study with large basis sets

The vertical ionization potentials of N2, F2 and H2O were calculated by perturbation corrections to Koopmans' theorem using six different basis sets. The largest set used includes several sets of polarization functions. Comparison is made with measured values and with results of computations using Green's functions.

Chong, D. P.↗
NASA NTRS1981

The effects of focusing on the efficiency of coherent anti-Stokes Raman scattering

The efficiency of coherent anti-Stokes Raman scattering (CARS) is calculated as a function of the input beam sizes of the Stokes and pump laser beams. A Green's function formalism is used to show that maximum efficiency occurs when the confocal parameters of the two input beams are unequal and when the phase mismatch between the anti-Stokes field and the nonlinear polarization is nonzero.

Guha, S.↗
NASA NTRS1990

New correction procedures for the fast field program which extend its range

A fast field program (FFP) algorithm was developed based on the method of Lee et al., for the prediction of sound pressure level from low frequency, high intensity sources. In order to permit accurate predictions at distances greater than 2 km, new correction procedures have had to be included in the algorithm. Certain functions, whose Hankel transforms can be determined analytically, are subtracted from the depth dependent Green's function. The distance response is then obtained as the sum of these transforms and the Fast Fourier Transformation (FFT) of the residual k dependent function. One procedure, which permits the elimination of most complex exponentials, has allowed significant changes in the structure of the FFP algorithm, which has resulted in a substantial reduction in computation time.

West, M.↗
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 NTRS1984

SASS wind ambiguity removal by direct minimization. II - Use of smoothness and dynamical constraints

A variational analysis method (VAM) is used to remove the ambiguity of the Seasat-A Satellite Scatterometer (SASS) winds. The VAM yields the best fit to the data by minimizing an objective function S which is a measure of the lack of fit. The SASS data are described and the function S and the analysis procedure are defined. Analyses of a single ship report which are analogous to Green's functions are presented. The analysis procedure is tuned and its sensitivity is described using the QE II storm. The procedure is then applied to a case study of September 6, 1978, south of Japan.

Hoffman, R. N.↗
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 NTRS1980

The control and estimation of large space structures

A shape control or estimation problem for a large space structure can be modeled by a partial differential equation which represents changes in shape with respect to space and time, together with spatially discrete forcing functions or observations which represent the placement of actuators or sensors at discrete points along the structure. The use of Green's functions to convert boundary value problems into integral equations provides a convenient treatment of this mixture of continuous and discrete mathematics. Control and estimation algorithms are developed for the one-dimensional static beam to illustrate this technique.

Weeks, C.↗