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Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
This paper explores a comparison between experimental data and numerical simulations of the historical baseline F31/A31 open rotor geometry. The experimental data were obtained at the NASA Glenn Research Center s Aeroacoustic facility and include performance and noise information for a variety of flow speeds (matching take-off and cruise). The numerical simulations provide both performance and aeroacoustic results using the NUMECA s Fine-Turbo analysis code. A non-linear harmonic method is used to capture the rotor/rotor interaction.
An Earth System Digital Twin (ESDT) is a dynamic, interactive, digital replica of the state and temporal evolution of Earth systems. It integrates multiple models along with observation data, and connecting them with analysis, AI, and visualization tools. Together, these enable users to explore the current state of the Earth system, predict future conditions, and run hypothetical scenarios to understand how the system would evolve under various assumptions. The NASA’s Advanced Information Systems Technology (AIST)’s Integrated Digital Earth Analysis System (IDEAS) project is to establish an extensible architectural solution to develop digital twins of our physical environment for Earth Science. IDEAS delivers a formal system architecture with mechanisms for the outputs of one model to feed into others; for driving models with observation data; and for harmonizing observation data and model outputs for analysis. To validate and demonstrate the IDEAS architecture, this project collaborates with the Space Climate Observatory (SCO)’s FloodDAM project and the Centre National d’Etudes Spatiales (CNES) to focus on floods detection, prediction and their impacts.
Analysis of 5.5 years of Lageos satellite range data reveal significant residual nodal signatures: an acceleration and annual and semiannual periods. These signatures primarily reflect variations in the zonal gravitational harmonic J2 coefficient and hence the polar moment of inertia. The implied decrease of J2 = -3 x 10 to the -11th/yr is consistent with both historical observations of the nontidal acceleration of the earth's rotation and models of viscous rebound of the solid earth from the decrease in load due to the last deglaciation.
A report presents further details regarding the subject matter of "Phase-Synchronized Enhancement Method for Engine Diagnostics" (MFS-26435), NASA Tech Briefs, Vol. 22, No. 1 (January 1998), page 54. To recapitulate: The phase-synchronized enhancement method (PSEM) involves the digital resampling of a quasi-periodic signal in synchronism with the instantaneous phase of one of its spectral components. This resampling transforms the quasi-periodic signal into a periodic one more amenable to analysis. It is particularly useful for diagnosis of a rotating machine through analysis of vibration spectra that include components at the fundamental and harmonics of a slightly fluctuating rotation frequency. The report discusses the machinery-signal-analysis problem, outlines the PSEM algorithms, presents the mathematical basis of the PSEM, and presents examples of application of the PSEM in some computational simulations.
A user-oriented computer program SISCAP (SIS Computer Analysis Program) for analyzing SIS mixers is described. The program allows arbitrary impedance terminations to be specified at all LO harmonics and sideband frequencies. It is therefore able to treat a much more general class of SIS mixers than the widely used three-frequency analysis, for which the harmonics are assumed to be short-circuited. An additional program, GETCHI, provides the necessary input data to program SISCAP. The SISCAP program performs a nonlinear analysis to determine the SIS junction voltage waveform produced by the local oscillator. The quantum theory of mixing is used in its most general form, treating the large signal properties of the mixer in the time domain. A small signal linear analysis is then used to find the conversion loss and port impedances. The noise analysis includes thermal noise from the termination resistances and shot noise from the periodic LO current. Quantum noise is not considered. Many aspects of the program have been adequately verified and found accurate.
Results are presented from an attempt to perform a relatively comprehensive analysis of the evidence for a periodicity, with harmonics, of the observed regular reversals of the earth's magnetic field. The database considered covers 296 reversals over the past 165 Myr. Histograms with bins 1 Myr apart reveal only 30 Myr reversal patterns. The reversal dates are fitted to a linear periodic function and a spectrum is computed for the residuals at the adopted dates. The possible presence of multiple periodicities is evaluated and over various time intervals. The analysis shows that a recently observed 15 Myr periodicity is probably a harmonic of the 29.5-30.5 Myr period. The calculations do not confirm an inherent magnetic reversal property of the earth. The reversals may arise from tectonic events or from impacts from extraterrestrial objects.
This report provides an updated version of analytical documentation for the V072 Rotor Wake/Stator Interaction Code. It presents the theoretical derivation of the equations used in the code and, where necessary, it documents the enhancements and changes made to the original code since its first release. V072 is a package of FORTRAN computer programs which calculate the in-duct acoustic modes excited by a fan/stator stage operating in a subsonic mean flow. Sound is generated by the stator vanes interacting with the mean wakes of the rotor blades. In this updated version, only the tonal noise produced at the blade passing frequency and its harmonics, is described. The broadband noise component analysis, which was part of the original report, is not included here. The code provides outputs of modal pressure and power amplitudes generated by the rotor-wake/stator interaction. The rotor/stator stage is modeled as an ensemble of blades and vanes of zero camber and thickness enclosed within an infinite hard-walled annular duct. The amplitude of each propagating mode is computed and summed to obtain the harmonics of sound power flux within the duct for both upstream and downstream propagating modes.
An analysis technique is described to calculate the harmonic response of the first-stage impeller of the Space Shuttle Main Engine high pressure fuel turbopump. The excitation is a complex pressure loading at various locations on the impeller blades. The pressure loading was predicted using computational fluid dynamic techniques and was given as a Fourier series at 48 different locations on each of the three impeller blade types. The analysis consisted of mapping the pressures onto a three-dimensional finite element model, then converting these pressure loads to complex nodal force vectors at specified equal time intervals. The resulting vectors were then converted to modal force time histories that were then transformed into the frequency domain where the frequency response was calculated directly. This technique resulted in an improvement to the previously used direct integration technique and in a substantial analysis cost reduction.
Acoustic characteristics predicted using a recently developed computer code were correlated with measured acoustic data for two helicopter rotors. The analysis, is based on a solution of the Ffowcs-Williams-Hawkings (FW-H) equation and includes terms accounting for both the thickness and loading components of the rotational noise. Computations are carried out in the time domain and assume free field conditions. Results of the correlation show that the Farrassat/Nystrom analysis, when using predicted airload data as input, yields fair but encouraging correlation for the first 6 harmonics of blade passage. It also suggests that although the analysis represents a valuable first step towards developing a truly comprehensive helicopter rotor noise prediction capability, further work remains to be done identifying and incorporating additional noise mechanisms into the code.
The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example, the removal of the Galactic plane data from the Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) sky maps compromises Fourier analysis of the cosmic microwave background (CMB) temperature distribution due to the loss of orthogonality of the spherical harmonics. An explicit method for constructing orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier analysis of the COBE DMR sky maps to provide the correct input for the determination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for other astronomical applications.
Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. Assessing the blade structural integrity is a complex task requiring an initial characterization of whether resonance is possible and then performing a forced response analysis if that condition is met. The standard technique for forced response analysis in rocket engine turbines is to decompose a computational fluid dynamics (CFD).generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies using cyclically symmetric structural dynamic models. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non ]harmonic excitation sources that become present in complex flows. This complex content can only be captured by a CFD flow field encompassing at least an entire revolution. A substantial development effort to create a series of software programs to enable application of the 360 degree forcing function in a frequency response analysis on cyclic symmetric models has been completed (to be described in a future paper), but the question still remains whether the frequency response analysis itself is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, of bladed-disks undergoing this complex flow environment have been performed. The first is of a bladed disk with each blade modeled by simple beam elements and the disk modeled with plates (using the finite element code MSC/NASTRAN). The focus of this model is to be representative of response of realistic bladed disks, and so the dimensions are roughly equivalent to the new J2X rocket engine 1st stage fuel pump turbine. The simplicity of the model allows the CFD load to be able to be readily applied, along with analytical and experimental variations in both the temporal and spatial fourier components of the excitation. In addition, this model is a first step in identifying response differences between transient and frequency forced response analysis techniques. The second phase assesses this difference for a much more realistic solid model of a bladed-disk in order to evaluate the effect of the spatial variation in loading on blade dominated modes. Neither research on the accuracy of the frequency response method when used in this context or a comprehensive study of the effect of test-observed variation on blade forced response have been found in the literature, so this research is a new contribution to practical structural dynamic analysis of gas turbines. The primary excitation of the upstream nozzles interacts with the blades on fuel pump of the J2X causes the 5th Nodal diameter modes to be excited, as explained by Tyler and Sofrin1, so a modal analysis was first performed on the beam/plate model and the 5ND bladed-disk mode at 40167 hz was identified and chosen to be the one excited at resonance (see figure 1). The first forced response analysis with this model focuses on identifying differences between frequency and transient response analyses. A hypothesis going into the analysis was that perhaps the frequency response was enforcing a temporal periodicity that did not really exist, and so therefore it would overestimate the response. As high dynamic response was a considerable source of stress in the J2X, examining this concept could potentially be beneficial for the program.
Cosmic ray neutron data from the cosmic ray stations from the worldwide network in 1966, 1967 and 1969 are analyzed by means of the three dimensional analysis method by Nagashima. The variations of the north-south anisotropy, which is the first zonal harmonic component obtained from the analysis are studied. The result obtained confirms earlier findings. Relationship of the anisotropy to the interplanetary magnetic field sector polarity is also studied.
This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.
This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.
The mechanisms for generating Alfven waves in the magnetosphere are determined, on the basis of a comprehensive survey of satellite magnetometer data. The mechanisms are classified in terms of the physical properties of standing Alfven waves such as the direction of the major axis of polarization, harmonic mode, and the azimuthal wave number. In an analysis of the statistical organization of the pulsations, it is shown that the most common transverse waves seem to be azimuthally polarized waves involving the fundamental and several harmonics, with radially polarized waves excited at the second harmonic. The former are probably driven externally, while the latter are likely to be excited internally through particle-wave interactions.
Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.