Search NASA⌕ Search

SEARCH · Search NASA

Results for “CORRELATION FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Follow-on Low Noise Fan Aerodynamic Study

The focus of the project was to investigate the effects of turbulence models on the prediction of rotor wake structures. The Advanced Ducted Propfan Analysis (ADPAC) code was modified through the incorporation of the Spalart-Allmaras one-equation turbulence model. Suitable test cases were solved numerically using ADPAC employing the Spalart-Allmaras turbulence model and another prediction code for comparison. A near-wall spacing study was also completed to determine the adequate spacing of the first computational cell off the wall. Solutions were also collected using two versions of the algebraic Baldwin-Lomax turbulence model in ADPAC. The effects of the turbulence model on the rotor wake definition was examined by obtaining ADPAC solutions for the Low Noise Fan rotor-only steady-flow case using the standard algebraic Baldwin-Lomax turbulence model, a modified version of the Baldwin-Lomax turbulence model and the one-equation Spalart-Allmaras turbulence model. The results from the three different turbulence modeling techniques were compared with each other and the available experimental data. These results include overall rotor performance, spanwise exit profiles, and contours of axial velocity taken along constant axial locations and along blade-to-blade surfaces. Wake characterizations were also performed on the experimental and ADPAC predicted results including the definition of a wake correlation function. Correlations were evaluated for wake width and wake depth. Similarity profiles of the wake shape were also compared between all numerical solutions and experimental data.

Heidegger, Nathan J.↗
NASA NTRS1994

Modeling the two-point correlation of the vector stream function

A new model for the two-point vector stream function correlation has been developed using tensor invariant arguments and evaluated by the comparison of model predictions with DNS data for incompressible homogeneous turbulent shear flow. This two-point vector stream function model correlation can then be used to calculate the two-point velocity correlation function and other quantities useful in turbulence modeling. The model assumes that the two-point vector stream function correlation can be written in terms of the separation vector and a new tensor function that depends only on the magnitude of the separation vector. The model has a single free model coefficient, which has been chosen by comparison with the DNS data. The relative error of the model predictions of the two-point vector stream function correlation is only a few percent for a broad range of the model coefficient. Predictions of the derivatives of this correlation, which are of interest in turbulence modeling, may not be this accurate.

Oberlack, M.↗
NASA NTRS1986

The Shane-Wirtanen counts - Observer and time-dependent effects

In a recent paper, de Lapparent, Kurtz, and Geller (1986) announce the discovery of possible observer and time-dependent effects in the counts of galaxies in the Lick catalog and suggest that these effects may have distorted the galaxy correlation function calculated by Groth and Peebles (1986) from the Lick counts. In particular, they suggest that these effects may have introduced a break where none exists or may have diluted a break stronger than that seen by Groth and Peebles. The Lick counts have been reexamined and it is found that the observer and time-dependent effects are marginal and that they can have had only a negligible effect on the estimates of the correlation functions. Correlation functions have been calculated for each observer and time period separately and it is found that they all depart from the small-angle power law at about the expected scale. Further, the average of these correlation functions agrees extremely well with the average correlation function published by Groth and Peebles.

Groth, Edward J.↗
NASA NTRS2002

The spectral correlation of functional clouds: a statistical test for theoretical models

We compute the spectral correlation function (SCF) of CO J=1-0 maps of moleculary cloud complexes. The SCF is a power law over approximately an order of magnitude in spatial separation in every map. The power law slope of the SCF, its normalization, and the spectral line width averaged over the whole map, are computed for all the observational maps.

turbulence kinematics↗
NASA NTRS2008

Stochastic Transport Theory for Investigating the Three-Dimensional Canopy Structure from Space Measurements

Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data.

Huang, Dong↗
NASA NTRS2009

Core Noise Diagnostics of Turbofan Engine Noise Using Correlation and Coherence Functions

Cross-correlation and coherence functions are used to look for periodic acoustic components in turbofan engine combustor time histories, to investigate direct and indirect combustion noise source separation based on signal propagation time delays, and to provide information on combustor acoustics. Using the cross-correlation function, time delays were identified in all cases, clearly indicating the combustor is the source of the noise. In addition, unfiltered and low-pass filtered at 400 Hz signals had a cross-correlation time delay near 90 ms, while the low-pass filtered at less than 400 Hz signals had a cross-correlation time delay longer than 90 ms. Low-pass filtering at frequencies less than 400 Hz partially removes the direct combustion noise signals. The remainder includes the indirect combustion noise signal, which travels more slowly because of the dependence on the entropy convection velocity in the combustor. Source separation of direct and indirect combustion noise is demonstrated by proper use of low-pass filters with the cross-correlation function for a range of operating conditions. The results may lead to a better idea about the acoustics in the combustor and may help develop and validate improved reduced-order physics-based methods for predicting direct and indirect combustion noise.

Miles, Jeffrey H.↗
NASA NTRS1992

Galaxy clusters and cold dark matter - A low-density unbiased universe?

Large-scale simulations of a universe dominated by cold dark matter (CDM) are tested against two fundamental properties of clusters of galaxies: the cluster mass function and the cluster correlation function. We find that standard biased CDM models are inconsistent with these observations for any bias parameter b. A low-density, low-bias CDM-type model, with or without a cosmological constant, appears to be consistent with both the cluster mass function and the cluster correlations. The low-density model agrees well with the observed correlation function of the Abell, Automatic Plate Measuring Facility (APM), and Edinburgh-Durham cluster catalogs. The model is in excellent agreement with the observed dependence of the correlation strength on cluster mean separation, reproducing the measured universal dimensionless cluster correlation. The low-density model is also consistent with other large-scale structure observations, including the APM angular galaxy-correlations, and for lambda = 1-Omega with the COBE results of the microwave background radiation fluctuations.

Bahcall, Neta A.↗
NASA NTRS1990

Hierarchical fragmentation model for the evolution of self-gravitating clouds

A hierarchical model for the fragmentation of cold, self-gravitating gas clouds is developed, and the model is applied to the collapse of matter accumulated at the boundaries of large-scale voids in the universe. In this model, the mass function for fragment sizes and the correlation function for fragment positions are naturally related. Using this relationship, the mass function for galaxies is derived from the observed galaxy-galaxy two-point correlation function. Assuming that galaxy masses and luminosities are proportional to one another, the derived luminosity function agrees with the empirical Schecter function at low luminosity. It is argued that the correlation function itself may be a natural outcome of large-scale gravitational instability at each stage of the hierarchy.

Newman, William I.↗
NASA NTRS1996

Electromagnetic Compatibility Testing Studies

This report discusses the results on analytical models and measurement and simulation of statistical properties from a study of microwave reverberation (mode-stirred) chambers performed at Texas Tech University. Two analytical models of power transfer vs. frequency in a chamber, one for antenna-to-antenna transfer and the other for antenna to D-dot sensor, were experimentally validated in our chamber. Two examples are presented of the measurement and calculation of chamber Q, one for each of the models. Measurements of EM power density validate a theoretical probability distribution on and away from the chamber walls and also yield a distribution with larger standard deviation at frequencies below the range of validity of the theory. Measurements of EM power density at pairs of points which validate a theoretical spatial correlation function on the chamber walls and also yield a correlation function with larger correlation length, R(sub corr), at frequencies below the range of validity of the theory. A numerical simulation, employing a rectangular cavity with a moving wall shows agreement with the measurements. The determination that the lowest frequency at which the theoretical spatial correlation function is valid in our chamber is considerably higher than the lowest frequency recommended by current guidelines for utilizing reverberation chambers in EMC testing. Two suggestions have been made for future studies related to EMC testing.

Trost, Thomas F.↗
NASA NTRS1977

Correlated wave functions for three-particle systems with Coulomb interaction - The muonic helium atom

A computational procedure for calculating correlated wave functions is proposed for three-particle systems interacting through Coulomb forces. Calculations are carried out for the muonic helium atom. Variational wave functions which explicitly contain interparticle coordinates are presented for the ground and excited states. General Hylleraas-type trial functions are used as the basis for the correlated wave functions. Excited-state energies of the muonic helium atom computed from 1- and 35-term wave functions are listed for four states.

Huang, K.-N.↗
NASA NTRS1999

Phase Time and Envelope Time in Time-Distance Analysis and Acoustic Imaging

Time-distance analysis and acoustic imaging are two related techniques to probe the local properties of solar interior. In this study, we discuss the relation of phase time and envelope time between the two techniques. The location of the envelope peak of the cross correlation function in time-distance analysis is identified as the travel time of the wave packet formed by modes with the same w/l. The phase time of the cross correlation function provides information of the phase change accumulated along the wave path, including the phase change at the boundaries of the mode cavity. The acoustic signals constructed with the technique of acoustic imaging contain both phase and intensity information. The phase of constructed signals can be studied by computing the cross correlation function between time series constructed with ingoing and outgoing waves. In this study, we use the data taken with the Taiwan Oscillation Network (TON) instrument and the Michelson Doppler Imager (MDI) instrument. The analysis is carried out for the quiet Sun. We use the relation of envelope time versus distance measured in time-distance analyses to construct the acoustic signals in acoustic imaging analyses. The phase time of the cross correlation function of constructed ingoing and outgoing time series is twice the difference between the phase time and envelope time in time-distance analyses as predicted. The envelope peak of the cross correlation function between constructed ingoing and outgoing time series is located at zero time as predicted for results of one-bounce at 3 mHz for all four data sets and two-bounce at 3 mHz for two TON data sets. But it is different from zero for other cases. The cause of the deviation of the envelope peak from zero is not known.

Chou, Dean-Yi↗
NASA NTRS1972

Very High-Frequency (VHF) ionospheric scintillation fading measurements at Lima, Peru

During the spring equinox of 1970, scintillating signals at VHF (136.4 MHz) were observed at Lima, Peru. The transmission originated from ATS 3 and was observed through a pair of antennas spaced 1200 feet apart on an east-west baseline. The empirical data were digitized, reduced, and analyzed. The results include amplitude probability density and distribution functions, time autocorrelation functions, cross correlation functions for the spaced antennas, and appropriate spectral density functions. Results show estimates of the statistics of the ground diffraction pattern to gain insight into gross ionospheric irregularity size, and irregularity velocity in the antenna planes.

Blank, H. A.↗
NASA NTRS1984

Strong fluctuation theory for electromagnetic wave scattering by a layer of random discrete scatterers

The strong fluctuation theory is applied to the study of electromagnetic wave scattering from a layer of random discrete scatterers. The singularity of the dyadic Green's function is taken into account in the calculation of the effective permittivity functions. The correlation functions for the random medium with different scatterer constituents and size distributions are derived. Applying the dyadic Green's function for a two-layer medium and using the bilocal and distorted Born approximations, the first and the second moments of the fields are then calculated. Both the backscattering and bistatic scattering coefficients are obtained, and the former is shown to match favorably with experimental data obtained from snow fields.

Jin, Y. Q.↗