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NASA NTRS1992

Variational derivation of equation for generalized pair correlation function

The wavefunction of a system is explicitly written down in a fully anti-symmetric way between a fermion pair and a medium, and the equations for each one of them are derived from the variation of total energy for bound systems and by forming appropriate scalar products for continuum states. High-energy particles, such as protons, electrons, and nuclei impinging upon spacecraft, produce secondary radiations. In order to protect the internal environment of spacecraft from these radiations, their intensities are determined in many instances theoretically, and an appropriate program has been developed in the High Energy Science Branch. The purpose of this research is to investigate the problem of indistinguishability of an incident projectile with one of the same in a target.

Malik, F. Bary↗

NASA NTRS1994

How cosmic microwave background correlations at large angles relate to mass autocorrelations in space

The Sachs-Wolfe effect is known to produce large angular scale fluctuations in the cosmic microwave background radiation (CMBR) due to gravitational potential fluctuations. We show how the angular correlation function of the CMBR can be expressed explicitly in terms of the mass autocorrelation function xi(r) in the universe. We derive analytic expressions for the angular correlation function and its multipole moments in terms of integrals over xi(r) or its second moment, J(sub 3)(r), which does not need to satisfy the sort of integral constraint that xi(r) must. We derive similar expressions for bulk flow velocity in terms of xi and J(sub 3). One interesting result that emerges directly from this analysis is that, for all angles theta, there is a substantial contribution to the correlation function from a wide range of distance r and that radial shape of this contribution does not vary greatly with angle.

Blumenthal, George R.↗

NASA NTRS1999

Towards a Rational Model for the Triple Velocity Correlations of Turbulence

This paper presents a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of Group Representation Theory to determine the most general tensorial form of these correlations in terms of all the second- and third-order tensor quantities that appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and therefore had to be developed specifically for this purpose by Professor G. F. Smith. The outcome of this work is a mathematical framework for the construction of algebraic, explicit, and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be an incomplete subset of this new representation, even to lowest order.

Younis, B. A.↗

NASA NTRS2002

Occupant Responses in a Full-Scale Crash Test of the Sikorsky ACAP Helicopter

A full-scale crash test of the Sikorsky Advanced Composite Airframe Program (ACAP) helicopter was performed in 1999 to generate experimental data for correlation with a crash simulation developed using an explicit nonlinear, transient dynamic finite element code. The airframe was the residual flight test hardware from the ACAP program. For the test, the aircraft was outfitted with two crew and two troop seats, and four anthropomorphic test dummies. While the results of the impact test and crash simulation have been documented fairly extensively in the literature, the focus of this paper is to present the detailed occupant response data obtained from the crash test and to correlate the results with injury prediction models. These injury models include the Dynamic Response Index (DRI), the Head Injury Criteria (HIC), the spinal load requirement defined in FAR Part 27.562(c), and a comparison of the duration and magnitude of the occupant vertical acceleration responses with the Eiband whole-body acceleration tolerance curve.

Jackson, Karen E.↗

NASA NTRS2002

Occupant Responses in a Full-Scale Crash Test of the Sikorsky ACAP Helicopter

Jackson, Karen E.↗

NASA NTRS1972

Root mean square fluctuation of a weak magnetic field in an infinite medium of homogeneous stationary turbulence.

The generation of a magnetic field by statistically homogeneous, stationary velocity turbulence is considered. The generation of rms magnetic fluctuation is explicitly demonstrated in the limit of short turbulence correlation time. It is shown that the fluctuation associated with a growing or stationary mean field grows with time such that the ratio of the fluctuation and the square of the mean field tends to a steady value, which is a monotonically decreasing function of the growth rate of the mean field.

Low, B.-C.↗

NASA NTRS1989

Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data

This paper develops techniques to evaluate the discrete Fourier transform (DFT), the autocorrelation function (ACF), and the cross-correlation function (CCF) of time series which are not evenly sampled. The series may consist of quantized point data (e.g., yes/no processes such as photon arrival). The DFT, which can be inverted to recover the original data and the sampling, is used to compute correlation functions by means of a procedure which is effectively, but not explicitly, an interpolation. The CCF can be computed for two time series not even sampled at the same set of times. Techniques for removing the distortion of the correlation functions caused by the sampling, determining the value of a constant component to the data, and treating unequally weighted data are also discussed. FORTRAN code for the Fourier transform algorithm and numerical examples of the techniques are given.

Scargle, Jeffrey D.↗

NASA NTRS1984

Investigation of the influence of the zeta-potential on the filtration rate in the presence of collectors

The value of the zeta-potential does not have an explicit effect, which is expressed by a simple math correlation, on filtration rate when a solution of the tested collector is filtered through a cake prepared under standard conditions from the examined particulate material. The zeta-potential measurements and filtration tests were carried out on silica and galena with solutions contg. a cationic container ANP and Et xanthane, resp. at PH = 6.5, varying concentration of the agent (0-2500 g/ton), and under a vacuum of 100 to 600 mm Hg.

Provirnina, E. V.↗

NASA NTRS2008

Comparison of ALE and SPH Simulations of Vertical Drop Tests of a Composite Fuselage Section into Water

Simulation of multi-terrain impact has been identified as an important research area for improved prediction of rotorcraft crashworthiness within the NASA Subsonic Rotary Wing Aeronautics Program on Rotorcraft Crashworthiness. As part of this effort, two vertical drop tests were conducted of a 5-ft-diameter composite fuselage section into water. For the first test, the fuselage section was impacted in a baseline configuration without energy absorbers. For the second test, the fuselage section was retrofitted with a composite honeycomb energy absorber. Both tests were conducted at a nominal velocity of 25-ft/s. A detailed finite element model was developed to represent each test article and water impact was simulated using both Arbitrary Lagrangian Eulerian (ALE) and Smooth Particle Hydrodynamics (SPH) approaches in LS-DYNA, a nonlinear, explicit transient dynamic finite element code. Analytical predictions were correlated with experimental data for both test configurations. In addition, studies were performed to evaluate the influence of mesh density on test-analysis correlation.

Jackson, Karen E.↗

NASA NTRS1989

The polarizabilities of neon

The static dipole polarizability, second hyperpolarizability, quadrupole polarizability and dipole-dipole-quadrupole hyperpolarizability for the Ne atom are computed, using large Gaussian basis sets and coupled cluster wavefunctions. Correlation effects are substantial, ranging from 15 percent for the dipole polarizability to 40 percent for the second hyperpolarizability. It is confirmed by explicit calculation earlier hypotheses that g-type and higher angular momentum functions and core correlation effects make almost no contribution to these properties in Ne. Triple excitations, on the other hand, are very important, accounting for as much as 25 percent of the correlation contribution to the second hyperpolarizability. The best estimate of the second hyperpolarizability is 119 + or - 4 au, in good agreement with the recent calculations of Maroulis and Thakkar (1989) and the latest experimental result of Shelton (1989).

Taylor, Peter R.↗

NASA NTRS1997

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Jongen, T.↗

NASA NTRS1990

Atomization modeling in a multiphase flow environment and comparison with experiments

An atomization model based on Reitz's instability wave analysis has been implemented into the ARICC3D multiphase CFD combustion code. Preliminary test runs with cold non-evaporating liquid jet and coaxial gas-liquid atomization cases appeared to have verified basic performance of the model, generating realistic-looking sprays. Furthermore, the extended liquid jet is explicitly resolved, and predicted jet lengths agree well with classical correlations. Fair agreement with test data is obtained for predicted spray tip penetrations and liquid mass flux radial distributions, with obvious room for improvement. Some numerical problems also appear to have resulted with the current implementation when low gas Mach number and high liquid velocities are involved.

Liang, P. Y.↗

NASA NTRS2002

Impact Testing and Simulation of a Crashworthy Composite Fuselage Section with Energy-Absorbing Seats and Dummies

A 25-ft/s vertical drop test of a composite fuselage section was conducted with two energy-absorbing seats occupied by anthropomorphic dummies to evaluate the crashworthy features of the fuselage section and to determine its interaction with the seats and dummies. The 5-ft diameter fuselage section consists of a stiff structural floor and an energy-absorbing subfloor constructed of Rohacel foam blocks. The experimental data from this test were analyzed and correlated with predictions from a crash simulation developed using the nonlinear, explicit transient dynamic computer code, MSC.Dytran. The anthropomorphic dummies were simulated using the Articulated Total Body (ATB) code, which is integrated into MSC.Dytran.

Fasanella, Edwin L.↗

NASA NTRS2002

Impact Testing and Simulation of a Crashworthy Composite Fuselage Section with Energy-Absorbing Seats and Dummies

A 25-ft/s vertical drop test of a composite fuselage section was conducted with two energy-absorbing seats occupied by anthropomorphic dummies to evaluate the crashworthy features of the fuselage section and to determine its interaction with the seats and dummies. The 5-ft. diameter fuselage section consists of a stiff structural floor and an energy-absorbing subfloor constructed of Rohacel foam blocks. The experimental data from this test were analyzed and correlated with predictions from a crash simulation developed using the nonlinear, explicit transient dynamic computer code, MSC.Dytran. The anthropomorphic dummies were simulated using the Articulated Total Body (ATB) code, which is integrated into MSC.Dytran.

Fasanella, Edwin L.↗

NASA NTRS2004

Crash Simulation of a Vertical Drop Test of a B737 Fuselage Section with Overhead Bins and Luggage

The focus of this paper is to describe a crash simulation of a 30-ft/s vertical drop test of a Boeing 737 (B737) fuselage section. The drop test of the 10-ft. long fuselage section of a B737 aircraft was conducted in November of 2000 at the FAA Technical Center in Atlantic City, NJ. The fuselage section was outfitted with two different commercial overhead stowage bins. In addition, 3,229-lbs. of luggage were packed in the cargo hold to represent a maximum take-off weight condition. The main objective of the test was to evaluate the response and failure modes of the overhead stowage bins in a narrow-body transport fuselage section when subjected to a severe, but survivable, impact. A secondary objective of the test was to generate experimental data for correlation with the crash simulation. A full-scale 3-dimensional finite element model of the fuselage section was developed and a crash simulation was conducted using the explicit, nonlinear transient dynamic code, MSC.Dytran. Pre-test predictions of the fuselage and overhead bin responses were generated for correlation with the drop test data. A description of the finite element model and an assessment of the analytical/experimental correlation are presented. In addition, suggestions for modifications to the model to improve correlation are proposed.

Jackson, Karen E.↗

NASA NTRS1981

Parameterization of linear wave chemical transport in planetary atmospheres by eddy diffusion

Two-dimensional transport by linear waves is parameterized by wave velocity and temperature correlations and nonconservative properties of the atmosphere in a residual Eulerian framework. Explicit expressions derived for the eddy tracer flux vector are written in eddy diffusion tensor form, but it is demonstrated that strong coupling of chemistry and temperature through the rate constants, as is the case for ozone, requires additional terms proportional to the mixing ratio and not to its gradient. A variety of limiting cases are discussed. In the residual Eulerian framework the K(yz), K(zy) components are nonzero for a nonconservative atmosphere and/or a reactive tracer. Tracers have common transport coefficients in the limit where their chemistry is negligible in comparison to transience. It is shown that the usual one-dimensional vertical eddy diffusion continuity equation is rigorously valid only when the temperature dependence of the rate constants is negligible and the tracer has strong vertical stratification relative to its horizontal variability.

Strobel, D. F.↗

NASA NTRS1998

Multiple GISS AGCM Hindcasts and MSU Versions of 1979-1998

Multiple realizations of the 1979-1998 time period have been simulated by the Goddard Institute for Space Studies Atmospheric General Circulation Model (GISS AGCM) to explore its responsiveness to accumulated forcings, particularly over sensitive agricultural regions. A microwave radiative transfer postprocessor has produced the AGCM's lower tropospheric, tropospheric and lower stratospheric brightness temperature (Tb) time series for correlations with the various Microwave Sounding Unit (MSU) time series available. MSU maps of monthly means and anomalies were also used to assess the AGCM's mean annual cycle and regional variability. Seven realizations by the AGCM were forced by observed sea surface temperatures (sst) through 1992 to gather rough standard deviations associated with internal model variability. Subsequent runs hindcast January 1979 through April 1998 with an accumulation of forcings: observed ssts, greenhouse gases, stratospheric volcanic aerosols. stratospheric and tropospheric ozone and tropospheric sulfate and black carbon aerosols. The goal of narrowing gaps between AGCM and MSU time series was complicated by MSU time series, by Tb simulation concerns and by unforced climatic variability in the AGCM and in the real world. Lower stratospheric Tb correlations between the AGCM and MSU for 1979-1998 reached as high as 0.91 +/-0.16 globally with sst, greenhouse gases, volcanic aerosol, stratospheric ozone forcings and tropospheric aerosols. Mid-tropospheric Tb correlations reached as high as 0.66 +/-.04 globally and 0.84 +/-.02 in the tropics. Oceanic lower tropospheric Tb correlations similarly reached 0.61 +/-.06 globally and 0.79 +/-.02 in the tropics. Of the sensitive agricultural areas considered, Nordeste in northeastern Brazil was simulated best with mid-tropospheric Tb correlations up to 0.75 +/- .03. The two other agricultural regions, in Africa and in the northern mid-latitudes, suffered from higher levels of non-sst variability. Zimbabwe had a maximum mid-tropospheric correlation of 0.54 +/- 0.11 while the U.S. Cornbelt had only 0.25 +/- .10. Precipitation and surface temperature performance are also examined over these regions. Correlations of MSU and AGCM time series mostly improved with addition of explicit atmospheric forcings in zonal bands but not in agricultural regional bins each encompassing only six AGCM gridcells.

Shah, Kathryn Pierce↗

NASA NTRS2003

Jet Noise Physics and Modeling Using First-principles Simulations

An extensive analysis of our jet DNS database has provided for the first time the complex correlations that are the core of many statistical jet noise models, including MGBK. We have also for the first time explicitly computed the noise from different components of a commonly used noise source as proposed in many modeling approaches. Key findings are: (1) While two-point (space and time) velocity statistics are well-fitted by decaying exponentials, even for our low-Reynolds-number jet, spatially integrated fourth-order space/retarded-time correlations, which constitute the noise "source" in MGBK, are instead well-fitted by Gaussians. The width of these Gaussians depends (by a factor of 2) on which components are considered. This is counter to current modeling practice, (2) A standard decomposition of the Lighthill source is shown by direct evaluation to be somewhat artificial since the noise from these nominally separate components is in fact highly correlated. We anticipate that the same will be the case for the Lilley source, and (3) The far-field sound is computed in a way that explicitly includes all quadrupole cancellations, yet evaluating the Lighthill integral for only a small part of the jet yields a far-field noise far louder than that from the whole jet due to missing nonquadrupole cancellations. Details of this study are discussed in a draft of a paper included as appendix A.

Freund, Jonathan B.↗