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NASA NTRS1991

Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer

The optimization of trajectories for coplanar, aeroassisted orbital transfer (AOT) from a high earth orbit (HEO) to a low earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous earth orbit (GEO). During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called a grazing trajectory. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the contrifugal force due to the earth's curvature, the weight, and the Coriolis force due to the earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. The real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

Miele, A.↗

NASA NTRS2007

Optimization of Acoustic Pressure Measurements for Impedance Eduction

As noise constraints become increasingly stringent, there is continued emphasis on the development of improved acoustic liner concepts to reduce the amount of fan noise radiated to communities surrounding airports. As a result, multiple analytical prediction tools and experimental rigs have been developed by industry and academia to support liner evaluation. NASA Langley has also placed considerable effort in this area over the last three decades. More recently, a finite element code (Q3D) based on a quasi-3D implementation of the convected Helmholtz equation has been combined with measured data acquired in the Langley Grazing Incidence Tube (GIT) to reduce liner impedance in the presence of grazing flow. A new Curved Duct Test Rig (CDTR) has also been developed to allow evaluation of liners in the presence of grazing flow and controlled, higher-order modes, with straight and curved waveguides. Upgraded versions of each of these two test rigs are expected to begin operation by early 2008. The Grazing Flow Impedance Tube (GFIT) will replace the GIT, and additional capabilities will be incorporated into the CDTR. The current investigation uses the Q3D finite element code to evaluate some of the key capabilities of these two test rigs. First, the Q3D code is used to evaluate the microphone distribution designed for the GFIT. Liners ranging in length from 51 to 610 mm are investigated to determine whether acceptable impedance eduction can be achieved with microphones placed on the wall opposite the liner. This analysis indicates the best results are achieved for liner lengths of at least 203 mm. Next, the effects of moving this GFIT microphone array to the wall adjacent to the liner are evaluated, and acceptable results are achieved if the microphones are placed off the centerline. Finally, the code is used to investigate potential microphone placements in the CDTR rigid wall adjacent to the wall containing an acoustic liner, to determine if sufficient fidelity can be achieved with 32 microphones available for this purpose. Initial results indicate 32 microphones can provide acceptable measurements to support impedance eduction with this test rig.

Jones, M. G.↗

NASA NTRS2010

Wavefront Sensing of X-Ray Telescopes

Phase Retrieval analysis of off-axis or defocused focal-plane data from telescope optics has been proven effective in understanding misalignments and optical aberrations in normal incidence telescopes. The approach is used, e.g., in commissioning of the James Webb Space Telescope (JWST) segmented primary mirror. There is a similar need for evaluating low-order figure errors of grazing incidence mirrors and nested telescope assemblies. When implemented in these systems, phase retrieval does not depend on normal incidence access to each mirror (shell) surface and, therefore, provides an effective means for evaluating nested x-ray telescopes during integration and test. We have applied a well-known phase retrieval algorithm to grazing incidence telescopes. The algorithm uses the Levenberg-Marquardt optimization procedure to perform a non-linear least-squares fit of the telescope Point Spread Function (PSF). The algorithm can also retrieve low order figure errors at visible wavelengths where optical diffraction is the dominant defect in the PSF. In this paper we will present the analytical approach and its implementation for grazing incidence mirrors of the International X-Ray Observatory (IXO). We analyze the effects of low order axial surface errors individually, and in combination on the system PSF at 633 nanometers. We demonstrate via modeling that the wavefront sensing algorithm can recover axial errors (of the grazing incidence mirrors) to a small fraction of the known axial figure errors using simulated PSFs as input data to the algorithm.

Saha, Timo↗

NASA NTRS1983

High efficiency spectrographs for the EUV and soft X-rays

The use of grazing incidence optics and reflection grating designs is shown to be a method that improves the performance of spectrographs at wavelengths shorter than 1200 A. Emphasis is laid on spectroscopic designs for X ray and EUV astronomy, with sample designs for an objective reflection grating spectrograph (ORGS) and an echelle spectrograph for wavelengths longer than 100 A. Conical diffraction allows operations at grazing incidence in the echelle spectrograph. In ORGS, the extreme distance of X ray objects aids in collimating the source radiation, which encounters conical diffraction within the instrument, proceeds parallel to the optical axis, and arrives at the detector. A series of gratings is used to achieve the effect. A grazing echelle is employed for EUV observations, and offers a resolution of 20,000 over a 300 A bandpass.

Cash, W.↗

NASA NTRS1984

The study of the physics of cometary nuclei

The observations of comet P/Holmes 1892III, exhibiting two 8 to 10 magnitude bursts, were carefully analyzed. The phenomena are consistent with the grazing encounter of a small satellite with the nucleus. The grazing encounter produced, besides the first great burst, an active area on the nucleus, which was rotating retrograde with a period of 16.3 hr and inclination nearly 180 deg. After the final encounter, the spin period was essentially unchanged, but two areas became active, separated some 164 deg in longitude on the nucleus. After the first burst the total magnitude fell less than two magnitudes, while the nuclear region remained diffuse or complex, rarely if ever showing a stellar appearance. The fading was much more rapid after the second burst (barely naked eye at maximum) while the nucleus frequently stellar after the first day. It seems reasonable to conclude that the grazing encounter distributed a volume of large chunks in the neighborhood of the nucleus, maintaining activity for weeks.

Whipple, F. L.↗

NASA NTRS1986

An extreme ultraviolet telescope with no soft X-ray response

While EUV grazing incidence telescopes of conventional design exhibit a substantial X-ray response as well as an extreme UV response, and existing bandpass filters for the transmission of radiation longward of 400 A also transmit soft X-rays, the grazing incidence telescope presented suppresses this soft X-ray throughput through the incorporation of a Wolter Schwarzschild Type II mirror with large graze angles. The desirable features of an EUV photometric survey telescope are retained. An instrument of this design will be flown on the EUE mission, in order to make a survey of the sky at wavelengths longer than 400 A.

Finley, David S.↗

NASA NTRS1987

X-ray optics - A technique for high resolution imaging

Both scattering and figure errors in grazing incidence optics are larger in the plane of incidence than out-of-plane by a factor equal to 1/sin theta, where theta is the graze angle. When the full annular aperture of a grazing incidence telescope is stopped down, the point spread function becomes highly elliptical with a width as much as sin theta times narrower than the full image. In practice, this means that improvements in resolution of up to 100 times can be achieved, and effective resolution can approach the diffraction limit. Laboratory data demonstrating the effect are presented.

Cash, Webster↗

NASA NTRS1989

X-ray/EUV optics for astronomy and microscopy; Proceedings of the Meeting, San Diego, CA, Aug. 7-11, 1989

Topics included in these proceedings are on X-ray/EUV zone plates, filters, and windows; X-ray/EUV microscopes, telescopes, and monochromators; the design, characterization, and test of multilayer optics; the fabrication of X-ray/EUV multilayer optics; and the design, characterization, and test of grazing incidence X-ray optics. Other topics are on the fabrication of grazing incidence X-ray optics, X-ray/EUV space observatories and missions, the test and calibration of X-ray/EUV instruments, X-ray polarimetry, and X-ray/EUV spectroscopy and instruments. Papers are presented on 8-keV X-ray zone plates, a cylindrical X-ray multilayer monochromator, multilayer mirrors for 182 A, advanced flow polishing of exotic optical materials, and optical analysis of grazing incidence ring resonators for free-electron lasers. Attention is also given to X-ray mirrors for the European Synchrotron Radiation Facility, the XUV wide-field camera for Rosat, an optical test and alignment method for the XMM mirror module, Bragg crystal polarimeters, and a liftoff process for multilayer phase gratings.

Hoover, Richard B.↗

NASA NTRS1993

Reflectance calibrations of AXAF mirror samples at absorption edges using synchrotron radiation

We are developing a system to calibrate reflectances of witness coupons to the AXAF flight mirrors at the National Synchrotron Light Source over the 0.05-12 keV energy range. These witness coupons will be coated in the same process as the AXAF mirror elements. One of the key issues is the accurate determination of mirror efficiencies across the absorption edges of the mirror coating elements. We present a series of reflectance measurements with 2 eV resolution of a nickel-coated flat mirror in the region of the Ni L-II (870 eV) and L-III (853 eV) absorption edges. Scans of reflectance versus grazing angle at fixed energies in this region show distinct interference fringes at grazing angles larger than the critical angle which are extinguished as the photon energy is increased beyond the low point of the L-III edge, indicating total absorption of the evanescent wave within the Ni film. At 51 arc minutes grazing angle, measured reflectance decreases smoothly by 35 percent and then recovers in an 8 eV band at the L-III edge. We have also measured reflectances in the M absorption edge region for gold, platinum, and iridium coated mirrors. We derive optical parameters n and k specific to the film for comparison to the existing data tables.

Graessle, D. E.↗

NASA NTRS2000

Optical Performance Modeling of FUSE Telescope Mirror

We describe the Metrology Data Processor (METDAT), the Optical Surface Analysis Code (OSAC), and their application to the image evaluation of the Far Ultraviolet Spectroscopic Explorer (FUSE) mirrors. The FUSE instrument - designed and developed by the Johns Hopkins University and launched in June 1999 is an astrophysics satellite which provides high resolution spectra (lambda/Delta(lambda) = 20,000 - 25,000) in the wavelength region from 90.5 to 118.7 nm The FUSE instrument is comprised of four co-aligned, normal incidence, off-axis parabolic mirrors, four Rowland circle spectrograph channels with holographic gratings, and delay line microchannel plate detectors. The OSAC code provides a comprehensive analysis of optical system performance, including the effects of optical surface misalignments, low spatial frequency deformations described by discrete polynomial terms, mid- and high-spatial frequency deformations (surface roughness), and diffraction due to the finite size of the aperture. Both normal incidence (traditionally infrared, visible, and near ultraviolet mirror systems) and grazing incidence (x-ray mirror systems) systems can be analyzed. The code also properly accounts for reflectance losses on the mirror surfaces. Low frequency surface errors are described in OSAC by using Zernike polynomials for normal incidence mirrors and Legendre-Fourier polynomials for grazing incidence mirrors. The scatter analysis of the mirror is based on scalar scatter theory. The program accepts simple autocovariance (ACV) function models or power spectral density (PSD) models derived from mirror surface metrology data as input to the scatter calculation. The end product of the program is a user-defined pixel array containing the system Point Spread Function (PSF). The METDAT routine is used in conjunction with the OSAC program. This code reads in laboratory metrology data in a normalized format. The code then fits the data using Zernike polynomials for normal incidence systems or Legendre-Fourier polynomials for grazing incidence systems. It removes low order terms from the metrology data, calculates statistical ACV or PSD functions, and fits these data to OSAC models for the scatter analysis. In this paper we briefly describe the laboratory image testing of FUSE spare mirror performed in the near and vacuum ultraviolet at John Hopkins University and OSAC modeling of the test setup performed at NASA/GSFC. The test setup is a double-pass configuration consisting of a Hg discharge source, the FUSE off-axis parabolic mirror under test, an autocollimating flat mirror, and a tomographic imaging detector. Two additional, small fold flats are used in the optical train to accommodate the light source and the detector. The modeling is based on Zernike fitting and PSD analysis of surface metrology data measured by both the mirror vendor (Tinsley) and JHU. The results of our models agree well with the laboratory imaging data, thus validating our theoretical model. Finally, we predict the imaging performance of FUSE mirrors in their flight configuration at far-ultraviolet wavelengths.

Saha, Timo T.↗

NASA NTRS2000

Sound Absorption of a 2DOF Resonant Liner with Negative Bias Flow

This report describes an experimental study conducted to determine the effect of negative bias flow on the sound absorption of a two degree-of-freedom liner. The backwall for the liner was designed to act as a double-Helmholtz resonator so as to act as a hard wall at all frequencies except at its resonant frequencies. All normal incident impedance data presented herein was acquired in an impedance tube. The effect of bias flow is investigated for a buried septum porosity of 2% and 19.5% for bias flow orifice mach numbers up to 03 11. As a porous backwall is needed for the flow to pass through, the effect of bias flow on this backwall all had to be evaluated first. The bias flow appears to modify the resistance and reactance of the backwall alone at lower frequencies up to about 2 kHz, with marginal effects at higher frequencies. Absorption coefficients close to unity are achieved for a frequency range of 500-4000 Hz for the overall liner for a septum porosity of 2% and orifice mach number of 0.128. Insertion loss tests performed in a flow duct facility for grazing flow Mach numbers up to 0.2 and septum mach numbers up to 0.15 showed that negative bias flow can increase insertion loss by as much as 10 dB at frequencies in the range of 500 - 1400 Hz compared to no grazing flow. The effectiveness of the negative bias flow is diminished as the grazing flow velocity is increased.

Ahuja, K. K.↗

NASA NTRS1998

A Numerical Study of the Effect of Periodic Nutrient Supply on Pathways of Carbon in a Coastal Upwelling Regime

A size-based ecosystem model was modified to include periodic upwelling events and used to evaluate the effect of episodic nutrient supply on the standing stock, carbon uptake, and carbon flow into mesozooplankton grazing and sinking flux in a coastal upwelling regime. Two ecosystem configurations were compared: a single food chain made up of net phytoplankton and mesozooplankton (one autotroph and one heterotroph, A1H1), and three interconnected food chains plus bacteria (three autotrophs and four heterotrophs, A3H4). The carbon pathways in the A1H1 simulations were under stronger physical control than those of the A3H4 runs, where the small size classes are not affected by frequent upwelling events. In the more complex food web simulations, the microbial pathway determines the total carbon uptake and grazing rates, and regenerated nitrogen accounts for more than half of the total primary production for periods of 20 days or longer between events. By contrast, new production, export of carbon through sinking and mesozooplankton grazing are more important in the A1H1 simulations. In the A3H4 simulations, the turnover time scale of the autotroph biomass increases as the period between upwelling events increases, because of the larger contribution of slow-growing net phytoplankton. The upwelling period was characterized for three upwelling sites from the alongshore wind speed measured by the NASA Scatterometer (NSCAT) and the corresponding model output compared with literature data. This validation exercise for three upwelling sites and a downstream embayment suggests that standing stock, carbon uptake and size fractionation were best supported by the A3H4 simulations, while the simulated sinking fluxes are not distinguishable in the two configurations.

Carr, Mary-Elena↗

NASA NTRS2000

Sound Absorption of a 2DOF Resonant Liner with Negative Bias Flow

This report describes an experimental study conducted to determine the effect of negative bias flow on the sound absorption of a two degree-of-freedom liner. The backwall for the liner was designed to act as a double-Helmholtz resonator so as to act as a hard wall at all frequencies except at its resonant frequencies. The effect of bias flow is investigated for a buried septum porosity of 2% and 19.5% for bias flow orifice Mach numbers up to 0.311. The bias flow appears to modify the resistance and reactance of the backwall alone at lower frequencies up to about 2 kHz, with marginal effects at higher frequencies. Absorption coefficients close to unity are achieved for a frequency range of 500 - 4000 Hz for the overall liner for a septum porosity of 2% and orifice Mach number of 0.128. Insertion loss tests performed in a flow duct facility for grazing flow Mach numbers up to 0.2 and septum Mach numbers up to 0.15 showed that negative bias flow can increase insertion loss by as much as 10 dB at frequencies in the range of 500 D 1400 Hz compared to no grazing flow. The effectiveness of the negative bias flow is diminished as the grazing flow velocity is increased.

Ahuja, K. K.↗

NASA NTRS2004

Design and Evaluation of Modifications to the NASA Langley Flow Impedance Tube

The need to minimize fan noise radiation from commercial aircraft engine nacelles continues to provide an impetus for developing new acoustic liner concepts. If the full value of such concepts is to be attained, an understanding of grazing flow effects is crucial. Because of this need for improved understanding of grazing flow effects, the NASA Langley Research Center Liner Physics Group has invested a large effort over the past decade into the development of a 2-D finite element method that characterizes wave propagation through a lined duct. The original test section in the Langley Grazing IncidenceTube was used to acquire data needed for implementation of this finite element method. This test section employed a stepper motor-driven axial-traversing bar, embedded in the wall opposite the test liner, to position a flush-mounted microphone at pre-selected locations. Complex acoustic pressure data acquired with this traversing microphone were used to educe the acoustic impedance of test liners using this 2-D finite element method and a local optimization technique. Results acquired in this facility have been extensively reported, and were compared with corresponding results from various U.S. aeroacoustics laboratories in the late 1990 s. Impedance data comparisons acquired from this multi-laboratory study suggested that it would be valuable to incorporate more realistic 3-D aeroacoustic effects into the impedance eduction methodology. This paper provides a description of modifications that have been implemented to facilitate studies of 3-D effects. The two key features of the modified test section are (1) the replacement of the traversing bar and its flush-mounted microphone with an array of 95 fixed-location microphones that are flush-mounted in all four walls of the duct, and (2) the inclusion of a suction device to modify the boundary layer upstream of the lined portion of the duct. The initial results achieved with the modified test section are provided in this report, and a comparison of these results with those achieved using the original test section is used to demonstrate that the data acquisition and analysis with the new test section can be confidently used for impedance eduction.

Jones, Michael G.↗

NASA NTRS2005

Status of Duct Liner Technology for Application to Aircraft Engine Nacelles

Grazing flows and high acoustic intensities impose unusual design requirements on acoustic liner treatments used in aircraft engine nacelles. Increased sound absorption efficiency (requiring increased accuracy of liner impedance specification) is particularly critical in the face of ever decreasing nacelle wall area available for liner treatments in modern, high-bypass ratio engines. This paper reviews the strategy developed at Langley Research Center for achieving a robust measurement technology that is crucial for validating impedance models for aircraft liners. Specifically, the paper describes the current status of computational and data acquisition technologies for reducing impedance in a flow duct. Comparisons of reduced impedances for a "validation liner" using 1980's and 2000's measurement technology are consistent, but show significant deviations (up to 0.5 c exclusive of liner anti-resonance region) from a first principles impedance prediction model as grazing flow centerline Mach numbers increase up to 0.5. The deviations, in part, are believed related to uncertainty in the choice of grazing flow parameters (e.g. cross-section averaged, core-flow averaged, or centerline Mach number?). Also, there may be an issue with incorporating the impedance discontinuities corresponding to the hard wall to liner interface (i.e. leading and trailing edge of test liner) within the discretized finite element model.

Parrott, Tony L.↗

NASA NTRS2011

On the Use of Experimental Methods to Improve Confidence in Educed Impedance

Results from impedance eduction methods developed by NASA Langley Research Center are used throughout the acoustic liner community. In spite of recent enhancements, occasional anomalies persist with these methods, generally at frequencies where the liner produces minimal attenuation. This investigation demonstrates an experimental approach to educe impedance with increased confidence over a desired frequency range, by combining results from successive tests with different cavity depths. A series of tests is conducted with three wire-mesh facesheets, for which the results should be weakly dependent on source sound pressure level and mean grazing flow speed. First, a raylometer is used to measure the DC flow resistance of each facesheet. These facesheets are then mounted onto a frame and a normal incidence tube is used to determine their respective acoustic impedance spectra. A comparison of the acoustic resistance component with the DC flow resistance for each facesheet is used to validate the measurement process. Next, each facesheet is successively mounted onto three frames with different cavity depths, and a grazing flow impedance tube is used to educe their respective acoustic impedance spectra with and without mean flow. The no-flow results are compared with those measured in the normal incidence tube to validate the impedance eduction method. Since the anti-resonance frequency varies with cavity depth, each sample provides robust results over a different frequency range. Hence, a combination of results can be used to determine the facesheet acoustic resistance. When combined with the acoustic reactance, observed to be weakly dependent on the source sound pressure level and grazing flow Mach number, the acoustic impedance can be educed with increased confidence. Representative results of these tests are discussed, and the complete database is available in electronic format upon request.

Jones, Michael G.↗

NASA NTRS2011

Implementation and Validation of an Impedance Eduction Technique

Implementation of a pressure gradient method of impedance eduction in two NASA Langley flow ducts is described. The Grazing Flow Impedance Tube only supports plane-wave sources, while the Curved Duct Test Rig supports sources that contain higher-order modes. Multiple exercises are used to validate this new impedance eduction method. First, synthesized data for a hard wall insert and a conventional liner mounted in the Grazing Flow Impedance Tube are used as input to the two impedance eduction methods, the pressure gradient method and a previously validated wall pressure method. Comparisons between the two results are excellent. Next, data measured in the Grazing Flow Impedance Tube are used as input to both methods. Results from the two methods compare quite favorably for sufficiently low Mach numbers but this comparison degrades at Mach 0.5, especially when the hard wall insert is used. Finally, data measured with a hard wall insert mounted in the Curved Duct Test Rig are used as input to the pressure gradient method. Significant deviation from the known solution is observed, which is believed to be largely due to 3-D effects in this flow duct. Potential solutions to this issue are currently being explored.

Watson, Willie R.↗

NASA NTRS2010

Wolter Optics for Neutron Focusing

Focusing optics based on Wolter optical geometries developed for x-ray grazing incidence beams can be designed for neutron beams. Wolter optics are formed by grazing incidence reflections from two concentric conic sections (for example, a paraboloid and a hyperboloid). This has transformed observational X-ray astronomy by increasing the sensitivity by many orders of magnitude for research in astrophysics and cosmology. To increase the collection area, many reflecting mirrors of different diameters are nested with a common focal plane. These mirrors are fabricated using nickel-electroformed replication techniques. We apply these ideas to neutron focusing using nickel mirrors. We show an initial test of a conical mirror using a beam of cold neutrons. key words: electroformed nickel replication, focusing optics, grazing angle incidence, mirror reflection, neutron focusing, Wolter optics

Mildner, D. F. R.↗