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NASA NTRS1974

A new formulation of the conservation equations of fluid dynamics

The computation of time-dependent flows has inspired a new, higher-dimensional formulation of the conservation equations of fluid dynamics in which time is treated as a fourth coordinate. The formulation is derived for a constant-density flow, and then extended to a variable-density flow by introducing a fifth, fictitious coordinate. This new coordinate can also act as a source coordinate, so that external source terms can be included. The analysis is carried out for both incompressible, stratified flow, and compressible equilibrium flow. The results are then extended to non-equilibrium and magnetohydrodynamic flows. Several applications of the new formulation to the computation of time-dependent flows are discussed.

Vinokur, M.↗

NASA NTRS2014

Acoustics of Jet Surface Interaction-Scrubbing Noise

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity of the structure or embedded in the airframe. While such integrated systems are intended to shield noise from community, they also introduce new sources of sound. Sound generation due to interaction of a jet flow past a nearby solid surface is investigated here using the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far field sound as governed by the variable density Pridmore-Brown equation. The propagation Greens function is solved numerically for a high aspect-ratio rectangular jet starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. It is shown the magnitude of the Greens function decreases with increasing source frequency andor jet temperature. The phase remains constant for a rigid surface, but varies with source location when subject to an impedance type boundary condition. The Greens function in the absence of the surface, and flight effect are also investigated.

Propulsion Noise↗

NASA NTRS2014

Acoustics of Jet Surface Interaction - Scrubbing Noise

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity to the structure or embedded in the airframe. While such integrated systems are intended to shield noise from the community, they also introduce new sources of sound. Sound generation due to interaction of a jet flow past a nearby solid surface is investigated here using the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far field sound as governed by the variable density Pridmore-Brown equation. The propagation Green's function is solved numerically for a high aspect-ratio rectangular jet starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. It is shown the magnitude of the Green's function decreases with increasing source frequency and/or jet temperature. The phase remains constant for a rigid surface, but varies with source location when subject to an impedance type boundary condition. The Green's function in the absence of the surface, and flight effects are also investigated

Jet Noise↗

NASA NTRS1973

Galactic gamma rays: Models involving variable cosmic-ray density

Mathematical models were developed to determine variable cosmic ray flux around the galactic plane. Data indicate point sources, molecular hydrogen concentration, increased cosmic ray density toward the galactic center, and neutral pion production combine to cause radiation density variables in the galactic plane.

Strong, A. W.↗

NASA NTRS1993

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

Moghaddam, M.↗

NASA NTRS2013

Jet Surface Interaction-Scrubbing Noise

Generation of sound due to scrubbing of a jet flow past a nearby solid surface is investigated within the framework of the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far-field sound as governed by the variable density Pridmore- Brown equation. The propagation Green's function should be solved numerically starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. The equivalent sources of aerodynamic sound are associated with non-linear momentum flux and enthalpy flux terms that appear in the linearized Navier-Stokes equations. These multi-pole sources should be modeled and evaluated with input from a Reynolds-Averaged Navier-Stokes (RANS) solver with an appropriate turbulence model.

Khavaran, Abbas↗

NASA NTRS1980

Application of remote sensing techniques to hydrography with emphasis on bathymetry

Remote sensing techniques are utilized for the determination of hydrographic characteristics, with emphasis in bathymetry. Two sensor systems were utilized: the Metric Camera Wild RC-10 and the Multispectral Scanner of LANDSAT Satellite (MSS-LANDSAT). From photographs of the metric camera, data of photographic density of points with known depth are obtained. A correlation between the variables density x depth is calculated through a regression straight line. From this line, the depth of points with known photographic density is determined. The LANDSAT MSS images are interpreted automatically in the Iterative Multispectral Analysis System (I-100) with the obtention of point subareas with the same gray level. With some simplifications done, it is assumed that the depth of a point is directly related with its gray level. Subareas with points of the same depth are then determined and isobathymetric curves are drawn. The coast line is obtained through the sensor systems already mentioned. Advantages and limitations of the techniques and of the sensor systems utilized are discussed and the results are compared with ground truth.

Dejesusparada, N.↗

NASA NTRS1990

Modeling the dust size distribution in comets with dust fragmentation

A hydrodynamic model was developed of a spherically symmetric dusty gas flow in a cometary atmosphere assuming a single fluid, inviscid, perfect gas. The hydrodynamics for gas and dust, which involves the gas drag force (momentum transfer), heat exchange between gas and dust, photodissociation energy for H2O gas, and radiative heating and cooling terms for dust particles, are solved using the Gear method for stiff, coupled differential equations. Calculations were done with a dust size distribution for radii alpha = 0.01 micron to 10 cm with densities variable with the size. A nucleus size of 4.0 km radius with a density of 0.5 g/cu cm and a total dust-to-gas mass ratio chi = 1 was adopted. There are indications from in situ observations that dust particle fragment into smaller ones. Fragmentation of dust particles was incorporated into the model. This is done by adding source and sink terms in the continuity equations for the dust. Lifetimes for the decay of dust particles were assumed as a function of particle size. It is also assumed that dust particles always fragment only into the next smaller size.

Konno, Ichishiro↗

NASA NTRS1996

The Favre-Reynolds Average Distinction and a Consistent Gradient Transport Expression for the Dissipation

Two equation and higher order closures for compressible turbulence fail to capture the compressible wall layers' log scaling. Accounting for the distinction between Favre and Reynolds averaged variables in the compressible moment equations indicate that turbulent transport expressions obtained using the 'variable density approximation' are in error. The error is related to the enstrophy, a Reynolds averaged variable appearing in the equation for the Favre averaged k; recognizing this fact an expression for the transport of dissipation consistent with simple mixing length arguments is obtained. Within the (limited) context of a gradient transport hypothesis a rational form for the turbulent transport of the dissipation is found. Modestly better agreement with the well established compressible Van Driest log scaling is found in k - epsilon calculation.

Ristorcelli, J. R.↗

NASA NTRS2003

Jet Noise Modeling for Coannular Nozzles Including the Effects of Chevrons

Development of good predictive models for jet noise has always been plagued by the difficulty in obtaining good quality data over a wide range of conditions in different facilities.We consider such issues very carefully in selecting data to be used in developing our model. Flight effects are of critical importance, and none of the means of determining them are without significant problems. Free-jet flight simulation facilities are very useful, and can provide meaningful data so long as they can be analytically transformed to the flight frame of reference. In this report we show that different methodologies used by NASA and industry to perform this transformation produce very different results, especially in the rear quadrant; this compels us to rely largely on static data to develop our model, but we show reasonable agreement with simulated flight data when these transformation issues are considered. A persistent problem in obtaining good quality data is noise generated in the experimental facility upstream of the test nozzle: valves, elbows, obstructions, and especially the combustor can contribute significant noise, and much of this noise is of a broadband nature, easily confused with jet noise. Muffling of these sources is costly in terms of size as well as expense, and it is particularly difficult in flight simulation facilities, where compactness of hardware is very important, as discussed by Viswanathan (Ref. 13). We feel that the effects of jet density on jet mixing noise may have been somewhat obscured by these problems, leading to the variable density exponent used in most jet noise prediction procedures including our own. We investigate this issue, applying Occam s razor, (e.g., Ref. 14), in a search for the simplest physically meaningful model that adequately describes the observed phenomena. In a similar vein, we see no reason to reject the Lighthill approach; it provides a very solid basis upon which to build a predictive procedure, as we believe we demonstrate in this report. Another feature of our approach is that the analyses are all conducted with lossless spectra, rather than Standard Day spectra, as is often done in industry. We feel that it is important to isolate the effects of as many physical processes as practical. Atmospheric attenuation can then be included using the relations developed for NASA by Shields and Bass (Ref. 15), which are available in both FOOTPR and ANOPP. The current approach to coannular jet noise prediction used in FOOTPR is reported in Reference 16, which updates the earlier conventional-velocity-profile (CVP, Ref. 17) and inverted-velocity-profile (IVP, Ref. 18) models.

Stone, James R.↗

NASA NTRS1981

Use of collateral information to improve LANDSAT classification accuracies

Methods to improve LANDSAT classification accuracies were investigated including: (1) the use of prior probabilities in maximum likelihood classification as a methodology to integrate discrete collateral data with continuously measured image density variables; (2) the use of the logit classifier as an alternative to multivariate normal classification that permits mixing both continuous and categorical variables in a single model and fits empirical distributions of observations more closely than the multivariate normal density function; and (3) the use of collateral data in a geographic information system as exercised to model a desired output information layer as a function of input layers of raster format collateral and image data base layers.

Strahler, A. H.↗

NASA NTRS2008

Large-Scale Structure of the Molecular Gas in Taurus Revealed by High Spatial Dynamic Range Spectral Line Mapping

Viewgraph topics include: optical image of Taurus; dust extinction in IR has provided a new tool for probing cloud morphology; observations of the gas can contribute critical information on gas temperature, gas column density and distribution, mass, and kinematics; the Taurus molecular cloud complex; average spectra in each mask region; mas 2 data; dealing with mask 1 data; behavior of mask 1 pixels; distribution of CO column densities; conversion to H2 column density; variable CO/H2 ratio with values much less than 10(exp -4) at low N indicated by UV results; histogram of N(H2) distribution; H2 column density distribution in Taurus; cumulative distribution of mass and area; lower CO fractional abundance in mask 0 and 1 regions greatly increases mass determined in the analysis; masses determined with variable X(CO) and including diffuse regions agrees well with the found from L(CO); distribution of young stars as a function of molecular column density; star formation efficiency; star formation rate and gas depletion; and enlarged images of some of the regions with numerous young stars. Additional slides examine the origin of the Taurus molecular cloud, evolution from HI gas, kinematics as a clue to its origin, and its relationship to star formation.

molecular clouds↗

NASA NTRS1977

90-GHz flux-density measurements of variable radio sources

Results are presented for measurements of the flux densities of 10 variable extragalactic sources at 85.2 or 90 GHz, which were made over a period of almost seven years with the NRAO 36-ft millimeter-wave antenna. The primary flux-density calibration standards used include Jupiter, Saturn, Mars, and the small-diameter Galactic source DR 21. Measured flux densities are given as a function of time (in years) for the sources 3C 84, NRAO 150, 3C 120, OJ 287, 4C 39.25, 3C 273, 3C 279, 3C 345, BL Lac, and 3C 454.3. No statistically meaningful flux-density changes during an observing interval (1 to 3 days) are detected for any source, and a high degree of correlation between flux-density variations at 85.2 or 90 GHz and those observed at lower frequencies is found in all 10 sources. Some variations observed at different frequencies in several individual sources are briefly discussed.

Hobbs, R. W.↗

NASA NTRS2005

Energy Finite Element Analysis for Computing the High Frequency Vibration of the Aluminum Testbed Cylinder and Correlating the Results to Test Data

The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.

Vlahopoulos, Nickolas↗

NASA NTRS1995

Long term variability of B supergiant winds

The object of this observing proposal was to sample wind variability in B supergiants on a daily basis over a period of several days in order to determine the time scale with which density variability occurs in their winds. Three stars were selected for this project: 69 Cyg (B0 Ib), HD 164402 (B0 Ib), and HD 47240 (B1 Ib). Three grey scale representations of the Si IV lambda lambda 1400 doublet in each star are attached. In these figures, time (in days) increases upward, and the wavelength (in terms of velocity relative to the rest wavelength of the violet component of the doublet) is the abscissa. The spectra are normalized by a minimum absorption (maximum flux) template, so that all changes appear as absorptions. As a result of these observations, we can now state with some certainty that typical B supergiants develop significant wind inhomogeneities with recurrence times of a few days, and that some of these events show signs of strong temporal coherence.

Massa, Derck L.↗

NASA NTRS2002

Optimal Design of Functionally Graded Metallic Foam Insulations

The focus of our work has been on developing an insight into the physics that govern the optimum design of thermal insulation for use in thermal protection systems of launch vehicle. Of particular interest was to obtain optimality criteria for designing foam insulations that have density (or porosity) distributions through the thickness for optimum thermal performance. We investigate the optimum design of functionally graded thermal insulation for steady state heat transfer through the foam. We showed that the heat transfer in the foam has competing modes, of radiation and conduction. The problem assumed a fixed inside temperature of 400 K and varied the aerodynamic surface heating on the outside surface from 0.2 to 1.0 MW/sq m. The thermal insulation develops a high temperature gradient through the thickness. Investigation of the model developed for heat conduction in foams showed that at high temperatures (as on outside wall) intracellular radiation dominates the heat transfer in the foam. Minimizing radiation requires reducing the pore size, which increases the density of the foam. At low temperatures (as on the inside wall), intracellular conduction (of the metal and air) dominates the heat transfer. Minimizing conduction requires increasing the pore size. This indicated that for every temperature there was an optimum value of density that minimized the heat transfer coefficient. Two optimization studies were performed. One was to minimize the heat transmitted though a fixed thickness insulation by varying density profiles. The second was to obtain the minimum mass insulation for specified thickness. Analytical optimality criteria were derived for the cases considered. The optimality condition for minimum heat transfer required that at each temperature we find the density that minimizes the heat transfer coefficient. Once a relationship between the optimum heat transfer coefficient and the temperature was found, the design problem reduced to the solution of a simple nonlinear differential equation. Preliminary results of this work were presented at the American Society of Composites meeting, and the final version was submitted for publication in the AIAA Journal. In addition to minimizing the transmitted heat, we investigated the optimum design for minimum weight given an acceptable level of heat transmission through the insulation. The optimality criterion developed was different from that obtained for minimizing beat transfer coefficient. For minimum mass design, we had to find for a given temperature the optimum density, which minimized the logarithmic derivative of the insulation thermal conductivity with respect to its density. The logarithmic derivative is defined as the ratio of relative change in the dependent response (thermal conductivity) to the relative change in the independent variable (density). The results have been documented as a conference paper that will be presented at the upcoming AIAA.

Haftka, Raphael T.↗

NASA NTRS2012

Testing of Candidate Rigid Heatshield Materials at LHMEL for the Entry, Descent, and Landing Technology Development Project

The material testing results described in this paper were part of a material development program of vendor-supplied, proposed heat shield materials. The goal of this program was to develop low density, rigid material systems with an appreciable weight savings over phenolic-impregnated carbon ablator (PICA) while improving material response performance. New technologies, such as PICA-like materials in honeycomb or materials with variable density through-the-thickness were tested. The material testing took place at the Wright-Patterson Air Force Base Laser Hardened Materials Laboratory (LHMEL) using a 10.6 micron CO2 laser operating with the test articles immersed in a nitrogen-gas environment at 1 atmosphere pressure. Test measurements included thermocouple readings of in-depth temperatures, pyrometer readings of surface temperatures, weight scale readings of mass loss, and sectioned-sample readings of char depth. Two laser exposures were applied. The first exposure was at an irradiance of 450 W/cm2 for 50 or 60 seconds to simulate an aerocapture maneuver. The second laser exposure was at an irradiance of 115 W/cm2 for 100 seconds to simulate a planetary entry. Results from Rounds 1 and 2 of these screening tests are summarized.

Sepka, Steven↗

NASA NTRS1983

Two-dimensional photometry of planetary nebulae

In connection with the study of planetary nebulae, problems still exist in understanding such basic properties as three-dimensional structure, optical opacity to the central star's ionizing flux, and electron temperature and electron density variations within the nebular gas. To study these properties, two-dimensional images taken in many spectral lines are required. However, such a study presents a formidable problem in data analysis. In the present investigation, an attempt has been made to overcome the difficulties by using an imaging system which encodes the data digitally. Calibrated intensity maps could be constructed to test models of ionization structure and to produce two-dimensional maps of electron temperature and density. Both the results of a uniform-shell test and the nature of the solutions for the volume emissivity were found to support a nebular model in which the bright ring is part of a closed shell of variable density that resembles the torus proposed by Minkowski and Osterbrock (1960).

Kupferman, P. N.↗