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Geometric Acoustics for Aircraft Noise Scattering

This paper discusses aircraft noise scattering by geometric acoustics, which consists of the basic features of sound propagation and reflection in rays or ray tubes, diffraction by smooth geometry in terms of surface creeping waves, and diffraction by abrupt geometry features such as the wing trailing edges. Based on the classic theories of these features, prediction methodologies can be constructed for aircraft noise scattering. The methodologies, however, require important modifications and extensions to account for unique features in aircraft noise applications, for both current conventional aircraft and future unconventional designs. These modifications and extensions include the derivation of a general reflection coefficient that contains the effects of surface geometry curvature, surface impedance, and mean flow. Corrections to the basic formulation of diffraction, both smooth geometry and sharp edges, are formulated to account for the finite dimensions of practical applications. For smooth geometry diffraction, a second order correction is used to continuously transition from insolified to shadow zones and an approach is presented to compute the properties of the geodesic path of surface wave propagation. A model is developed to make use of the ray propagation formulation for incoherent and partially coherent propagation and scattering, which is an important phenomenon in aircraft noise. Mean flow effect is also included in the methodology for low Mach number flows. Examples of calculations based on these theoretical developments are presented to illustrate the unique features in aircraft noise applications.

Yueping Guo↗

NASA NTRS1994

Time-dependent simulation of cosmic-ray shocks, including Alfven transport

Time evolution of plane, cosmic-ray modified shocks has been simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven-wave energy transport equations. Nonlinear feedback from the cosmic rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier, Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the timescale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.

Jones, T. W.↗

NASA NTRS1993

Time dependent simulation of cosmic-ray shocks including Alfven transport

Time evolution of plane, cosmic-ray modified shocks was simulated numerically for the case with parallel magnetic fields. Computations were done in a 'three-fluid' dynamical model incorporating cosmic-ray and Alfven wave energy transport equations. Nonlinear feedback from the cosmic-rays and Alfven waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfven waves. Exploratory results confirm earlier, steady state analyses that found these Alfven transport effects to be potentially important when the upstream Alfven speed and gas sound speeds are comparable. As noted earlier Alfven transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the time scale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfven transport are strongly model dependent and that both advection of cosmic-rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfven wave intensity. No really substantive differences were found between them.

Jones, T. W.↗

NASA NTRS2005

Flight Demonstration Of Low Overpressure N-Wave Sonic Booms And Evanescent Waves

The recent flight demonstration of shaped sonic booms shows the potential for quiet overland supersonic flight, which could revolutionize air transport. To successfully design quiet supersonic aircraft, the upper limit of an acceptable noise level must be determined through quantitative recording and subjective human response measurements. Past efforts have concentrated on the use of sonic boom simulators to assess human response, but simulators often cannot reproduce a realistic sonic boom sound. Until now, molecular relaxation effects on low overpressure rise time had never been compared with flight data. Supersonic flight slower than the cutoff Mach number, which generates evanescent waves, also prevents loud sonic booms from impacting the ground. The loudness of these evanescent waves can be computed, but flight measurement validation is needed. A novel flight demonstration technique that generates low overpressure N-waves using conventional military aircraft is outlined, in addition to initial quantitative flight data. As part of this demonstration, evanescent waves also will be recorded.

Haering, Edward A., Jr.↗

NASA NTRS2010

Saturn's Equatorial Oscillation: Evidence of Descending Thermal Structure from Cassini Radio Occultations

Ground-based and Cassini CIRS thermal-infrared data have characterized the spatial and temporal characteristics of an equatorial oscillation in Saturn's middle atmosphere above the 100-mbar level. The CIRS data indicate a vertical pattern of alternating warm and cold anomalies at the equator. From the thermal wind equation this implies a concomitant reversal of zonal winds with attitude, relative to the cloud-top winds, with peak-to-peak amplitude approximately 200 meters per second. The ground-based observations do not having the altitude range or vertical resolution of the CIRS observations, but they cover several years and indicate an oscillation cycle of 1 years, roughly half of Saturn's year. Equatorial oscillations in Earth's middle atmosphere have primarily exhibited either quasi-biennial or semi-annual "periodicities," and both types have been extensively observed and modeled. They exhibit a vertical pattern of alternating warmer and cooler zonal-mean temperatures and zonal winds analogous to that described above for Saturn. Moreover, the pattern of winds and temperatures descends with time. Momentum deposition by damped vertically propagating easterly and westerly waves is thought to play a key role in forcing both types of oscillation, and it can plausibly account for the descent. Here we report the direct observation of this descent in Saturn's equatorial atmosphere from Cassini radio occultation soundings in 2005 and 2009. The retrieved temperatures are consistent with a descent of 0.6 x the pressure scale height over this time period. The descent rate is related to the magnitude of the wave forcing, radiative damping, and induced meridional circulations. A simple calculation implies that vertical wave fluxes of zonal momentum approximately 0.05 square meters per square second could account for the observed vertical descent on Saturn, which is comparable to the magnitude of the wave fluxes associated with the terrestrial quasi-biennial oscillation.

Flasar, F. M.↗

NASA NTRS1986

Zonal wave number variance spectra of stratospheric microwave brightness temperatures

Well-known theoretical predictions suggest that variances of large-scale atmospheric fluctuations, for scales somewhat shorter than those of the forcing mechanisms, should obey a power law, k exp -b, where k is the horizontal wave number. The invariance of the exponent b with season, hemisphere, and latitude is tested using satellite-measured brightness temperatures. Global grids of Tiros-N Microwave Sounding Unit channel 4 measurements, which closely approximate the 30- to 150-mbar layer mean temperature, are constructed for January, March, and August 1979. These grids are zonally Fourier-transformed, and the resulting spectra are averaged over four 18 deg-wide latitude bands. Fits of a power law to these spectra over wave numbers 10-36 and 10-26 give values of b which are independent of season, hemisphere, and latitude band, to within statistical uncertainties. The observed values of b are about 3.6, as compared to theoretical predictions of 3.

Martin, Russell L.↗

NASA NTRS1993

The structure of supersonic jet flow and its radiated sound

Large-eddy simulation of a supersonic jet is presented with emphasis on capturing the unsteady features of the flow pertinent to sound emission. A high-accuracy numerical scheme is used to solve the filtered, unsteady, compressible Navier-Stokes equations while modelling the subgrid-scale turbulence. For random inflow disturbance, the wave-like feature of the large-scale structure is demonstrated. The large-scale structure was then enhanced by imposing harmonic disturbances to the inflow. The limitation of using the full Navier-Stokes equation to calculate the far-field sound is discussed. Application of Lighthill's acoustic analogy is given with the objective of highlighting the difficulties that arise from the non-compactness of the source term.

Mankbadi, Reda R.↗

NASA NTRS1994

Radio sounding of the magnetosphere from a lunar-based VLF array

Using a lunar-based active radio transmitter and receiver system operating in the 'free space' wave modes, we can obtain much information on the structures and dynamics of remote magnetospheric plasma regions in a way similar to ionosondes. Powerful, narrow-band electromagnetic pulses can be transmitted over a wide frequency range (from 10 kHz to 1 MHz). The signals would be refracted and reflected off magnetospheric structures such as the plasmapause, plasmasheet, magnetopause, and the high and low latitude boundary layers. With a series of long dipole antennas, ranging in size from 400 m to 20 km with an output voltage ranging from 6 kV to less than 0.2 kV, a target plasma region at up to 100 R(sub E) can be explored. We illustrate this remote sensing technique by using the plasmasphere as a remote target, and modeling the propagations of the sounder transmitted and received pulses by ray tracing calculations.

Green, James L.↗

NASA NTRS1975

Sound scattering from atmospheric turbulence

Sound propagation through a turbulent flow field with nonvanishing mean-flow velocity has been studied. The effects of compressibility on sound scattering are discussed. Using an analysis describing moving sources in a fixed frame, particular results are obtained for the far-field scattered sound intensity due to uniformly moving scattering turbulence. A formula is obtained showing the factor by which the scattered sound intensity is amplified due to the motion of the turbulence. In addition, this analysis was extended to include wave propagating through mean flow with constant gradient.

Huang, M. N.↗

NASA NTRS1980

Rigorous solutions for sound radiation from circular ducts with hyperbolic horns or infinite plane baffle

A rigorous treatment is presented of sound radiation from circular ducts with either a hyperbolic horn or an infinite plane baffle. In the analysis hyperboloidal wave functions are used, which are defined here, for the first time, as a class of eigensolutions of the wave equation for oblate spheroidal co-ordinates. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for various incident wave modes, spinning modes as well as axisymmetric modes. The solutions are valid for the whole frequency range including frequencies above and below the cut-off frequencies of the duct modes involved.

Cho, Y. C.↗

NASA NTRS1981

Experiments on the nonlinear characteristics of noise propagation from low and moderate Reynolds number supersonic jets

A series of experiments were conducted on high-speed model jets to identify and quantify the distortion of radiated noise by nonlinear propagation effects. The jets were operated in a low to moderate Reynolds number range, and the radiated noise was either broadband or discrete in frequency. Three condenser microphones were used to measure the waveforms propagated by the axisymmetric, cold model jets of Mach numbers 2.1 and 2.5. Relatively low Reynolds numbers were obtained by exhausting the jets into a low pressure anechoic test chamber. Nonlinear propagation distortion effects, such as wave steepening, harmonic generation and wave merging, were easily quantified. At a moderate Reynolds number, low frequency production and wave amalgamation, measured by a decrease in the zero crossings per unit time, were quantified in the propagation of sound away from the jet.

Gallagher, J. A.↗

NASA NTRS1987

Time-domain robotic vision application

The quest for the highest resolution microwaves imaging and the principle of time-domain imaging is the primary motivation for recent developments in time-domain techniques. With the present technology fast time varying signals can now be measured and recorded both in magnitude and in phase. It has also enhanced the ability to extract relevant details concerning the scattering object. In the past, the inference of object geometry or shape from scattered signals has received substantial attention in radar technology. Various inverse scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequenty swept holography, and the synthetic radar imaging, all of which have two things in common: the physical optic far-field approximation and the utilization of the channels as an extra physical dimension, were also advanced significantly. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The use of time-domain imaging for space robotic vision applications was proposed. A multisensor approach to vision was shown to have several advantages over the video-only approach.

Tolliver, C. L.↗

NASA NTRS1988

Computer simulation of the Farley-Buneman instability and anomalous electron heating in the auroral ionosphere

The nonlinear saturation of the Farley-Buneman instability in a collisional plasma is studied by a 2 1/2 dimensional electrostatic particle simulation which includes inelastic and elastic collisions of electrons and elastic collision of ions with neutrals. In the simulation, a uniform convection electric field is applied externally so that the relative velocity between the electrons and ions is greater than the ion sound speed and destabilizes the instability. A nonlinear frequency shift from higher to lower frequencies and diffusion of the wave spectrum in two dimensional wave number space are found. It is found that the dominant mechanism for electron heating is due to an enhanced effective electron collision frequency and hence enhanced resistive heating as suggested by Primdahl (1986) and not due to the heating of electrons by the electric field of the waves parallel to the magnetic field. For the ionospheric conditions discussed by Schlegel and St.-Maurice (1981)an anomalous heating rate of about 4 x 10 to the 7th W/cu cm is found.

Machida, S.↗

NASA NTRS1989

Time-domain imaging

The quest for the highest resolution microwave imaging and principle of time-domain imaging has been the primary motivation for recent developments in time-domain techniques. With the present technology, fast time varying signals can now be measured and recorded both in magnitude and in-phase. It has also enhanced our ability to extract relevant details concerning the scattering object. In the past, the interface of object geometry or shape for scattered signals has received substantial attention in radar technology. Various scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequency swept holography, and the synthetic radar imaging, have two things in common: (1) the physical optic far-field approximation, and (2) the utilization of channels as an extra physical dimension, were also advanced. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The development of time-domain techniques are studied through the theoretical aspects as well as experimental verification. The use of time-domain imaging for space robotic vision applications has been suggested.

Tolliver, C. L.↗

NASA NTRS1991

Prediction of the acoustic field in a three-dimensional rectangular duct using the boundary element method

A boundary element formulation, along with detailed solution procedure for determining the acoustic field inside a three-dimensional, rectangular duct is presented in this paper. The results of classical and boundary element solutions are compared for a typical rectangular duct by restricting the input frequency in such a way that only plane wave propagation is possible. The effect of changing the type and number of discrete boundary elements on the computed sound pressure levels inside the duct is also presented.

Pates, Carl S., III↗

NASA NTRS2015

Experimental and Computational Sonic Boom Assessment of Lockheed-Martin N+2 Low Boom Models

Flight at speeds greater than the speed of sound is not permitted over land, primarily because of the noise and structural damage caused by sonic boom pressure waves of supersonic aircraft. Mitigation of sonic boom is a key focus area of the High Speed Project under NASA's Fundamental Aeronautics Program. The project is focusing on technologies to enable future civilian aircraft to fly efficiently with reduced sonic boom, engine and aircraft noise, and emissions. A major objective of the project is to improve both computational and experimental capabilities for design of low-boom, high-efficiency aircraft. NASA and industry partners are developing improved wind tunnel testing techniques and new pressure instrumentation to measure the weak sonic boom pressure signatures of modern vehicle concepts. In parallel, computational methods are being developed to provide rapid design and analysis of supersonic aircraft with improved meshing techniques that provide efficient, robust, and accurate on- and off-body pressures at several body lengths from vehicles with very low sonic boom overpressures. The maturity of these critical parallel efforts is necessary before low-boom flight can be demonstrated and commercial supersonic flight can be realized.

Cliff, Susan E.↗

NASA NTRS2022

Comparable Bulk Radar Attenuation Characteristics Across Both Martian Polar Layered Deposits

The dust-laden and predominantly water ice south polar layered deposits (SPLD) exhibit unique radar behavior at Shallow Radar (SHARAD) frequencies that is not seen in the NPLD. A vertically extensive scattering phenomenon leads to diffuse echoes that obscure radar stratigraphy within the SPLD, referred to as “fog.” Here, we use 2-D and 3-D SHARAD data to measure the areal extent in which the SPLD basal interface can be identified. We also measure reflected power of SPLD basal reflectors and compare those values to ice thickness, regional geomorphology, and the presence of radar echo scattering, to constrain any influence these factors may have on the propagation of radio waves and detectability of the base. Approximately 33% of the area in which the basal interface is observed in Mars Advanced Radar for Subsurface and Ionosphere Sounding data is also detected in SHARAD data. As expected, basal power shows a negative correlation with ice thickness, but the effects of radar fog are less clear. Areas of “column” radar fog patterns exhibit higher average basal power values than regions without radar fog, and areas with only near-surface radar fog have the lowest average basal power values. Our study results suggest that these diffuse echoes may not be associated with radio wave attenuation. Average loss tangent for the SPLD (0.0019 ± 0.0012) indicates no distinguishable difference from previously reported NPLD values in terms of bulk loss properties. We speculate that the SPLD's infrequent reflections compared to the NPLD may be due to the former's dust being less densely packed together to facilitate radar detection.

N Abu Hashmeh↗

NASA NTRS1980

Prediction of sound radiated from different practical jet engine inlets

Existing computer codes for calculating the far field radiation patterns surrounding various practical jet engine inlet configurations under different excitation conditions were upgraded. The computer codes were refined and expanded so that they are now more efficient computationally by a factor of about three and they are now capable of producing accurate results up to nondimensional wave numbers of twenty. Computer programs were also developed to help generate accurate geometrical representations of the inlets to be investigated. This data is required as input for the computer programs which calculate the sound fields. This new geometry generating computer program considerably reduces the time required to generate the input data which was one of the most time consuming steps in the process. The results of sample runs using the NASA-Lewis QCSEE inlet are presented and comparison of run times and accuracy are made between the old and upgraded computer codes. The overall accuracy of the computations is determined by comparison of the results of the computations with simple source solutions.

Zinn, B. T.↗