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NASA NTRS2010

Proton Lateral Broadening Distribution Comparisons Between GRNTRN, MCNPX, and Laboratory Beam Measurements

Recent developments in NASA s deterministic High charge (Z) and Energy TRaNsport (HZETRN) code have included lateral broadening of primary ion beams due to small-angle multiple Coulomb scattering, and coupling of the ion-nuclear scattering interactions with energy loss and straggling. This new version of HZETRN is based on Green function methods, called GRNTRN, and is suitable for modeling transport with both space environment and laboratory boundary conditions. Multiple scattering processes are a necessary extension to GRNTRN in order to accurately model ion beam experiments, to simulate the physical and biological-effective radiation dose, and to develop new methods and strategies for light ion radiation therapy. In this paper we compare GRNTRN simulations of proton lateral broadening distributions with beam measurements taken at Loma Linda University Proton Therapy Facility. The simulated and measured lateral broadening distributions are compared for a 250 MeV proton beam on aluminum, polyethylene, polystyrene, bone substitute, iron, and lead target materials. The GRNTRN results are also compared to simulations from the Monte Carlo MCNPX code for the same projectile-target combinations described above.

Mertens, Christopher J.↗

NASA NTRS2015

Analytic Thermoelectric Couple Modeling: Variable Material Properties and Transient Operation

To gain a deeper understanding of the operation of a thermoelectric couple a set of analytic solutions have been derived for a variable material property couple and a transient couple. Using an analytic approach, as opposed to commonly used numerical techniques, results in a set of useful design guidelines. These guidelines can serve as useful starting conditions for further numerical studies, or can serve as design rules for lab built couples. The analytic modeling considers two cases and accounts for 1) material properties which vary with temperature and 2) transient operation of a couple. The variable material property case was handled by means of an asymptotic expansion, which allows for insight into the influence of temperature dependence on different material properties. The variable property work demonstrated the important fact that materials with identical average Figure of Merits can lead to different conversion efficiencies due to temperature dependence of the properties. The transient couple was investigated through a Greens function approach; several transient boundary conditions were investigated. The transient work introduces several new design considerations which are not captured by the classic steady state analysis. The work helps to assist in designing couples for optimal performance, and also helps assist in material selection.

Seebeck Effect↗

NASA NTRS2015

Jet Surface Interaction Scrubbing Noise from High Aspect-Ratio Rectangular Jets

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity of the airframe. Distributed propulsion system with exhaust configurations that resemble a high aspect ratio rectangular jet are among geometries of interest. Nearby solid surfaces could provide noise shielding for the purpose of reduced community noise. Interaction of high-speed jet exhaust with structure could also generate new sources of sound as a result of flow scrubbing past the structure, and or scattered noise from sharp edges. The present study provides a theoretical framework to predict the scrubbing noise component from a high aspect ratio rectangular exhaust in proximity of a solid surface. The analysis uses the Greens function (GF) to the variable density Pridmore-Brown equation in a transversely sheared mean flow. Sources of sound are defined as the auto-covariance function of second-rank velocity fluctuations in the jet plume, and are modeled using a RANS-based acoustic analogy approach. Acoustic predictions are presented in an 8:1 aspect ratio rectangular exhaust at three subsonic Mach numbers. The effect of nearby surface on the scrubbing noise component is shown on both reflected and shielded sides of the plate.

Propulsion Noise↗

NASA NTRS1989

A closed form solution to HZE propagation

An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The Green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.

Wilson, John W.↗

NASA NTRS1990

A closed-form solution to HZE propagation

An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.

Wilson, John W.↗

NASA NTRS2005

Verification and Validation: High Charge and Energy (HZE) Transport Codes and Future Development

In the present paper, we give the formalism for further developing a fully three-dimensional HZETRN code using marching procedures but also development of a new Green's function code is discussed. The final Green's function code is capable of not only validation in the space environment but also in ground based laboratories with directed beams of ions of specific energy and characterized with detailed diagnostic particle spectrometer devices. Special emphasis is given to verification of the computational procedures and validation of the resultant computational model using laboratory and spaceflight measurements. Due to historical requirements, two parallel development paths for computational model implementation using marching procedures and Green s function techniques are followed. A new version of the HZETRN code capable of simulating HZE ions with either laboratory or space boundary conditions is under development. Validation of computational models at this time is particularly important for President Bush s Initiative to develop infrastructure for human exploration with first target demonstration of the Crew Exploration Vehicle (CEV) in low Earth orbit in 2008.

Wilson, John W.↗

NASA NTRS1995

Efficient modeling of interconnects and capacitive discontinuities in high-speed digital circuits

Modeling of interconnects and associated discontinuities with the recent advances high-speed digital circuits has gained a considerable interest over the last decade although the theoretical bases for analyzing these structures were well-established as early as the 1960s. Ongoing research at the present time is focused on devising methods which can be applied to more general geometries than the ones considered in earlier days and, at the same time, improving the computational efficiency and accuracy of these methods. In this thesis, numerically efficient methods to compute the transmission line parameters of a multiconductor system and the equivalent capacitances of various strip discontinuities are presented based on the quasi-static approximation. The presented techniques are applicable to conductors embedded in an arbitrary number of dielectric layers with two possible locations of ground planes at the top and bottom of the dielectric layers. The cross-sections of conductors can be arbitrary as long as they can be described with polygons. An integral equation approach in conjunction with the collocation method is used in the presented methods. A closed-form Green's function is derived based on weighted real images thus avoiding nested infinite summations in the exact Green's function; therefore, this closed-form Green's function is numerically more efficient than the exact Green's function. All elements associated with the moment matrix are computed using the closed-form formulas. Various numerical examples are considered to verify the presented methods, and a comparison of the computed results with other published results showed good agreement.

Oh, K. S.↗

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

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↗

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↗

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.↗

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↗