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NASA NTRS1996

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

Gerritsen, Margot↗

NASA NTRS1996

Two Different Squeeze Transformations

Lorentz boosts are squeeze transformations. While these transformations are similar to those in squeezed states of light, they are fundamentally different from both physical and mathematical points of view. The difference is illustrated in terms of two coupled harmonic oscillators, and in terms of the covariant harmonic oscillator formalism.

Han, D.↗

NASA NTRS1996

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Zingg, David W.↗

NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for Aircraft Acoustic Nacelle Design

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, Kenneth J.↗

NASA NTRS1995

Correlations of Different Surface Tests: Tire Behavior Math Model for the High Speed Civil Transport (HSCT) and Michelin Tire Properties Tests for Boeing 777

In the surfaces correlation study, several different volumetric and drainage measurement techniques for classifying surface texture were evaluated as part of a major study to develop and improve methods for predicting tire friction performance on all types of pavement. The objective of the evaluation was to seek relationships between the different techniques, and to relate those results to surface frictional characteristics. We needed to know how each of the tests could be related to each other. Another of my assigned projects was to make a tire behavior math model for the High Speed Civil Transport (HSCT) using the same methods used for the space shuttle a few years ago. A provided third order equation with two variables was used. This model will also be used for studies with the Boeing 777. Only a few changes will be necessary to adapt it for this other aircraft, which is the newest offered by Boeing. In my final project I was involved with testing the tires for this new aircraft using the Aircraft Landing Dynamics Facility (ALDF) test carriage within the carriage house at LaRC. A 50 inch diameter radial tire manufactured by Michelin Aircraft Tire Corporation had to be tested to double overload of 114,000 pounds. The rated load of each tire is 57,000 pounds, but Boeing required tests assuming failure of a companion tire that could have cost Michelin approximately $12 million to build a facility to provide the required test capability. Here at LaRC, only minimum modifications to the facility were required to perform this specific test.

Roman, Ivan↗

NASA NTRS1994

Do Right- and Left-Handed Monkeys Differ on Cognitive Measures?

Twelve left- and 14 right-handed monkeys were compared on 6 measures of cognitive performance (2 maze-solving tasks, matching-to-sample, delayed matching-to-sample, delayed response using spatial cues, and delayed response using form cues). The dependent variable was trials-to-training criterion for each of the 6 tasks. Significant differences were found between left- and right-handed monkeys on the 2 versions of the delayed response task. Right-handed monkeys reached criterion significantly faster on the form cue version of the task, whereas left-handed monkeys reached criterion significantly faster on delayed response for spatial position (p less than .05). The results suggest that sensitive hand preference measures of laterality can reveal differences in cognitive performance, which in turn may reflect underlying laterality in functional organization of the nervous system.

Hopkins, William D.↗

NASA NTRS1991

Finite Difference Time Domain Electromagnetic Scattering from Frequency-Dependent Lossy Materials

During this effort the tasks specified in the Statement of Work have been successfully completed. The extension of Finite Difference Time Domain (FDTD) to more complicated materials has been made. A three-dimensional FDTD code capable of modeling interactions with both dispersive dielectric and magnetic materials has been written, validated, and documented. This code is efficient and is capable of modeling interesting targets using a modest computer work station platform. However, in addition to the tasks in the Statement of Work, a significant number of other FDTD extensions and calculations have been made. RCS results for two different plate geometries have been reported. The FDTD method has been extended to computing far zone time domain results in two dimensions. Finally, the capability to model nonlinear materials has been incorporated into FDTD and validated. The FDTD computer codes developed have been supplied, along with documentation, and preprints describing the other FDTD advances have been included with this report as attachments.

Luebbers, Raymond J.↗

NASA NTRS1997

Finite Difference Radiative Transfer Model Calculations Compared to Measurements at the Top and Bottom of the Atmosphere

A finite difference radiative transfer program was developed to handle most anisotropic scattering and reflectance problems encountered in the Earth's atmospheric system. The model has been used to reproduce the radiance received by both satellite and ground based radiation measuring instruments. It accurately replicates the radiance measured by both narrow and wide field-of-view instruments with either narrow or broadband wavelength ranges located on the surface and at satellite altitudes. The output of the finite difference code is compared to the measurements by surface pyranometers and a spectroradiometer aboard a high flying aircraft. The program output is also compared to ERBE measurements aboard the ERBS and NOAA-9 satellites as well as the visible bands aboard the GOES-6 and GOES-7 satellites and AVHRR bands 1 and 2 of the NOAA-9 and NOAA-1 1 satellites. The model is within 0.2 % of the radiance received by pyranometers, within 0.6 % of the ERBE radiances, and within 3 % of the radiances measured by the visible bands of the GOES and NOAA AVHRR radiometers.

LeCroy, Stuart R.↗

NASA NTRS1996

Finite Difference Time Marching in the Frequency Domain: A Parabolic Formulation for the Convective Wave Equation

An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Baumeister, K. J.↗

NASA NTRS1988

Phenotype and Age Differences in Blood Gas Characteristics, Electrolytes, Hemoglobin, Plasma Glucose and Cortisol in Female Squirrel Monkeys

Due to its small size, lower cost, tractable nature, successful breeding in captivity and its status near the middle of the primate phylogenetic scale, the squirrel monkey has become an attractive primate model for basic and biomedical research. Although the squirrel monkey now is being used more extensively in many laboratories with diverse interests, only fragmentary reports have been published regarding basic physiological characteristics, or baseline blood reference values of different phenotypes, particularly blood gases, hematology and serum chemical constituents. It is becoming recognized increasingly that these baseline blood reference values are important not only in the care and maintenance of the squirrel monkey, but are critical for assessing normal physiological status, as well as the effects of various experimental treatments. The purpose of this study was to compare differences in blood gases, electrolytes, hematology, blood glucose and cortisol among young and old Bolivian (Roman type) and Colombian (Gothic type) phenotypes of the squirrel monkey.

Brizzee, K. R.↗

NASA NTRS1997

Reflection Coefficients on Surfaces of Different Periodic Structure

Diffraction properties of lossy periodic gratings with the metal base were investigated by solving Maxwell's equations numerically using the differential method. Two periodic surfaces were employed in the simulation: triangle structure and tilting triangle structure. Based on the numerical solution and in conjunction with the algorithm of Adams-Moulton, we computed reflection coefficients of plane waves with different wavelengths and different incident angles. The dielectric properties were also explored using various dielectric constants. The results show that the reflection coefficients of both TE and TM waves are quite sensitive to the incident angles of the plane waves when the metal sheet exists, which is in good agreement with the experimental data.

Niu, Pengfei↗

NASA NTRS1998

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

Nordstrom, Jan↗

NASA NTRS1961

The Use of Higher-Order Difference Methods in Beam Vibration Analysis

Simple and higher-order difference methods for the solution for the natural frequencies of vibration of a uniform beam are compared. The same basic higher-order method is used throughout for the interior cells, but three different methods of boundary-condition representation are given. Tables and graphs of the error in mode frequencies, as compared with a continuous beam, are given for the various methods as a function of the number of cells. It is concluded that higher-order methods improve accuracy for a given number of cells, with essentially no change in the quantity of computing equipment required.

Greenwood, Donald T.↗

NASA NTRS1959

Performance of Typical Rear-Stage Axial-Flow Compressor Rotor Blade Row at Three Different Blade Setting Angles

A comparison of the performance of a single-stage rotor run at three different blade setting angles is presented. The rotor was of a design typical for a last stage of a multistage compressor. At each setting angle, the rotor blade row was operated from 53 to 100 percent of equivalent maximum speed (850 ft/sec tip speed) at constant inlet pressure. Hot-wire anemometry was used to observe rotating-stall and surge patterns in time unsteady flow. Results indicated that an increase in peak pressure ratio and an increase in maximum equivalent weight flow were obtained at each speed investigated when the blade setting angle was decreased. An increase in peak efficiency was achieved with decrease in blade setting angle for part of the range of speeds investigated. However, the peak efficiencies for the three blade setting angles were approximately the same at the maximum speed investigated. The flow ranges for all three configurations were about the same at minimum speed and decreased at almost the same rate when the rotative speed was increased through part of the range of speeds investigated. At maximum speed, the flow range for the smallest setting angle was considerably less than the flow range for the other two configurations. A decrease in efficiency and flow range for the smallest blade setting angle at maximum speed can be attributed primarily to a Mach number effect. In addition, because of the difference in projected axial chord lengths at the casing wall, some effect on performance could be expected from the change in three-dimensional flow occurring at the tip. Rotating-stall characteristics for the two smaller blade setting angles were essentially the same. Only surge could be detected for the largest blade setting angle in the unstable-flow region of operation.

Kussoy, Marvin I.↗

NASA NTRS1998

Modal Analysis of Embedded Passive Damping Materials in Composite Plates with Different Orientations

This report presents an experimental and numerical investigation of the free vibration of cantilevered composite plates with and without passive damping. A total of seven composite material plates are considered. The lay-up sequences for the two plates without damping are [90/90/0/0], and [90/0/90/0]; the other five plates are the same as the first two with two embedded layers of passive damping material. The passive damping material is embedded at different locations in the plate with orientation [90/0/90/0],. The damping material employed is a 3M material (SJ-2015 ISD 112) with peak damping properties in the ambient temperature range (32 F to 140 F). The composite material used is a carbon fiber (977-2)/epoxy resin (IM7). The effect of the passive damping system employed in this study for the composite plates are discussed. Modal testing is performed on these plates to determine resonant frequencies, amplitude and mode shape information. Numerical results are obtained using COSMOS/M software for the plates without damping. The experimental and numerical results are in very good agreement for different laminated plates without damping layers.

Kehoe, Michael↗

NASA NTRS1997

The Identification of Two Different Spectral Types of Pulses in Gamma-Ray Bursts

It is shown in this study that two different types of spectral emission are generally produced in gamma-ray bursts. A subset of bursts is identified that exhibits a marked lack of fluence above 300 keV, and these bursts are shown to have luminosities about an order of magnitude lower than bursts with significant fluence above 300 keV. The bursts lacking emission above 300 keV exhibit an effectively homogeneous intensity distribution. In addition, it is shown that both types of emission are common in many bursts, demonstrating that a single source object is capable of generating both of them. These results strongly favor a gamma-ray burst source object that produces two different types of emission with varying degrees of superposition. The impact of this behavior is strong enough that it affects the properties of the burst intensity distribution, as well as the burst spectral characteristics.

Pendleton, G. N.↗

NASA NTRS1997

The Identification of Two Different Spectral Types of Pulses in Gamma-Ray Bursts

Pendleton, G. N.↗

NASA NTRS1999

Acoustic Treatment Design Scaling Methods: Numerical Simulation of the Nonlinear Acoustic Impedance of a Perforated Plate Single-Degree-of-Freedom Resonator Using a Time-Domain Finite Difference Method - Volume 4

Single-degree-of-freedom resonators consisting of honeycomb cells covered by perforated facesheets are widely used as acoustic noise suppression liners in aircraft engine ducts. The acoustic resistance and mass reactance of such liners are known to vary with the intensity of the sound incident upon the panel. Since the pressure drop across a perforated liner facesheet increases quadratically with the flow velocity through the facesheet, this is known as the nonlinear resistance effect. In the past, two different empirical frequency domain models have been used to predict the Sound Pressure Level effect of the incident wave on the perforated liner impedance, one that uses the incident particle velocity in isolated narrowbands, and one that models the particle velocity as the overall velocity. In the absence of grazing flow, neither frequency domain model is entirely accurate in predicting the nonlinear effect that is measured for typical perforated sheets. The time domain model is developed in an attempt to understand and improve the model for the effect of spectral shape and amplitude of multi-frequency incident sound pressure on the liner impedance. A computer code for the time-domain finite difference model is developed and predictions using the models are compared to current frequency-domain models.

Kraft, R. E.↗