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At least 325 records · Page 18

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

Young, Gerald W.↗

Transport of liquid state nitrogen through long length service lines during thermal/vacuum testing

Physical and analytical aspects associated with the transport are presented. Included is a definition of the problems and difficulties imposed by the servicing of a typical solid cryogen system, as well as a discussion of the transport requirements and of the rationale which governed their solution. A successful detailed transport configuration is defined, and the application of established mathematics to the design approach is demonstrated. The significance of head pressure, pressure drop, line friction, heat leak, Reynolds number, and the fundamental equilibrium demands of pressure and temperature were examined as they relate to the achievement of liquid state flow. Performance predictions were made for the transport system, and several analytical quantities are tabulated. These data are analyzed and compared with measured and calculated results obtained while actually servicing a solid cryogen system during thermal/vacuum testing.

Florio, F. A.↗

Preliminary numerical analysis of improved gas chromatograph model

A mathematical model for the gas chromatograph was developed which incorporates the heretofore neglected transport mechanisms of intraparticle diffusion and rates of adsorption. Because a closed-form analytical solution to the model does not appear realizable, techniques for the numerical solution of the model equations are being investigated. Criteria were developed for using a finite terminal boundary condition in place of an infinite boundary condition used in analytical solution techniques. The class of weighted residual methods known as orthogonal collocation is presently being investigated and appears promising.

Woodrow, P. T.↗

Effects of several factors on theoretical predictions of airplane spin characteristics

The influence of different mathematical and aerodynamic models on computed spin motion was investigated along with the importance of some of the aerodynamic and nonaerodynamic quantities defined in these models. An analytical technique was used which included the aerodynamic forces and moments acting on a spinning aircraft due to steady rotational flow and the contribution of the rotary derivatives to the oscillatory component of the total angular rates. It was shown that (1) during experimental-analytical correlation studies, the flight-recorded control time histories must be faithfully duplicated since the spinning motion can be sensitive to a small change in the application of the spin entry controls; (2) an error in the assumed inertias, yawing moments at high angle of attack, and initial spin entry bank angle do not influence the developed spin significantly; (3) damping in pitch derivatives and the center of gravity location play a role in the spinning motion; and (4) the experimental spin investigations conducted in a constant atmospheric density environment duplicate the Froude number only at the initial full-scale spin altitude (since the full-scale airplane at high altitudes experiences large density changes during the spin.)

Bihrle, W., Jr.↗

Parameter identification methods for improving structural dynamic models

There is an increasing need to develop Parameter Identification methods for improving structural dynamic models, based on the inability of engineers to produce mathematical models which correlate with experimental data. This research explores the efficiency of combining Component Mode Synthesis (substructuring) methods with Parameter Identification procedures in order to improve analytical modeling of structural components and their connections. Improvements are computed in terms of physical stiffness and damping parameters in order that the physical characteristics of the model can be better understood. Connections involving both viscous and friction damping are investigated. Substructuring methods are utilized to reduce the complexity of the identification problem. Component and inter-component structural connection properties are evaluated and identified independently, thus simplifying the identification problem. It is shown that modal test data is effective for identifying modeling problems associated with structural components, and for determining the stiffness and damping properties of intercomponent connections. In general, Parameter Identification is improved when greater quantities of experimental data are available.

Lawrence, Charles↗

An Analytical Treatment of Aircraft Propeller Precession Instability

An analytical investigation is made of a precession-type instability which can occur in a flexibly supported aircraft-engine-propeller combination. By means of an idealized mathematical model which is comprised of a rigid power-plant system flexibly mounted in pitch and yaw to a fixed backup structure, the conditions required for neutral stability are determined. The paper also examines the sensitivity of the stability boundaries to changes in such parameters as stiffness, damping, and asymmetries in the engine mount, propeller speed, airspeed, Mach number, propeller thrust, and location of pitch and yaw axes. Stability is found to depend strongly on the damping and stiffness in the system. With the use of nondimensional charts, theoretical stability boundaries are compared with experimental results obtained in wind-tunnel tests of an aeroelastic airplane model. In general, the theoretical results, which do not account for wing response, show the same trends as observed experimentally; however, for a given set of conditions calculated airspeeds for neutral stability are consistently lower than the measured values. Evidently, this result is due to the fact that wing response tends to add damping to the system.

Reed, Wilmer H., III↗

Analytic representations of secondary-electron spectra

A general method for systematizing a bulk of data on the secondary-electron spectrum into a small number of indices is shown. The method is based on thorough examination of the mathematical physics that governs the spectrum. Several examples of the analysis of recent experimental data on proton impact are presented.

Inokuti, Mitio↗

Analytical evaluation of a surface integral expressing the coupling between interior and exterior volumes in a FE-IE approach

Recently an approach which combines the finite element technique and an integral equation to determine the fields scattered by inhomogeneous bodies of complicated shape has been proposed. Basically, a mathematical surface which encloses the scatterers is introduced, thus dividing the space into an interior and an exterior volume, in which the finite element technique and an integral equation for EM scattering, respectively, are applied. The integral equation is set up for the tangential components of the fields at the surface, while the interior volume the unknowns are the total fields. Continuity of the tangential fields at the boundary, as required by Maxwell's equations, is imposed, thus coupling the two methods to obtain a consistent solution. The coupling term is expressed by a surface integral formed by the dot product of a FE basis function and an IE testing function, or viceversa. By choosing the boundary to be a surface of revolution and by making a convenient selection of IE basis (testing) functions, it is possible to evaluate the integrals analytically on surfaces such as curved triangles, curved quadrilaterals and curved pentagons. We will illustrate the salient steps involved in setting up and carrying out these integrals and discuss what class of basis (testing) functions and analytic surfaces of revolution they are applicable to. Analytic calculations offer the advantage of better accuracy than purely numerical ones, and, when combined with them, often shed light on issues of numerical convergence and limiting values. Furthermore, they may reduce computation time and storage requirements.

Zuffada, C.↗

Analysis of the Injection of a Heated, Turbulent Jet into a Moving Mainstream, with Emphasis on a Thermal Discharge in a Waterway

An experimental and theoretical investigation was undertaken to study the trajectory and growth of thermal effluents having a range of discharge velocities and temperatures. The discharge of a turbulent effluent into a waterway was mathematically modeled as a submerged jet injection process by using an integral method which accounts for natural fluid mechanisms such as turbulence, entrainment, buoyancy, and heat transfer. The analytical results are supported by experimental data and demonstrate the usefulness of the theory for estimating the location and size of the effluent with respect to the discharge point. The capability of predicting jet flow properties, as well as two- and three-dimensional jet paths, was enhanced by obtaining the jet cross-sectional area during the solution of the conservation equations. Realistic estimates of temperature in the effluent were acquired by accounting for heat losses in the jet flow due to forced convection and to entrainment of free-stream fluid into the jet.

Campbell, J. F.↗

Users manual for Streamtube Curvature Analysis: Analytical method for predicting the pressure distribution about a nacelle at transonic speeds, volume 1

The computer program, Streamtube Curvature Analysis, is described for the engineering user and for the programmer. The user oriented documentation includes a description of the mathematical governing equations, their use in the solution, and the method of solution. The general logical flow of the program is outlined and detailed instructions for program usage and operation are explained. General procedures for program use and the program capabilities and limitations are described. From the standpoint of the grammar, the overlay structure of the program is described. The various storage tables are defined and their uses explained. The input and output are discussed in detail. The program listing includes numerous comments so that the logical flow within the program is easily followed. A test case showing input data and output format is included as well as an error printout description.

Keith, J. S.↗

The heating of a thermally conducting stratified medium. II - A simple plane model of an atmosphere

Exact solutions of the following theoretical problem are presented: A plane atmosphere is in hydrostatic equilibrium with a uniform gravity. The ideal gas law is assumed. Heat is generated everywhere at a rate proportional to the local density. The atmosphere is maintained in a steady state through cooling by thermal conduction and radiation. This problem is reducible to quadratures for a thermal conductivity which is an arbitrary, but prescribed, function of the temperature, and for a radiative loss which is expressible as the product of the density and an arbitrary, but prescribed, function of the pressure. The analysis is carried out for the case of power law thermal conductivity, and a radiative loss proportional to the square of the density and to the first power of the temperature. The radiative cooling function adopted here has the basic mathematical form for an optically thin medium. The solutions reproduce the macroscopic ordering of a hot 'corona' separated from a 'photosphere' by a layer of temperature minimum. The analytic solutions allow direct illustration of the interplay between steady energy transport and the requirements of hydrostatic equilibrium.

Lerche, I.↗

Atmosphere behavior in gas-closed mouse-algal systems - An experimental and modelling study

A NASA-sponsored research program initiated using mathematical modelling and laboratory experimentation aimed at examining the gas-exchange characteristics of artificial animal/plant systems closed to the ambient atmosphere is studied. The development of control techniques and management strategies for maintaining the atmospheric levels of carbon dioxide and oxygen at physiological levels is considered. A mathematical model simulating the behavior of a gas-closed mouse-algal system under varying environmental conditions is described. To verify and validate the model simulations, an analytical system with which algal growth and gas exchange characteristics can be manipulated and measured is designed, fabricated, and tested. The preliminary results are presented.

Averner, M. M.↗

A multiple-scales model of the shock-cell structure of imperfectly expanded supersonic jets

The present investigation is concerned with the development of an analytical model of the quasi-periodic shock-cell structure of an imperfectly expanded supersonic jet. The investigation represents a part of a program to develop a mathematical theory of broadband shock-associated noise of supersonic jets. Tam and Tanna (1982) have suggested that this type of noise is generated by the weak interaction between the quasi-periodic shock cells and the downstream-propagating large turbulence structures in the mixing layer of the jet. In the model developed in this paper, the effect of turbulence in the mixing layer of the jet is simulated by the addition of turbulent eddy-viscosity terms to the momentum equation. Attention is given to the mean-flow profile and the numerical solution, and a comparison of the numerical results with experimental data.

Tam, C. K. W.↗

Table look-up estimation of signal and noise parameters from quantized observables

A table look-up algorithm for estimating underlying signal and noise parameters from quantized observables is examined. A general mathematical model is developed, and a look-up table designed specifically for estimating parameters from four-bit quantized data is described. Estimator performance is evaluated both analytically and by means of numerical simulation, and an example is provided to illustrate the use of the look-up table for estimating signal-to-noise ratios commonly encountered in Voyager-type data.

Vilnrotter, V. A.↗

Software Models Impact Stresses

Generalized Impact Stress Software designed to assist engineers in predicting stresses caused by variety of impacts. Program straightforward, simple to implement on personal computers, "user friendly", and handles variety of boundary conditions applied to struck body being analyzed. Applications include mathematical modeling of motions and transient stresses of spacecraft, analysis of slamming of piston, of fast valve shutoffs, and play of rotating bearing assembly. Provides fast and inexpensive analytical tool for analysis of stresses and reduces dependency on expensive impact tests. Written in FORTRAN 77. Requires use of commercial software package PLOT88.

Hanshaw, Timothy C.↗

The influence of wind-tunnel walls on discrete frequency noise

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

Mosher, M.↗