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At least 289 records · Page 16

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis

The purpose of this study is the development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates and the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The procedure was also modified to allow coarse parallelization of the solution algorithm. This document is a final report outlining the development and techniques used in the procedure. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Numerical dissipation is used to gain solution stability but is reduced in viscous dominated flow regions. Local time stepping and implicit residual smoothing are used to increase the rate of convergence. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes being generated by the system (TIGG3D) developed earlier under this contract. The grid generation scheme meets the average-passage requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. Pure internal flow solutions were obtained as well as solutions with flow about the cowl/nacelle and various engine core flow conditions. The efficiency of the solution procedure was shown to be the same as the original analysis.

Crook, Andrew J.↗

Investigation of an Optimum Detection Scheme for a Star-Field Mapping System

An investigation was made to determine the optimum detection scheme for a star-field mapping system that uses coded detection resulting from starlight shining through specially arranged multiple slits of a reticle. The computer solution of equations derived from a theoretical model showed that the greatest probability of detection for a given star and background intensity occurred with the use of a single transparent slit. However, use of multiple slits improved the system's ability to reject the detection of undesirable lower intensity stars, but only by decreasing the probability of detection for lower intensity stars to be mapped. Also, it was found that the coding arrangement affected the root-mean-square star-position error and that detection is possible with error in the system's detected spin rate, though at a reduced probability.

Aldridge, M. D.↗

Role of Multiple Atmospheric Reflections in Formation of Electron Distribution Function in the Diffuse Aurora Region

The precipitation of high-energy magnetospheric electrons (E greater than 500-600 electronvolts) in the diffuse aurora contributes significant energy flux into Earth's ionosphere. In the diffuse aurora, precipitating electrons initially injected from the plasmasheet via wave-particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These initially precipitating electrons of magnetospheric origin can be additionally reflected back into the magnetosphere by the two magnetically conjugated atmospheres, leading to a series of multiple reflections that can greatly influence the initially precipitating flux at the upper ionospheric boundary (700-800 kilometers) and the resultant population of secondary electrons and electrons cascading toward lower energies. We present the solution of the Boltzmann.Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E is less than or equal to 600 electronvolts) and their energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account the role of multiple atmospheric reflections of the precipitated electrons that were initially moved into the loss cone via wave.particle interaction processes in Earth's plasmasheet.

Khazanov, George V.↗

TRW vortex-lattice method subsonic aerodynamic analysis for multiple-lifting-surfaces (N. surface) TRW program number HA010B

The program was designed to provide solutions of engineering accuracy for determining the aerodynamic loads on single- or multiple-lifting-surface configurations that represent vehicles in subsonic flight, e.g., wings, wing-tail, wing-canard, lifting bodies, etc. The preparation is described of the input data, associated input arrangement, and the output format for the program data, including specification of the various operational details of the program such as array sizes, tape numbers utilized, and program dumps. A full description of the underlying theory used in the program development and a review of the program qualification tests are included.

Gomez, A. V.↗

Optimization of Residual Stresses in MMC's Using Compensating/Compliant Interfacial Layers. Part 2: OPTCOMP User's Guide

A user's guide for the computer program OPTCOMP is presented in this report. This program provides a capability to optimize the fabrication or service-induced residual stresses in uni-directional metal matrix composites subjected to combined thermo-mechanical axisymmetric loading using compensating or compliant layers at the fiber/matrix interface. The user specifies the architecture and the initial material parameters of the interfacial region, which can be either elastic or elastoplastic, and defines the design variables, together with the objective function, the associated constraints and the loading history through a user-friendly data input interface. The optimization procedure is based on an efficient solution methodology for the elastoplastic response of an arbitrarily layered multiple concentric cylinder model that is coupled to the commercial optimization package DOT. The solution methodology for the arbitrarily layered cylinder is based on the local-global stiffness matrix formulation and Mendelson's iterative technique of successive elastic solutions developed for elastoplastic boundary-value problems. The optimization algorithm employed in DOT is based on the method of feasible directions.

Pindera, Marek-Jerzy↗

Conductance measurement circuit with wide dynamic range

A conductance measurement circuit to measure conductance of a solution under test with an output voltage proportional to conductance over a 5-decade range, i.e., 0.01 uS to 1000 uS or from 0.1 uS to 10,000 uS. An increase in conductance indicates growth, or multiplication, of the bacteria in the test solution. Two circuits are used each for an alternate half-cycle time periods of an alternate squarewave in order to cause alternate and opposite currents to be applied to the test solution. The output of one of the two circuits may be scaled for a different range optimum switching frequency dependent upon the solution conductance and to enable uninterrupted measurement over the complete 5-decade range. This circuitry provides two overlapping ranges of conductance which can be read simultaneously without discontinuity thereby eliminating range switching within the basic circuitry. A VCO is used to automatically change the operating frequency according to the particular value of the conductance being measured, and comparators indicate which range is valid and also facilitate computer-controlled data acquisition. A multiplexer may be used to monitor any number of solutions under test continuously.

Mount, Bruce E.↗

A Spacecraft Housekeeping System-on-Chip in a Radiation Hardened Structured ASIC

Housekeeping systems are essential to health monitoring of spacecraft and instruments. Typically, sensors are distributed across various sub-systems and data is collected using components such as analog-to-digital converters, analog multiplexers and amplifiers. In most cases programmable devices are used to implement the data acquisition control and storage, and the interface to higher level systems. Such discrete implementations require additional size, weight, power and interconnect complexity versus an integrated circuit solution, as well as the qualification of multiple parts. Although commercial devices are readily available, they are not suitable for space applications due the radiation tolerance and qualification requirements. The Housekeeping System-o n-A-Chip (HKSOC) is a low power, radiation hardened integrated solution suitable for spacecraft and instrument control and data collection. A prototype has been designed and includes a wide variety of functions including a 16-channel analog front-end for driving and reading sensors, analog-to-digital and digital-to-analog converters, on-chip temperature sensor, power supply current sense circuits, general purpose comparators and amplifiers, a 32-bit processor, digital I/O, pulse-width modulation (PWM) generators, timers and I2C master and slave serial interfaces. In addition, the device can operate in a bypass mode where the processor is disabled and external logic is used to control the analog and mixed signal functions. The device is suitable for stand-alone or distributed systems where multiple chips can be deployed across different sub-systems as intelligent nodes with computing and processing capabilities.

Suarez, George↗

Sensing Small Uncrewed Aerial Vehicles with Distributed Radars for Advanced Air Mobility Surveillance

In the context of Advanced and Urban Air Mobility major attention is being reserved to the development of sensing strategies for small Uncrewed Aerial Vehicles (sUAVs) to enable their safe operations in and around urban areas. Such strategies should rely on non-cooperative distributed sensors to strengthen the surveillance solution towards the unreliability of Global Navigation Satellite System (GNSS) positioning information, which is typical for low-altitude-flying platforms in urban regions, and increase the monitored airspace volume. To this aim, this paper proposes a fusion solution for a network of distributed ground-based radars, which can be exploited to not only increase the coverage over large airspace volumes but also improve the overall detectability and traceability of sUAVs by leveraging on multiple views over the same area. The solution exploits a centralized fusion scheme in which measurements collected by each radar are shared with a Fusion Center where Kalman Filtering is exploited to build a unique, fused track. Tests conducted on experimental data collected using two sUAVs as flying targets and three distributed radars showed that the proposed solution can produce an increase in coverage from about 20 % (single radar configuration) to about 80 % of the targets’ flight path, as well as a finer accuracy yielding meter and meter-per-second root mean square error values on position and velocity components.

Federica Vitiello↗

A study of equation solvers for linear and non-linear finite element analysis on parallel processing computers

Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.

Watson, Brian C.↗

Propagation of wide bandwidth signals through strongly turbulent ionized media

Analytic and numerical techniques are presented which directly address the problem of propagation of wide bandwidth signals through random ionized media. This work is applicable to the problems of satellite communication and space based radar observation through a disturbed ionospheric propagation channel that would result from a high altitude chemical release or nuclear detonation. An analytic solution is presented for the two-position, two-frequency mutual coherence function for spherical wave propagation in the strong scattering limit. This solution is used to derive simple expressions for the power impulse response function and to determine its relationship to the important parameters of decorrelation distance and coherence bandwidth which describe the disturbed propagation channel. Results for mean time delay and time delay jitter are presented and compared to direct simulation results and to other theoretical calculations. A numerical/analytical solution to the parabolic wave equation is presented in the form of a multiple phase-screen (MPS) propagation simulation. In this very general solution technique, the random medium is divided into a finite number of layers. The field fluctuation through each layer is obtained by replacing the layer by a centrally located thin phase-screen, whose statistical properties are determined from the statistics of the electron-density irregularities. The waveform then propagates from phase-screen to phase-screen via an exact solution to the Fresnel-Kirchnoff equation. For wide bandwidth waveforms, numerical solutions are obtained at a number of discrete frequencies centered about the carrier and then time-domain solutions are obtained by Fourier transform techniques. Detailed results are presented for a number of interesting cases including propagation of a 20 MHz bandwidth signal through a finite barium cloud at a carrier frequency of 100 MHz. One of the major uses of the MPS propagation simulation has been to provide realizations of the received signal after propagation through a disturbed channel. The MPS simulation obtains a general solution of the parabolic wave equation under both weak and strong scattering conditions. A second technique to directly obtain realizations of wide bandwidth waveforms is presented here. This technique is limited to the case of strong scattering but requires only a fraction of the computer resources needed for MPS signal generation. Detailed comparisons of the two signal generation techniques are presented.

Random Media↗

A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows

An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered.

Nayfeh, A. H.↗

Method and apparatus for producing microshells

A method is described for forming hollow particles, or shells, of extremely small size. The shell material is heated to a molten temperature in the presence of a gas that is at least moderately soluble in the shell material, to form a solution of the molten shell material and the soluble gas. The solution is atomized to form a multiplicity of separate droplets that are cooled while in free fall. Cooling of a droplet from the outside traps the desolved gas and forces it to form a gas bubble at the center of the droplet which now forms a gas filled shell. The shell is reheated and then cooled in free fall, in an environment having a lower pressure than the gas pressure in the shell. This causes expansion of the shell and the formation of a shell having a small wall thickness compared to its diameter.

Lee, Mark C.↗

Nongray gas analyses for reflecting walls utilizing a flux technique

A flux formulation for a planar slab of molecular gas radiation bounded by diffuse reflecting walls is developed. While this formulation is limited to the planar geometry, it is useful for studying approximations necessary in modeling nongray radiative heat transfer. The governing equations are derived by considering the history of multiple reflections between the walls. Accurate solutions are obtained by explicitly accounting for a finite number of reflections and approximating the spectral effects of the remaining reflections. Four approximate methods are presented and compared using a single absorption band of H2O. All four methods reduce to an identical zeroth-order formulation, which accounts for all reflections approximately but does handle nonreflected radiation correctly. A single absorption band of CO2 is also considered using the best-behaved approximation for higher orders. A zeroth-order formulation is sufficient to predict the radiative transfer accurately for many cases considered. For highly reflecting walls, higher order solutions are necessary for better accuracy. Including all the important bands of H2O, the radiative source distributions are also obtained for two different temperature and concentration profiles.

Menart, J. A.↗

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Chew, W. C.↗