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NASA NTRS1990

Boundary element analysis of sound scattered by a moving surface

A solution for the acoustic field scattered from a uniformly moving rigid body in the presence of a harmonic incident source has been obtained using a boundary integral method. A derivation of the Kirchhoff formula given by Farassat and Myers (1988) for moving surfaces forms the basis for the analysis, and the development of a boundary integral method for the solution of scattering problems from moving rigid bodies is described. Finite elements are used in conjunction with the Galerkin method in order to solve the integral equation that results from the Kirchhoff formula when the observer point is placed on the moving body surface. Once appropriate surface field values are known they are inserted back into the formula in order to predict the field scattered off the body. Tests, including the so called superposition method, are carried out in order to validate the technique and to establish some confidence in its accuracy. Application of the superposition method to moving bodies is presented, and results of the two approaches are discussed. Sample calculations of scattering from a simple body are presented to illustrate the effects of variations in relevant parameters.

Myers, M. K.↗

NASA NTRSDate not supplied

Global Analysis of Nonlinear Second-Mode Development in a Mach-6 Boundary Layer From High-Speed Schlieren Data

The second-mode instability on a 7◦ half-angle sharp cone at Mach 6 is analyzed using high-speed calibrated schlieren imagery at a frame rate near the expected fundamental frequency. Experiments were conducted in the NASA Langley 20-Inch Mach 6 facility at unit Reynolds number between 6.56×106 and 9.71×106 m−1. Time-resolved pixel intensity signals throughout the boundary layer are reconstructed using spatially available data in the schlieren images to recover an effective sampling rate of over 10 MHz; these are then converted to quantitative density gradients using a thin-lens-based calibration technique. A global analysis is performed on the schlieren data to investigate the nonlinear growth of the second-mode fundamental and harmonic content. Point-wise measures of the auto-bicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities were found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s time-series and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. Comparisons between the bispectral quantities and second-mode power show that nonlinear interactions, particularly resonance interactions, are closely correlated with space-time modulation of disturbances during the nonlinear stage of transition.

boundary layer transition↗

NASA NTRS2012

Local Lunar Gravity Field Analysis over the South Pole-aitken Basin from SELENE Farside Tracking Data

We present a method with which we determined the local lunar gravity field model over the South Pole-Aitken (SPA) basin on the farside of the Moon by estimating adjustments to a global lunar gravity field model using SELENE tracking data. Our adjustments are expressed in localized functions concentrated over the SPA region in a spherical cap with a radius of 45deg centered at (191.1 deg E, 53.2 deg S), and the resolution is equivalent to a 150th degree and order spherical harmonics expansion. The new solution over SPA was used in several applications of geophysical analysis. It shows an increased correlation with high-resolution lunar topography in the frequency band l = 40-70, and admittance values are slightly different and more leveled when compared to other, global gravity field models using the same data. The adjustments expressed in free-air anomalies and differences in Bouguer anomalies between the local solution and the a priori global solution correlate with topographic surface features. The Moho structure beneath the SPA basin is slightly modified in our solution, most notably at the southern rim of the Apollo basin and around the Zeeman crater

Lunar Gravity↗

NASA NTRS1992

Analysis of crustal structure of Venus utilizing residual Line-of-Sight (LOS) gravity acceleration and surface topography data. A trial of global modeling of Venus gravity field using harmonic spline method

To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.

Fang, Ming↗

NASA NTRS1998

Mesogranulation as A Distinct Scale of Convection in the Sun

We present evidence for the existence of mesogranulation as a scale of convection distinct from granulation and supergranulation through analysis of full-disk Doppler velocity images of the Sun collected by the Michelson Doppler Imager (MDI) aboard the NASA/ESA Solar and Heliospheric Observatory (SOHO). Our analysis procedures isolate nearly steady flows in the solar photosphere and yield power spectra of convection for spherical harmonic degrees up to I = 1000. Each spectrum exhibits an obvious supergranulation peak at I approximately 130 and a broad secondary peak at I approximately 600 with a distinct break in the spectrum between these peaks at I approximately 300. We believe that this secondary peak is a signature of mesogranulation with typical cell diameters of about 7 Mm. Our standard analysis procedure is to first remove the p-mode oscillation signal by averaging individual Dopplergrams over 17-minute intervals. Next, by fitting to standard functional forms we remove Doppler signals due to the motion of the spacecraft, the convective blueshift, solar rotation including differential rotation, and the meridional circulation in order to produce Dopplergrams dominated by convective motions. By mapping these processed images onto heliographic coordinates and projecting onto spherical harmonics, we produce a power spectrum of solar convection for each 17-minute period. We construct synthetic images and pass them through the same analysis procedure in order to determine the actual solar convection spectrum that reproduces the analyzed results. We find that a small but increasing percentage of high-degree convective power is lost in the analysis as we approach the limit of resolution of the detector but'that the broad, mesogranulation peak at I approximately 600 must be included in the convection spectrum of the synthetic images.

Bachmann, Kurt T.↗

NASA NTRSDate not supplied

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nosetip, and the mechanisms underlying the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy layer experience appreciable energy amplification for moderate to large nosetip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the perturbation form of the 2D, harmonic Navier-Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton-Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the GMRES iterative method with a preconditioner corresponding to a simplified Jacobian without the cross derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation (NPSE) results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over the blunt cone. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher frequency Mack’s second-mode instabilities further downstream.

boundary layer transition↗

NASA NTRSDate not supplied

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

boundary layer transition↗

NASA NTRS1975

Correlation of the earth's rotation rate and the secular change of the geomagnetic field

Power spectral density analysis using Burg's maximum entropy method was applied to the geomagnetic dipole field and its rate of change for the years 1901 to 1969. Both spectra indicate relative maxima at 0.015 cycles/year and its harmonics. These maxima correspond approximately to 66, 33, 22, 17, 13, 11, and 9-year spectral lines. The application of the same analysis techniques to the length-of-day (l.o.d) fluctuations for the period 1865 to 1961 reveal similar spectral characteristics. Although peaks were observed at higher harmonics of the fundamental frequency, the 22-year and 11-year lines are not attributed unambiguously to the solar magnetic cycle and the solar cycle. It is suggested that the similarity in the l.o.d fluctuations and the dipole field variations is related to the motion within the earth's fluid core during the past one hundred years.

Jin, R. S.↗

NASA NTRS1979

Oceanic geoid and tides derived from GEOS 3 satellite data in the Northwestern Atlantic Ocean

Two sets of GEOS 3 altimeter data which fall within about a 2.5-deg width are analyzed for ocean geoid and tides. One set covers a path from Newfoundland to Cuba, and the other a path from Puerto Rico to the North Carolina coast. Forty different analyses using various parameters are performed in order to investigate convergence. Profiles of the geoid and four tides, M2, O1, S2, and K1, are derived along the two strips. While the analyses produced convergent solutions for all 40 cases, the uncertainty caused by the linear orbital bias error of the satellite is too large to claim that the solutions represent the true ocean tides in the area. A spot check of the result with the Mode deep-sea tide gauge data shows poor agreement. A positive conclusion of this study is that despite the uncertain orbital error the oceanic geoid obtained through this analysis can improve significantly the short-wavelength structure over existing spherical harmonic geoid models.

Won, I. J.↗

NASA NTRS1982

Coupled rotor/airframe vibration analysis

A coupled rotor/airframe vibration analysis developed as a design tool for predicting helicopter vibrations and a research tool to quantify the effects of structural properties, aerodynamic interactions, and vibration reduction devices on vehicle vibration levels is described. The analysis consists of a base program utilizing an impedance matching technique to represent the coupled rotor/airframe dynamics of the system supported by inputs from several external programs supplying sophisticated rotor and airframe aerodynamic and structural dynamic representation. The theoretical background, computer program capabilities and limited correlation results are presented in this report. Correlation results using scale model wind tunnel results show that the analysis can adequately predict trends of vibration variations with airspeed and higher harmonic control effects. Predictions of absolute values of vibration levels were found to be very sensitive to modal characteristics and results were not representative of measured values.

Sopher, R.↗

NASA NTRS1984

The importance of nonlinearity on the higher harmonic control of helicopter vibration

The effect of nonlinearity on the higher harmonic control (HHC) of helicopter vibration is investigated using a nonlinear aeroelastic simulation. A nonlinear solution is proposed which relates the HHC inputs to vibration outputs on the basis of a Volterra functional series. The Volterra series solution is shown to reduce to a vector polynomial equation relating HHC inputs to vibration outputs at any harmonic frequency. The nonlinear transfer relationship is identified from a nonlinear vibration analysis computer program, and the identification model is examined in detail. Improvements to current HHC algorithms are presented, and several Kalman filter divergence problems are quantified.

Molusis, J. A.↗

NASA NTRS1985

Cosmic ray intensity variations at primary rigidities near 1900 GV

Preliminary analysis of an experiment monitoring cosmic ray muons yields a first sidereal harmonic amplitude for rigidities around 1900 GV of (7.95 + or - 3.97) 10 to the 0.001 power at 5.1 + or - 1.9h right ascention. A significant anti-sidereal first harmonic is, however, also seen.

Lee, Y. W.↗

NASA NTRS1991

Coupled rotor-fuselage vibration reduction with multiple frequency blade pitch control

A nonlinear coupled rotor/flexible fuselage analysis has been developed and used to study the effects of higher harmonic blade pitch control on the vibratory hub loads and fuselage acceleration levels. Previous results, obtained with this model have shown that conventional higher harmonic control (HHC) inputs aimed at hub shear reduction cause an increase in the fuselage accelerations and vice-versa. It was also found that for simultaneous reduction of hub shears and fuselage accelerations, a pitch input representing a combination of two higher harmonic components of different frequencies was needed. Subsequently, it was found that this input could not be implemented through a conventional swashplate. This paper corrects a mistake originally made in the representation of the multiple frequency pitch input and shows that such a pitch input can be only implemented in the rotating reference frame. A rigorous mathematical solution is found, for the pitch input in the rotating reference frame, which produces simultaneous reduction of hub shears and fuselage acceleration. New insight on vibration reduction in coupled rotor/fuselage systems is obtained from the sensitivity of hub shears to the frequency and amplitude of the open loop HHC signal in the rotating reference frame. Finally the role of fuselage flexibility in this class of problems is determined.

Papavassiliou, I.↗

NASA NTRS2010

Reliability and Stability of VLBI-Derived Sub-Daily EOP Models

Recent investigations have shown significant shortcomings in the model which is proposed by the IERS to account for the variations in the Earth s rotation with periods around one day and less. To overcome this, an empirical model can be estimated more or less directly from the observations of space geodetic techniques. The aim of this paper is to evaluate the quality and reliability of such a model based on VLBI observations. Therefore, the impact of the estimation method and the analysis options as well as the temporal stability are investigated. It turned out that, in order to provide a realistic accuracy measure of the model coefficients, the formal errors should be inflated by a factor of three. This coincides with the noise floor and the repeatability of the model coefficients and it captures almost all of the differences that are caused by different estimation techniques. The impact of analysis options is small but significant when changing troposphere parameterization or including harmonic station position variations.

Artz, Thomas↗

NASA NTRS1995

Harmonic oscillators and resonance series generated by a periodic unstable classical orbit

The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.

Kazansky, A. K.↗

NASA NTRS1980

Ozone data and mission sampling analysis

A methodology was developed to analyze discrete data obtained from the global distribution of ozone. Statistical analysis techniques were applied to describe the distribution of data variance in terms of empirical orthogonal functions and components of spherical harmonic models. The effects of uneven data distribution and missing data were considered. Data fill based on the autocorrelation structure of the data is described. Computer coding of the analysis techniques is included.

Robbins, J. L.↗

NASA NTRS2004

BASS Code Development

The BASS computational aeroacoustic code solves the fully nonlinear Euler equations in the time domain in two-dimensions. The acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vortical gust of the rotor. The spatial mode generation, propagation and decay characteristics are predicted by assuming the acoustic field away from the stator can be represented as a uniform flow with small harmonic perturbations superimposed. The computed field is then decomposed using a joint temporal-spatial transform to determine the wave amplitudes as a function of rotor harmonic and spatial mode order. This report details the following technical aspects of the computations and analysis. 1) the BASS computational technique; 2) the application of periodic time shifted boundary conditions; 3) the linear theory aspects unique to rotor-stator interactions; and 4) the joint spatial-temporal transform. The computational results presented herein are twofold. In each case, the acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vortical gust of the rotor. The fan under consideration here like modern fans is cut-off at +, and propagating acoustic waves are only expected at 2BPF and 3BPF. In the first case, the computations showed excellent agreement with linear theory predictions. The frequency and spatial mode order of acoustic field was computed and found consistent with linear theory. Further, the propagation of the generated modes was also correctly predicted. The upstream going waves propagated from the domain without reflection from the in ow boundary. However, reflections from the out ow boundary were noticed. The amplitude of the reflected wave was approximately 5% of the incident wave. The second set of computations were used to determine the influence of steady loading on the generated noise. Toward this end, the acoustic response was determined with three steady loading conditions: design, low-loading, high-loading. The overall trend showed significant (approximately 10 dB) increases in the generated noise for the highly loaded stator.

Sawyer, Scott↗

NASA NTRS1983

The vibration characteristics of a coupled helicopter rotor-fuselage by a finite element analysis

The dynamic coupling between the rotor system and the fuselage of a simplified helicopter model in hover was analytically investigated. Mass, aerodynamic damping, and elastic and centrifugal stiffness matrices are presented for the analytical model; the model is based on a beam finite element, with polynomial mass and stiffness distributions for both the rotor and fuselage representations. For this analytical model, only symmetric fuselage and collective blade degrees of freedom are treated. Real and complex eigen-analyses are carried out to obtain coupled rotor-fuselage natural modes and frequencies as a function of rotor speed. Vibration response results are obtained for the coupled system subjected to a radially uniform, harmonic blade loading. The coupled response results are compared with response results from an uncoupled analysis in which hub loads for an isolated rotor system subjected to the same sinusoidal blade loading as the coupled system are applied to a free-free fuselage.

Rutkowski, M. J.↗