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NASA NTRS1989

ECR plasma thruster research - Preliminary theory and experiments

A preliminary theory of the operation of the electron-cyclotron-resonance (ECR) plasma thruster is described along with an outline of recent experiments. This work is presented to communicate the status of an ongoing research effort directed at developing a unified theory to quantitatively describe the operation of the ECR plasma thruster. The theory is presented as a set of nonlinear ordinary differential equations and boundary conditions which describe the plasma density, velocity, and electron temperature. Diagnostic tools developed to measure plasma conditions in the existing research device are described.

Sercel, Joel C.↗

NASA NTRS1989

Gravitational consequences of modern field theories

Some gravitational consequences of certain extensions of Einstein's general theory of relativity are discussed. These theories are not alternative theories of gravity in the usual sense. It is assumed that general relativity is the appropriate description of all gravitational phenomena which were observed to date.

Horowitz, Gary T.↗

NASA NTRS1989

A Van der Waals-like theory of plasma double layers

A theory describing plasma double layers in terms of multiple roots of the charge density expression is presented. The theory presented uses the fact that equilibrium plasmas shield small potential perturbations linearly; for high potentials, the shielding decreases. The approach is analogous to Van der Waals' theory of simple fluids in which inclusion of approximate expressions for both excluded volume and long range attractive forces sufficiently describes the first-order liquid-gas phase transition.

Katz, Ira↗

NASA NTRS1990

Mars atmospheric D/H - Consistent with polar volatile theory?

Current theories on the Martian water history are discussed on the basis of data for the D/H ratio in the Martian atmosphere (which was found to be enhanced by a factor of 6 + or - relative to the value on earth). In particular, the calculations of Yung et al. (1988), on the basis of their photochemical model, are found to be inconsistent with current theories for the evolution of the polar deposits on Mars. While the photochemical model predicts that about 95 percent of the Martian water has escaped over geologic time and the nonatmospheric reservoir is now only 02 m thick, the polar volatile theory suggest that polar deposits contain the equivalent of tens of meters of water, requiring a more rapid escape of H and D to space than predicted by the photochemical model to match the observed D/H ratio. The paper examines the behavior of the polar caps and the atmospheric water vapor over geologic time and the loss of H and D to space. It is concluded that, at present, it is premature to accept a specific history for water on Mars.

Jakosky, Bruce M.↗

NASA NTRS1991

Applications of fuzzy theories to multi-objective system optimization

Most of the computer aided design techniques developed so far deal with the optimization of a single objective function over the feasible design space. However, there often exist several engineering design problems which require a simultaneous consideration of several objective functions. This work presents several techniques of multiobjective optimization. In addition, a new formulation, based on fuzzy theories, is also introduced for the solution of multiobjective system optimization problems. The fuzzy formulation is useful in dealing with systems which are described imprecisely using fuzzy terms such as, 'sufficiently large', 'very strong', or 'satisfactory'. The proposed theory translates the imprecise linguistic statements and multiple objectives into equivalent crisp mathematical statements using fuzzy logic. The effectiveness of all the methodologies and theories presented is illustrated by formulating and solving two different engineering design problems. The first one involves the flight trajectory optimization and the main rotor design of helicopters. The second one is concerned with the integrated kinematic-dynamic synthesis of planar mechanisms. The use and effectiveness of nonlinear membership functions in fuzzy formulation is also demonstrated. The numerical results indicate that the fuzzy formulation could yield results which are qualitatively different from those provided by the crisp formulation. It is felt that the fuzzy formulation will handle real life design problems on a more rational basis.

Rao, S. S.↗

NASA NTRS1991

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 2: Development of theory for wing shielding

A unified theory for aerodynamics and noise of advanced turboprops is presented. The theory and a computer code developed for evaluation at the shielding benefits that might be expected by an aircraft wing in a wing-mounted propeller installation are presented. Several computed directivity patterns are presented to demonstrate the theory. Recently with the advent of the concept of using the wing of an aircraft for noise shielding, the case of diffraction by a surface in a flow has been given attention. The present analysis is based on the case of diffraction of no flow. By combining a Galilean and a Lorentz transform, the wave equation with a mean flow can be reduced to the ordinary equation. Allowance is also made in the analysis for the case of a swept wing. The same combination of Galilean and Lorentz transforms lead to a problem with no flow but a different sweep. The solution procedures for the cases of leading and trailing edges are basically the same. Two normalizations of the solution are given by the computer program. FORTRAN computer programs are presented with detailed documentation. The output from these programs compares favorably with the results of other investigators.

Amiet, R. K.↗

NASA NTRS1991

Aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics

Recent developments in the field of nonequilibrium thermodynamics associated with viscous flows are examined and related to developments to the understanding of specific phenomena in aerodynamics and aeroacoustics. A key element of the nonequilibrium theory is the principle of minimum entropy production rate for steady dissipative processes near equilibrium, and variational calculus is used to apply this principle to several examples of viscous flow. A review of nonequilibrium thermodynamics and its role in fluid motion are presented. Several formulations are presented of the local entropy production rate and the local energy dissipation rate, two quantities that are of central importance to the theory. These expressions and the principle of minimum entropy production rate for steady viscous flows are used to identify parallel-wall channel flow and irrotational flow as having minimally dissipative velocity distributions. Features of irrotational, steady, viscous flow near an airfoil, such as the effect of trailing-edge radius on circulation, are also found to be compatible with the minimum principle. Finally, the minimum principle is used to interpret the stability of infinitesimal and finite amplitude disturbances in an initially laminar, parallel shear flow, with results that are consistent with experiment and linearized hydrodynamic stability theory. These results suggest that a thermodynamic approach may be useful in unifying the understanding of many diverse phenomena in aerodynamics and aeroacoustics.

Horne, W. Clifton↗

NASA NTRS1991

Equivalent crystal theory of alloys

Equivalent Crystal Theory (ECT) is a new, semi-empirical approach to calculating the energetics of a solid with defects. The theory has successfully reproduced surface energies in metals and semiconductors. The theory of binary alloys to date, both with first-principles and semi-empirical models, has not been very successful in predicting the energetics of alloys. This procedure is used to predict the heats of formation, cohesive energy, and lattice parameter of binary alloys of Cu, Ni, Al, Ag, Au, Pd, and Pt as functions of composition. The procedure accurately reproduces the heats of formation versus composition curves for a variety of binary alloys. The results are then compared with other approaches such as the embedded atom and lattice parameters of alloys from pure metal properties more accurately than Vegard's law is presented.

Bozzolo, Guillermo↗

NASA NTRS1990

Melt migration in a silicate liquid-olivine system - An experimental test of compaction theory

An experimentally derived melt migration profile is compared with those obtained from compaction theory. A couple is prepared in which a source-for-melt (a disk composed of a silicate glass and olivine) was placed in contact with a sink-for-melt (a disk of polycrystalline olivine) in order to induce melt migration under laboratory conditions. It is noted that melt infiltrates into the sink disk along triple junctions driven by capillary forces. In order to analyze the melt migration profile in terms of compaction theory, the equations developed by McKenzie (1984) to describe porous flow of a liquid in a deformable matrix were modified. The bouyancy force term is replaced with a capillary force term and governing equations are then solved numerically with the initial boundary conditions specified by the experimental design. Also, it is determined that compaction theory provides a good description of the experimental results provided that the permeability of these solid-liquid materials increases linearly with increasing liquid fraction.

Riley, G. N., Jr.↗

NASA NTRS1990

Theory of instability and transition

The strongly nonlinear area of theory is discussed, as well as linear and weakly nonlinear (i.e., perturbation) theories, and it is noted that the weaknesses of the weakly nonlinear theory are essentially the inappropriate formulation in earlier works and the lack of guidance for the choice of the lowest-order basis. Attention is focused on the areas of theoretical/numerical development contributing to understanding the transition mechanism and new means for analyzing and predicting transition quantitatively. The nonlinear stability of nonparallel flows, linear secondary instability, and nonlinear wave interaction are analyzed. The incompressible flow over a flat plate with zero-pressure gradient is chosen as an example, while applications range to other shear flows including three-dimensional and compressible boundary layers.

Herbert, Thorwald↗

NASA NTRS1991

Robust control systems design by H-infinity optimization theory

In this paper, step-by-step procedures of applying the H-infinity theory to robust control systems design are given. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H-infinity control theory and to clear up some misconceptions about H-infinity theory like high-gain controller and numerical obstacles, etc. An efficient algorithm is used to compute the optimal H-infinity norm. The Glover and Doyle (1988) controller formulas are slightly modified and used to construct an optimal controller without any numerical difficulties.

Chang, B. C.↗

NASA NTRS1992

A weakly nonlinear theory for wave-vortex interactions in curved channel flow

A weakly nonlinear theory is developed to study the interaction of Tollmien-Schlichting (TS) waves and Dean vortices in curved channel flow. The predictions obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. Some discrepancies in the results of a previous theory with direct numerical simulations are resolved.

Singer, Bart A.↗

NASA NTRS1991

Universal, computer facilitated, steady state oscillator, closed loop analysis theory and some applications to precision oscillators

The theory of oscillator analysis in the immittance domain should be read in conjunction with the additional theory presented here. The combined theory enables the computer simulation of the steady state oscillator. The simulation makes the calculation of the oscillator total steady state performance practical, including noise at all oscillator locations. Some specific precision oscillators are analyzed.

Benjamin Parzen↗

NASA NTRS1992

The Pekeris problem, and the interior of the pulsating sphere, first success of exact ray theory, and what rays?

This paper presents what is probably the first application of exact ray theory to provide nontrivial exact solutions of the Helmholtz equation. First, the Pekeris problem is considered. This is followed by consideration of the problem of the field maintained within a uniformly pulsating sphere. In the Pekeris problem, an iterative solution provides the exact solution on the second iteration. In the second problem, it is shown that the exact ray theory eliminates the focus of the geometric theory.

Mcaninch, Gerry L.↗

NASA NTRS1991

Nonlinear response of resin matrix laminates using endochronic theory

The nonlinear response of laminated, resin matrix fibrous composites is modeled using orthotropic endochronic theory. The theory is formulated in terms of elastic constants and endochronic parameters characterizing the linear and nonlinear response, respectively, of unidirectional composites. All constants and parameters can be determined from normal (tension and/or compression) and shear tests on unidirectional and off-axis specimens. The nonlinear constitutive response relations for the unidirectional lamina are presented and the procedure for determining constants and parameters from test is described. The results are then used to predict the nonlinear response of unidirectional laminae and angle-ply laminates. Comparison between theory and experiment for compression loading of AS4/3502 graphite-epoxy, angle-ply laminates shows excellent correlation.

Mathison, S. R.↗

NASA NTRS1992

The arcing rate for a High Voltage Solar Array - Theory, experiment and predictions

All solar arrays have biased surfaces which can be exposed to the space environment. It has been observed that when the array bias is less than a few hundred volts negative then the exposed conductive surfaces may undergo arcing in the space plasma. A theory for arcing is developed on these high voltage solar arrays which ascribes the arcing to electric field runaway at the interface of the plasma, conductor and solar cell dielectric. Experiments were conducted in the laboratory for the High Voltage Solar Array (HVSA) experiment which will fly on the Japanese Space Flyer Unit (SFU) in 1994. The theory was compared in detail to the experiment and shown to give a reasonable explanation for the data. The combined theory and ground experiments were then used to develop predictions for the SFU flight.

Hastings, Daniel E.↗

NASA NTRS1992

Theory of anisotropic thin-walled closed-section beams with hygrothermal effects

A variationally consistent theory is developed in order to derive the governing equations of anisotropic thin-walled beams with closed sections subjected to axial load, torsion, bending and hygrothermal loads. The theory is based on an asymptotical analysis of two-dimensional shell theory. Closed-form expressions for the beam stiffness coefficients, equivalent hygrothermal loads, stress and displacement fields are provided. The influence of material anisotropy and hygrothermal coefficients on the displacement field is identified. The analysis is applied to predict the response of composite beams under thermomechanical loading.

Badir, Ashraf M.↗

NASA NTRS1992

Aircraft ride quality controller design using new robust root clustering theory for linear uncertain systems

The aspect of controller design for improving the ride quality of aircraft in terms of damping ratio and natural frequency specifications on the short period dynamics is addressed. The controller is designed to be robust with respect to uncertainties in the real parameters of the control design model such as uncertainties in the dimensional stability derivatives, imperfections in actuator/sensor locations and possibly variations in flight conditions, etc. The design is based on a new robust root clustering theory developed by the author by extending the nominal root clustering theory of Gutman and Jury to perturbed matrices. The proposed methodology allows to get an explicit relationship between the parameters of the root clustering region and the uncertainty radius of the parameter space. The current literature available for robust stability becomes a special case of this unified theory. The bounds derived on the parameter perturbation for robust root clustering are then used in selecting the robust controller.

Yedavalli, R. K.↗