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NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗

NASA NTRS1993

Theory for noise of propellers in angular inflow with parametric studies and experimental verification

This report presents the derivation of a frequency domain theory and working equations for radiation of propeller harmonic noise in the presence of angular inflow. In applying the acoustic analogy, integration over the tangential coordinate of the source region is performed numerically, permitting the equations to be solved without approximation for any degree of angular inflow. Inflow angle is specified in terms of yaw, pitch, and roll angles of the aircraft. Since these can be arbitrarily large, the analysis applies with equal accuracy to propellers and helicopter rotors. For thickness and loading, the derivation is given in complete detail with working equations for near and far field. However, the quadrupole derivation has been carried only far enough to show feasibility of the numerical approach. Explicit formulas are presented for computation of source elements, evaluation of Green's functions, and location of observer points in various visual and retarded coordinate systems. The resulting computer program, called WOBBLE has been written in FORTRAN and follows the notation of this report very closely. The new theory is explored to establish the effects of varying inflow angle on axial and circumferential directivity. Also, parametric studies were performed to evaluate various phenomena outside the capabilities of earlier theories, such as an unsteady thickness effect. Validity of the theory was established by comparison with test data from conventional propellers and Prop Fans in flight and in wind tunnels under a variety of operating conditions and inflow angles.

Propeller acoustics↗

NASA NTRS2000

Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model

The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotation mode response is shown to be more sensitive to input torque than translational mode response.

Parker, Robert G.↗

NASA NTRS2002

Submillimeter Laboratory Investigations: Spectroscopy and Collisions

Currently, millimeter-wave and submillimeter-wave spectroscopy is conducted in our laboratory on several different types of spectrometers. Our standard spectrometer utilizes the output of a phase-locked klystron operating in the 40-60 GHz region, which is sent into a crossed-waveguide harmonic generator, or "multiplier". The high frequency millimeter-and submillimeter-wave radiation is transmitted via quasi-optical techniques through an absorption cell and then onto a detector, which is either an InSb hot electron bolometer cooled to 1.4 K or a Si bolometer cooled to 0.3 K. The detector response is sent to a computer for measurement and analysis. The frequency range produced and detected in this manner goes from 80 GHz to upwards of 1 THz. Spectra are normally taken with source modulation, with line frequencies typically measured to an accuracy of 50-100 kHz. Higher accuracy is available when needed. Recently, we developed a new, broad-band spectrometer in our laboratory based on a free-running backward wave oscillator (BWO) of Russian manufacture as the primary source of radiation. The so-called FASSST (fast-scan submillimeter spectroscopic technique) system uses fast-scan and optical calibration methods rather than the traditional locking techniques. The output power from the BWO is split such that 90% goes into the absorption cell while 10% is coupled to a 40-meter Fabry-Perot cavity, which yields fringe? for frequency measurement. Results from this spectrometer on the spectrum of nitric acid (HNO3) show that 100 GHz of spectral data can be obtained in 5 seconds with a measurement accuracy of 50 kHz. Currently, the frequency range of the FASSST system in our laboratory is roughly 100-700 GHz.

Herbst, Eric↗

NASA NTRS1995

Effect of higher harmonic control on helicopter rotor blade-vortex interaction noise: Prediction and initial validation

The paper presents a status of theoretical tools of AFDD, DLR, NASA and ONERA for prediction of the effect of HHC on helicopter main rotor BVI noise. Aeroacoustic predictions from the four research centers, concerning a wind tunnel simulation of a typical descent flight case without and with HHC are presented and compared. The results include blade deformation, geometry of interacting vortices, sectional loads and noise. Acoustic predictions are compared to experimental data. An analysis of the results provides a first insight of the mechanisms by which HHC may affect BVI noise.

Beaumier, P.↗

NASA NTRS1988

Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Described are methods for reducing vibration in helicopter rotor blades by determining optimum sizes and locations of tuning masses through formal mathematical optimization techniques. An optimization procedure is developed which employs the tuning masses and corresponding locations as design variables which are systematically changed to achieve low values of shear without a large mass penalty. The finite-element structural analysis of the blade and the optimization formulation require development of discretized expressions for two performance parameters: modal shaping parameter and modal shear amplitude. Matrix expressions for both quantities and their sensitivity derivatives are developed. Three optimization strategies are developed and tested. The first is based on minimizing the modal shaping parameter which indirectly reduces the modal shear amplitudes corresponding to each harmonic of airload. The second strategy reduces these amplitudes directly, and the third strategy reduces the shear as a function of time during a revolution of the blade. The first strategy works well for reducing the shear for one mode responding to a single harmonic of the airload, but has been found in some cases to be ineffective for more than one mode. The second and third strategies give similar results and show excellent reduction of the shear with a low mass penalty.

Pritchard, Jocelyn I.↗

NASA NTRS1992

Solid-state lasers for coherent communication and remote sensing

Semiconductor-diode laser-pumped solid-state lasers have properties that are superior to other lasers for the applications of coherent communication and remote sensing. These properties include efficiency, reliability, stability, and capability to be scaled to higher powers. We have demonstrated that an optical phase-locked loop can be used to lock the frequency of two diode-pumped 1.06 micron Nd:YAG lasers to levels required for coherent communication. Monolithic nonplanar ring oscillators constructed from solid pieces of the laser material provide better than 10 kHz frequency stability over 0.1 sec intervals. We have used active feedback stabilization of the cavity length of these lasers to demonstrate 0.3 Hz frequency stabilization relative to a reference cavity. We have performed experiments and analysis to show that optical parametric oscillators (OPO's) reproduce the frequency stability of the pump laser in outputs that can be tuned to arbitrary wavelengths. Another measurement performed in this program has demonstrated the sub-shot-noise character of correlations of the fluctuations in the twin output of OPO's. Measurements of nonlinear optical coefficients by phase-matched second harmonic generation are helping to resolve inconsistency in these important parameters.

Byer, Robert L.↗

NASA NTRS2000

Estimation of EOP From VLBI: Direct Approach

The currently adopted strategy of Earth Orientation Parameters (EOP) estimation from Very Long Baseline Interferometry (VLBI) is to estimate six parameters: Universal Time 1 (UT1), UT1 rate, pole positions, and nutation offsets for each 24-hour session independently. Then the resulting time series of raw EOP are filtered and a regression analysis is performed to obtain nutation coefficients, polhode of the pole, and other physical parameters. Thus, the latter parameters are obtained indirectly in two stages. An alternative approach of direct estimation of the final EOP is presented. Pole coordinates and UT1 are considered as a sum of three components: the low-period component that is modeled by a cubic spline, the harmonic component that includes forced nutation, precession and sub-daily variations of EOP, and the stochastic component that is modeled by a linear spline with segment length 1-2 hours. All parameters are obtained in a single LSQ solution using all available data.

POLAR MOTION↗

NASA NTRS2019

Application of GRACE to the Estimation of Groundwater Storage Change in a Data-poor Region: A Case Study of Ngadda Catchment in the Lake Chad Basin

The present study is to explore the feasibility of GRACE-based estimation of a groundwater storage change in a data-poor region using a case study of the Ngadda catchment in the Lake Chad Basin. Although the Ngadda catchment has only one set of in situ time series data of groundwater from 2006 to 2009 and a limited number of groundwater measurements in 2005 and 2009, GRACE-based groundwater storage change can be evaluated against thein situ groundwater measurements combined with specific yield data. The cross-correlation analysis in the Ngadda catchment shows that maximum rainfall reached in July and August, whereas both the maximum total water storage anomaly and the maximum groundwater storage anomaly occurred 2months later. Whereas the mean annual amplitude of total water storage anomaly is about 17cm from both the average total water storage anomaly from three mascon products and the one from three spherical harmonic products, the mean annual amplitude of soil moisture storage anomaly is substantially varied from5.58cm for CLM to about 14cm for NOAH and Mosaic. The goodness-of-fit tests show that CLM soil moisture produces the closest estimation of groundwater storage anomaly to thein situ groundwater measurements. The present study shows that GRACE-based estimation for groundwater storage anomaly can be a cost-effective and alternative tool to observe how groundwater changes in a basin scale under the limitation of modelling and in situ data availability.

GRACE↗

NASA NTRS1993

A preliminary error analysis of the gravity field recovery from a lunar Satellite-to-Satellite mission

A low cost lunar Satellite-to-Satellite radio tracking mission in a low-low configuration could considerably improve the existing knowledge about the lunar gravity field. The impact of various mission parameters that may contribute to the recovery of the gravity field, such as satellite altitude, satellite separation mission duration, measurement precision and sampling interval were quantified using the Jekeli-Rapp algorithm. Preliminary results indicate that the gravity field resolution up to harmonic degree 40 to 80 is feasible depending on various mission configurations. Radio tracking data from a six-month mission with a precision of 1 mm/s every 10 s and 300 km satellite separation at 150 km altitude will permit the determination of 5 deg x 5 deg mean gravity anomalies with an error of approximately 15 mgals. Consideration of other unaccounted error sources of instrumental, operational, and environmental nature may lower this resolution.

Iz, Huseyin B.↗

NASA NTRS2004

Membrane Vibration Analysis Above the Nyquist Limit with Fluorescence Videogrammetry

A new method for generating photogrammetric targets by projecting an array of laser beams onto a membrane doped with fluorescent laser dye has recently been developed. In this paper we review this new fluorescence based technique, then proceed to show how it can be used for dynamic measurements, and how a short pulsed (10 ns) laser allows the measurement of vibration modes at frequencies several times the sampling frequency. In addition, we present experimental results showing the determination of fundamental and harmonic vibration modes of a drum style dye-doped polymer membrane tautly mounted on a 12-inch circular hoop and excited with 30 Hz and 62 Hz sinusoidal acoustic waves. The projected laser dot pattern was generated by passing the beam from a pulsed Nd:YAG laser though a diffractive optical element, and the resulting fluorescence was imaged with three digital video cameras, all of which were synchronized with a pulse and delay generator. Although the video cameras are capable of 240 Hz frame rates, the laser s output was limited to 30 Hz and below. Consequently, aliasing techniques were used to allow the measurement of vibration modes up to 186 Hz with a Nyquist limit of less than 15 Hz.

Dorrington, Adrian A.↗

NASA NTRS1973

The Mariner 9 celestial mechanics experiment

There are two main objectives in the Mars gravity field analysis. The first is to generate a picture of the gravity field which can be used in conjunction with other types of data to elucidate the interior, surface structure, and history of Mars. The second is to aid the orbit determination aspect of the relativity experiment. In an effort to extract from the data a Mars gravity model of reasonable fidelity, various spherical harmonic models have been made. A parallel effort using a surface mass representation involves the differentiation of Doppler residuals for acceleration contours.

Lorell, J.↗

NASA NTRS1992

LDEF radiation measurements: preliminary results

The Long Duration Exposure Facility (LDEF), retrieved by the Space Shuttle mission STS-32 after nearly 6 yr in orbit, is the focus of a broad-based study of the radiation environment in low Earth orbit (LEO) and its effects on materials. A combination of passive techniques has been used to study this environment via detectors which were contained in experiments aboard the LDEF spacecraft and through analysis of induced radioactivities. Preliminary results for absorbed dose measurements and for induced activities in various materials are presented. A number of effects have been observed which reflect the anisotropy of the charged particle flux in low Earth orbit. Quantitative results from these measurements should provide an accurate means of confirming environmental flux models and techniques for predicting radiation encountered in future LEO missions, particularly those of extended duration.

NASA Discipline Number 00-00↗

NASA NTRS1978

Analysis of Satellite-to-Satellite Tracking (SST) and altimetry data from GEOS-C

Radar altimetry and satellite-to-satellite (SST) range and range rate tracking measurements were used to infer the exterior gravitational field of the earth and the structure of the geoid from GEOS-C metric data. Under the SST analysis, a direct point-by-point estimate of gravity disturbance by means of a recursive filter with backward smoothing was attempted but had to be forsaken because of poor convergence. The adopted representation consists of a more or less uniform grid of discrete masses at a depth of approximately 400 km from the earth's surface. The layer is superimposed on a spherical harmonics model. The procedure for smoothing the altimetry and inferring the fine-structured gravity field over the Atlantic test area is described. The local disturbances are represented by means of a density layer. The altimeter height biases were first estimated by a least squares adjustment at orbital crossover points. After taking out the bias, long wavelength contributions from GEM-6 as well as a calibration correction were subtracted. The residual heights were then represented by a mass distribution beneath the earth's surface.

Wong, L.↗

NASA NTRS1978

Variation of fan tone steadiness for several inflow conditions

An amplitude probability density function analysis technique for quantifying the degree of fan noise tone steadiness has been applied to data from a fan tested under a variety of inflow conditions. The test conditions included typical static operation, inflow control by a honeycomb/screen device and forward velocity in a wind tunnel simulating flight. The ratio of mean square sinusoidal-to-random signal content in the fundamental and second harmonic tones was found to vary by more than an order-of-magnitude. Some implications of these results concerning the nature of fan noise generation mechanisms are discussed.

Balombin, J. R.↗

NASA NTRS1978

Variation of fan tone steadiness for several inflow conditions

Balombin, J. R.↗

NASA NTRS1989

Reflection of solar radiation by a cylindrical cloud

Potential applications of an analytic method for computing the solar radiation reflected by a cylindrical cloud are discussed, including studies of radiative transfer within finite clouds and evaluations of these effects on other clouds and on remote sensing problems involving finite clouds. The pattern of reflected sunlight from a cylindrical cloud as seen at a large distance has been considered and described by the bidirectional function method for finite cloud analysis, as previously studied theoretically for plane-parallel atmospheres by McKee and Cox (1974); Schmetz and Raschke (1981); and Stuhlmann et al. (1985). However, the lack of three-dimensional radiative transfer solutions for anisotropic scattering media have hampered theoretical investigations of bidirectional functions for finite clouds. The present approach permits expression of the directional variation of the radiation field as a spherical harmonic series to any desired degree and order.

Smith, G. L.↗

NASA NTRS1993

Beamforming in an acoustic shadow

The sound field deep within an acoustic shadow region is less well understood than that outside the shadow region. Signal levels are substantially lower within the shadow, but beamforming difficulties arise for other reasons such as loss of spatial coherence. Based on analysis of JAPE-91 data, and other data, three types of characteristic signals within acoustic shadow regions are identified. These signal types may correspond to different, intermittent signal propagation conditions. Detection and classification algorithms might take advantage of the signal characteristics. Frequency coherence is also discussed. The extent of coherence across frequencies is shown to be limited, causing difficulties for source classification based on harmonic amplitude relationships. Discussions emphasize short-term characteristics on the order of one second. A video presentation on frequency coherence shows the similarity, in the presence of atmospheric turbulence, between the received signal from a stable set of harmonics generated by a loudspeaker and that received from a helicopter hovering behind a hill.

Havelock, David↗