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NASA NTRS1993

On the prediction of multigrid efficiency through local mode analysis

A single grid local mode analysis is used to predict the smoothing properties of numerical schemes for solving the Navier-Stokes equations with factorization based on Stone's Strongly Implicit Method. Four difference approximations for the convection terms are considered, namely, hybrid, central, second-order upwind, and third-order upwind. Smoothing factors from the analysis are compared with practical convergence factors in a multigrid method for flow over a backward facing step and it is found that the local mode analysis correctly predicts the effects of Reynolds number and higher-order schemes.

Wilson, R. V.↗

NASA NTRS1993

Flow interaction experiment. Volume 1: Aerothermal modeling, phase 2

An experimental and computational study is reported for the flow of a turbulent jet discharging into a rectangular enclosure. The experimental configurations consisting of primary jets only, annular jets only, and a combination of annular and primary jets are investigated to provide a better understanding of the flow field in an annular combustor. A laser Doppler velocimeter is used to measure mean velocity and Reynolds stress components. Major features of the flow field include recirculation, primary and annular jet interaction, and high turbulence. A significant result from this study is the effect the primary jets have on the flow field. The primary jets are seen to create statistically larger recirculation zones and higher turbulence levels. In addition, a technique called marker nephelometry is used to provide mean concentration values in the model combustor. Computations are performed using three levels of turbulence closures, namely k-epsilon model, algebraic second moment (ASM), and differential second moment (DSM) closure. Two different numerical schemes are applied. One is the lower-order power-law differencing scheme (PLDS) and the other is the higher-order flux-spline differencing scheme (FSDS). A comparison is made of the performance of these schemes. The numerical results are compared with experimental data. For the cases considered in this study, the FSDS is more accurate than the PLDS. For a prescribed accuracy, the flux-spline scheme requires a far fewer number of grid points. Thus, it has the potential for providing a numerical error-free solution, especially for three-dimensional flows, without requiring an excessively fine grid. Although qualitatively good comparison with data was obtained, the deficiencies regarding the modeled dissipation rate (epsilon) equation, pressure-strain correlation model, and the inlet epsilon profile and other critical closure issues need to be resolved before one can achieve the degree of accuracy required to analytically design combustion systems.

Nikjooy, M.↗

NASA NTRS1993

Flow interaction experiment. Volume 2: Aerothermal modeling, phase 2

Nikjooy, M.↗

NASA NTRS1992

HDL to verification logic translator

The increasingly higher number of transistors possible in VLSI circuits compounds the difficulty in insuring correct designs. As the number of possible test cases required to exhaustively simulate a circuit design explodes, a better method is required to confirm the absence of design faults. Formal verification methods provide a way to prove, using logic, that a circuit structure correctly implements its specification. Before verification is accepted by VLSI design engineers, the stand alone verification tools that are in use in the research community must be integrated with the CAD tools used by the designers. One problem facing the acceptance of formal verification into circuit design methodology is that the structural circuit descriptions used by the designers are not appropriate for verification work and those required for verification lack some of the features needed for design. We offer a solution to this dilemma: an automatic translation from the designers' HDL models into definitions for the higher-ordered logic (HOL) verification system. The translated definitions become the low level basis of circuit verification which in turn increases the designer's confidence in the correctness of higher level behavioral models.

Gambles, J. W.↗

NASA NTRS1993

Towards the formal verification of the requirements and design of a processor interface unit: HOL listings

This technical report contains the Higher-Order Logic (HOL) listings of the partial verification of the requirements and design for a commercially developed processor interface unit (PIU). The PIU is an interface chip performing memory interface, bus interface, and additional support services for a commercial microprocessor within a fault tolerant computer system. This system, the Fault Tolerant Embedded Processor (FTEP), is targeted towards applications in avionics and space requiring extremely high levels of mission reliability, extended maintenance-free operation, or both. This report contains the actual HOL listings of the PIU verification as it currently exists. Section two of this report contains general-purpose HOL theories and definitions that support the PIU verification. These include arithmetic theories dealing with inequalities and associativity, and a collection of tactics used in the PIU proofs. Section three contains the HOL listings for the completed PIU design verification. Section 4 contains the HOL listings for the partial requirements verification of the P-Port.

Fura, David A.↗

NASA NTRS1993

Constraints on the Martian cratering rate imposed by the SNC meteorites and Vallis Marineris layered deposits

Following two independent lines of evidence -- estimates of the age and formation time of a portion of the Martian geologic column exposed in the layered deposits and the crystallization and ejection ages of the SNC meteorites -- it appears that the Martian cratering rate must be double the lunar rate or even higher. This means models such as NHII or NHIII (Neukum and Hiller models II and III), which estimate the Martian cratering rate as being several times lunar are probably far closer to reality on Mars than lunar rates. The effect of such a shift is profound: Mars is transformed from a rather Moon-like place into a planet with vigorous dynamics, multiple large impacts, erosion, floods, and volcanism throughout its history. A strong shift upward in cratering rates on Mars apparently solves some glaring problems; however, it creates others. The period of time during which Earth-like atmospheric conditions existed, the liquid water era on Mars, persists in NHIII up to only 0.5 b.y. ago. Scenarios of extended Earth-like conditions on Mars have been discounted in the past because they would have removed many of the craters from the early bombardment era found in the south. It does appear that some process of crater removal was quite vigorous in the north during Mars' past. Evidence exists that the northern plains may have been the home of long-lived seas or perhaps even a paleo-ocean, so models exist for highly localized destruction of craters in the north. However, the question of how the ancient crater population could be preserved in the south under a long liquid-water era found in any high-cratering-rate models is a serious question that must be addressed. It does appear to be a higher-order problem because it involves low-energy dynamics acting in localized areas, i.e., erosion of craters in the south of Mars, whereas the two problems with the low-cratering-rate models involve high-energy events acting over large areas: the formation of the Vallis Marineris, the SNC ejecting impacts, and the global atmospheric pressure and temperature conditions that allow liquid water to exist as a robust entity anywhere on the Martian surface. In any case, it appears Mars is a more complex and dynamic planet than previously supposed. It has canyons dating from the middle to late period of its history that contain apparent lake sediments bedded deeper than most sediments on Earth. Recent multiple, violent impacts on Mars have apparently provided us with multiple random samples of its surface that all crystallized less than 1.5 b.y. ago. These things cannot be accommodated in our present cratering chronologies of Mars, based on 1x lunar cratering rates, without great difficulties. These difficulties suggest that a new chronology, probably based on NHII or even NHIII, should be adopted; this new chronology will provide us with a new view of Mars as a dynamic planet of rich history.

Brandenburg, J. E.↗

NASA NTRS1993

Alignment of dust grains in ionized regions

The rate at which charged dust grains in a plasma are torqued by passing ions and electrons is calculated. When photo-emission of electrons is not important, attraction of ions by the grain monopole potential increases the rate at which the grains' spins are dealigned by nearly an order of magnitude. Consequently, the energy density of the magnetic field required to align grains in an H II region may be increased by about an order of magnitude. In contrast, electric dipole and quadrupole moments are unlikely to produce large dealignment rates for grains of modest length-to-width ratio. Nonetheless, for positively charged grains these higher-order moments likely prevent monopole repulsion of ions from reducing the dealignment rate far below that for neutral grains. The presence of positive grain charge therefore does not greatly facilitate grain alignment in an H II region.

Anderson, Nels↗

NASA NTRS1994

Velocity-modulation atomization of liquid jets

A novel atomizer based on high-amplitude velocity atomization has been developed. Presently, the most common methods of atomization can use only the Rayleigh instability of a liquid cylinder and the Kelvin-Helmholtz instability of a liquid sheet. Our atomizer is capable of atomizing liquid jets by the excitation and destabilization of many other higher-order modes of surface deformation. The potential benefits of this sprayer are more uniform fuel air mixtures, faster fuel-air mixing, extended flow ranges for commercial nozzles, and the reduction of nozzle plugging by producing small drops from large nozzles.

Dressler, John L.↗

NASA NTRS1994

Dynamo generation of magnetic field in the white dwarf GD 358

On the basis of Whole Earth Telescope observations of the g-mode oscillation spectrum of the white dwarf GD 358, Winget et al. find evidence for significant differential rotation and for a time-varying magnetic field concentrated in the surface layers of this star. Here we argue on theoretical grounds that this magnetic field is produced by an alpha omega dynamo operating in the lower part of a surface convection zone in GD 358. Our argument is based on numerical solutions of the nonlinear, local dynamo equations of Robinson & Durney, with specific parameters based on our detailed models of white-dwarf convective envelopes, and universal constants determined by a calibration with the the Sun's dynamo. The calculations suggest a dynamo cycle period of about 6 years for the fundamental mode, and periods as short as 1 year for the higher-order modes that are expected to dominate in view of the large dynamo number we estimate for GD 358. These dynamo periods are consistent with the changes in the magnetic field of GD 358 over the span of 1 month inferred by Winget et. al. from their observations. Our calculations also suggest a peak dynamo magnetic field strength at the base of the surface convection zone of about 1800 G, which is consistent with the field strength inferred from the observations.

Markiel, J. Andrew↗

NASA NTRS1994

A multi-ion generalized transport model of the polar wind

The higher-order generalizations of the equations of standard hydrodynamics, known collectively as generalized transport theories, have been used since the early 1980s to describe the terrestrial polar wind. Inherent in the structure of generalized transport theories is the ability to describe not only interparticle collisions but also certain non-Maxwellian processes, such as heat flow and viscous stress, that are characteristic of any plasma flow that is not collision dominated. Because the polar wind exhibits a transition from collision-dominated to collisionless flow, generalized transport theories possess advantages for polar wind modeling not shared by either collision-dominated models (such as standard hydrodynamics) or collisionless models (such as those based on solving the collisionless Boltzmann equation). In general, previous polar wind models have used generalized transport equations to describe electrons and only one species of ion (H(+)). If other ion species were included in the models at all, it was in a simplified or semiempirical manner. The model described in this paper is the first polar wind model that uses a generalized transport theory (bi-Maxwellian-based 16-moment theory) to describe all of the species, both major and minor, in the polar wind plasma. In the model, electrons and three ion species (H(+), He(+), O(+)) are assumed to be major and several ion species are assumed to be minor (NO(+), Fe(+), O(++)). For all species, a complete 16-moment transport formulation is used, so that profiles of density, drift velocity, parallel and perpendicular temperatures, and the field-aligned parallel and perpendicular energy flows are obtained. In the results presented here, emphasis is placed on describing those constituents of the polar wind that have received little attention in past studies. In particular, characteristic solutions are presented for supersonic H(+) outflow and for both supersonic and subsonic outflows of the major ion He(+). Solutions are also presented for various minor ions, both atomic and molecular and both singly and multiply charged.

Demars, H. G.↗

NASA NTRS1994

A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

Hamilton, Douglas P.↗

NASA NTRS1994

Unique determination of solutions to the Burnett equations

Recent success in applying the Burnett equations to the one-dimensional shock-structure problem has raised the issue of whether the full Burnett equations can be used replace the Navier-Stokes equations for solving boundary-value problems in rarefied gasdynamics. As is familiar from the classical rarefied gasdynamics literature, the Burnett equations, if not solved as a successive approximation to the Navier-Stokes equations for a small Knudsen number, would require more boundary conditions than those in the Navier-Stokes system, owing to the presence of the higher-order derivatives. In this paper, this issue is examined with concrete solution examples for the steady Couette flows, addressing specifically whether solutions to the full Burnett equations can be uniquely determined without adding more boundary conditions than those in the Navier-Stokes system. The analysis, supported by detailed numerical solutions, confirms that additional boundary conditions are needed as long as the Knudsen number is not identically zero, lest the solution to the Burnett equations is not unique.

Lee, C. J.↗

NASA NTRS1994

Distributions of the interplanetary magnetic field revisited

The adequacy of the power spectrum to characterize the variations of a parameter depends on whether or not the parameter has a Gaussian distribution. We here perform very simple tests of Gaussianity on the distribution. We here perform very simple tests of Gaussianity on the distributions of the magnitudes of the interplanetary magnetic field, and on the distributions of the components; that is, we find the first four cumulants of the distributions (mean, variance, skewness, and kurtosis) and their solar cycle variations. We find, consistent with other recent analyses, that the traditional distributions of the 1-hour averaged magnitude are not distributed normally or lognomally as has often been assumed and the 1-hour averaged z component is found to have a nonzero kurtosis. Thus the power spectrum is insufficient to completely characterize these variations and polyspectra are needed. We have isolated variations in the 1/f frequency region of the spectrum and show that the distributions of the magnitudes have nonzero skewness and kurtosis, the magnitudes are not distributed lognormally, and the distributions of the components have nonzero kurtosis. Thus higher-order spectra are again needed for a full characterization.

Feynman, Joan↗

NASA NTRS1991

On the Power of Abstract Interpretation

Increasingly sophisticated applications of static analysis place increased burden on the reliability of the analysis techniques. Often, the failure of the analysis technique to detect some information my mean that the time or space complexity of the generated code would be altered. Thus, it is important to precisely characterize the power of static analysis techniques. We follow the approach of Selur et. al. who studied the power of strictness analysis techniques. Their result can be summarized by saying 'strictness analysis is perfect up to variations in constants.' In other words, strictness analysis is as good as it could be, short of actually distinguishing between concrete values. We use this approach to characterize a broad class of analysis techniques based on abstract interpretation including, but not limited to, strictness analysis. For the first-order case, we consider abstract interpretations where the abstract domain for data values is totally ordered. This condition is satisfied by Mycroft's strictness analysis that of Sekar et. al. and Wadler's analysis of list-strictness. For such abstract interpretations, we show that the analysis is complete in the sense that, short of actually distinguishing between concrete values with the same abstraction, it gives the best possible information. We further generalize these results to typed lambda calculus with pairs and higher-order functions. Note that products and function spaces over totally ordered domains are not totally ordered. In fact, the notion of completeness used in the first-order case fails if product domains or function spaces are added. We formulate a weaker notion of completeness based on observability of values. Two values (including pairs and functions) are considered indistinguishable if their observable components are indistinguishable. We show that abstract interpretation of typed lambda calculus programs is complete up to this notion of indistinguishability. We use denotationally-oriented arguments instead of the detailed operational arguments used by Selur et. al.. Hence, our proofs are much simpler. They should be useful for further future improvements.

Reddy, Uday S.↗

NASA NTRS1994

Optical Analysis of an Ultra-High resolution Two-Mirror Soft X-Ray Microscope

This work has summarized for a Schwarzschild microscope some relationships between numerical aperture (NA), magnification, diameter of the primary mirror, radius of curvature of the secondary mirror, and the total length of the microscope. To achieve resolutions better than a spherical Schwarzschild microscope of 3.3 Lambda for a perfectly aligned and fabricated system. it is necessary to use aspherical surfaces to control higher-order aberrations. For an NA of 0.35, the aspherical Head microscope provides diffraction limited resolution of 1.4 Lambda where the aspherical surfaces differ from the best fit spherical surface by approximately 1 micrometer. However, the angle of incidence varies significantly over the primary and the secondary mirrors, which will require graded multilayer coatings to operate near peak reflectivities. For higher numerical apertures, the variation of the angle of incidence over the secondary mirror surface becomes a serious problem which must be solved before multilayer coatings can be used for this application. Tolerance analysis of the spherical Schwarzschild microscope has shown that water window operations will require 2-3 times tighter tolerances to achieve a similar performance for operations with 130 A radiation. Surface contour errors have been shown to have a significant impact on the MTF and must be controlled to a peak-to-valley variation of 50-100 A and a frequency of 8 periods over the surface of a mirror.

Shealy, David L.↗

NASA NTRS1982

Handling Qualities Specifications for U.S. Military Helicopters

Inadequacies in the military specification for helicopter handling qualities, MIL-H-8501A, have long been recognized, and the latest procurements by the U.S. Army used special Prime Item Development Specifications (PIDS). This paper assesses the efficacy of these PIDS and suggests that changes should be made. In particular, the structure developed in MIL-F-8785B (ASG) (the specification for flying qualities of piloted airplanes) should be incorporated. Improved requirements must be based on a systematic data base and concentrated on topics most important in preliminary design: static and dynamic stability, control power and sensitivity, and interaction with controllers and displays. Emphasis should be on current military helicopter missions and helicopter idiosyncrasies such as cross-coupling, nonlinearities, and higher-order dynamics.

Key, David L.↗

NASA NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗

NASA NTRS1991

A definition of the domains Archaea, Bacteria and Eucarya in terms of small subunit ribosomal RNA characteristics

The number of small subunit rRNA sequences is now great enough that the three domains Archaea, Bacteria and Eucarya (Woese et al., 1990) can be reliably defined in terms of their sequence "signatures". Approximately 50 homologous positions (or nucleotide pairs) in the small subunit rRNA characterize and distinguish among the three. In addition, the three can be recognized by a variety of nonhomologous rRNA characters, either individual positions and/or higher-order structural features. The Crenarchaeota and the Euryarchaeota, the two archaeal kingdoms, can also be defined and distinguished by their characteristic compositions at approximately fifteen positions in the small subunit rRNA molecule.

NASA Program Exobiology↗