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NASA NTRS1989

Compact finite volume methods for the diffusion equation

An approach to treating initial-boundary value problems by finite volume methods is described, in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and alternating direction implicit (ADI) methods. The treatment of general curvilinear coordinates is shown to result from a specialization of these general results.

Rose, Milton E.↗

NASA NTRS1989

Compact finite volume methods for the diffusion equation

The paper describes an approach to treating initial-boundary-value problems by finite volume methods in which the parallel between differential and difference arguments is closely maintained. By using intrinsic geometrical properties of the volume elements, it is possible to describe discrete versions of the div, curl, and grad operators which lead, using summation-by-parts techniques, to familiar energy equations as well as the div curl = 0 and curl grad = 0 identities. For the diffusion equation, these operators describe compact schemes whose convergence is assured by the energy equations and which yield both the potential and the flux vector with second-order accuracy. A simplified potential form is especially useful for obtaining numerical results by multigrid and ADI methods.

Rose, Milton E.↗

NASA NTRS1992

Performance of a four-element Ka-band high-temperature superconducting microstrip antenna

Superconducting four-element microstrip array antennas operating at 30 GHz have been designed and fabricated on a lanthanum aluminate (LaAlO3) substrates. The experimental performance of these thin film Y-Ba-Cu-O superconducting antennas is compared with that of identical antenna patterned with evaporated gold. Efficiency measurements of these antennas show an improvement of 2 dB at 70 K and as much as 3.5 dB at 40 K in the superconducting antenna over the gold antenna.

Richard, M. A.↗

NASA NTRS1994

Kupier prize lecture: Sources of solar-system carbon

We have tried to deconvolve Solar-System carbon into its sources, on the basis of C-12/C-13 ratios (equivalent to R). Interstellar SiC in meteorites, representing greater than 4.6-Ga-old stardust from carbon stars, is isotopically heavier (bar R = 38 +/- 2) than Solar-System carbon (89), implying that the latter contains an additional, light component. A likely source are massive stars, mainly Type II supernovae and Wolf-Rayet stars, which, being O-rich, eject their C largely as CO rather than carbonaceous dust. The fraction of such light C in the Solar System depends on R(sub light) in the source. For R(sub light) = 180-1025 (as in 'Group 4' meteoritic graphite spherules, which apparently came from massive stars greater than 4.6 Ga ago), the fraction of light C is 0.79-0.61. Similar results are obtained for present-day data on red giants and interstellar gas. Although both have become enriched in C-13 due to galactic evolution (to bar-R = 20 and 57), the fraction of the light component in interstellar gas again is near 0.7. (Here bar R represents the mean of a mixture calculated via atom fractions; it is not identical to the arithmetic mean R). Interstellar graphite, unlike SiC, shows a large peak at R approximately equal 90, near the solar value. Although some of the grains may be of local origin, others show anomalies in other elements and hence are exotic. Microdiamonds, with R = 93, also are exotic on the basis of their Xe and N. Apparently R approximately 90 was a fairly common composition 4.6 Ga ago, of stars as well as the ISM.

Anders, Edward↗

NASA NTRS2011

Correctness Proof of a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

This report presents a deductive proof of a self-stabilizing distributed clock synchronization protocol. It is focused on the distributed clock synchronization of an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. This protocol does not rely on assumptions about the initial state of the system, and no central clock or a centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. We present a deductive proof of the correctness of the protocol as it applies to the networks with unidirectional and bidirectional links. We also confirm the claims of determinism and linear convergence.

Malekpour, Mahyar R.↗

NASA NTRS2003

High Temperature Propulsion System Structural Seals for Future Space Launch Vehicles

Durable, flexible sliding seals are required in advanced hypersonic engines to seal the perimeters of movable engine ramps for efficient, safe operation in high heat flux environments at temperatures of 2000 to 2500 F. Current seal designs do not meet the demanding requirements for future engines, so NASA's Glenn Research Center is developing advanced seals and preloading devices to overcome these shortfalls. An advanced ceramic wafer seal design and two types of seal preloading devices were evaluated in a series of compression, scrub, and flow tests. Silicon nitride wafer seals survived 2000 in. (1000 cycles) of scrubbing at room temperature against an Inconel 625 rub surface with no chips or signs of damage. Flow rates measured for the wafers before and after scrubbing were almost identical and were much lower than those recorded for the best braided rope seal flow blockers. Canted coil springs and silicon nitride compression springs showed promise conceptually as potential seal preloading devices to help maintain seal resiliency. A finite element model of the canted coil spring revealed that it should be possible to produce a spring out of high temperature materials for applications at 2000+ F.

Dunlap, Patrick H., Jr.↗

NASA NTRS1987

Optical region elemental abundance analyses of B and A stars. VII - The metallic-lined star 32 Aquarii

An abundance analysis using photographic region spectrograms and fully line-blanketed model atmospheres has been performed for the metallic-lined (Am) star 32 Aquarii consistent with previous papers of this series. Its pattern of abundance anomalies is not identical with those of the hot Am stars although there are definite similarities. Changes of up to order 1 dex are foundly by comparison with the previous analysis by Smith. Slightly better agreement is found with the recent analyses of singly-ionized rare earth lines by Magazzu and Cowley. Results are also presented for a model selected on the basis of photometric indices according to the formula of Moon and Dworetsky.

Kocer, D.↗

NASA NTRS1986

Large Deformation Dynamic Bending of Composite Beams

Studies were conducted on the large deformation response of composite beams subjected to a dynamic axial load. The beams were loaded with a moderate eccentricity to promote bending. The study was primarily experimental but some finite element results were obtained. Both the deformation and the failure of the beams were of interest. The static response of the beams was also studied to determine potential differences between the static and dynamic failure. Twelve different laminate types were tested. The beams tested were 23 in. by 2 in. and generally 30 plies thick. The beams were loaded dynamically with a gravity-driven impactor traveling at 19.6 ft/sec and quasi-static tests were conducted on identical beams in a displacement controlled manner. For laminates of practical interest, the failure modes under static and dynamic loadings were identical. Failure in most of the laminate types occurred in a single event involving 40% to 50% of the plies. However, failure in laminates with 300 or 150 off-axis plies occurred in several events. All laminates exhibited bimodular elastic properties. The compressive flexural moduli in some laminates was measured to be 1/2 the tensile flexural modulus. No simple relationship could be found among the measured ultimate failure strains of the different laminate types. Using empirically determined flexural properties, a finite element analysis was reasonably accurate in predicting the static and dynamic deformation response.

Derian, E. J.↗

NASA NTRS1981

A multi-purpose method for analysis of spur gear tooth loading

A large digitized approach was developed for the static and dynamic load analysis of spur gearing. An iterative procedure was used to calculate directly the "variable-variable" gear mesh stiffness as a function of transmitted load, gear tooth profile errors, gear tooth deflections and gear hub torsional deformation, and position of contacting profile points. The developed approach can be used to analyze the loads, Hertz stresses, and PV for the normal and high contrast ratio gearing, presently the modeling is limited to the condition that for a given gear all teeth have identical spacing and profiles (with or without surface imperfections). Certain types of simulated sinusoidal profile errors and pitting can cause interruptions of the gear mesh stiffness function and, thus, increase the dynamic loads in spur gearing. In addition, a finite element stress and mesh subprogram was developed for future introduction into the main program for calculating the gear tooth bending stresses under dynamic loads.

Kasuba, R.↗

NASA NTRS1993

Impact mineralogy and chemistry of the cretaceous-tertiary boundary at DSDP site 576

We have identified the K/T boundary in pelagic clay sediments from cores at DSDP Site 576 in the western North Pacific. Detailed geochemical and trace mineralogical analyses of this boundary section are in progress and initial results indicate similarities and differences relative to the only other clay core investigated in detail; DSDP Site 596, a locality in the western South Pacific. Peak Ir concentrations of 13 ng/g in DSDP Hole 576B are virtually identical with those observed in the South Pacific, but in the North Pacific this peak is much narrower and the integrated Ir fluence of 85 ng cm(exp -2) is 4 times lower (320 in Hole 596). Of the 34 elements measured, only Ir and Cr were found to have anomalous concentrations in K/T boundary samples. Trace mineral residues were obtained by washing away clays and sequential chemical leaches (including HF) to remove typical hydrogenous and biogenous sediment components (e.g., zeolites and radiolarian opal). We attempted to quantitatively recover the entire trace mineral assemblage for grains greater than 30 micrometers in diameter. Our mineral residues were dominated by two phases: quartz and magnesioferrite spinel. Other non-opaque mineral grains we have positively identified were trace K-feldspar, plagioclase, corundum, and muscovite. Of these only K-feldspar exhibited planar deformation features (PDF). We have not found abundant plagioclase, as in the South Pacific suggesting that this phase was either not preserved in the North Pacific, or that in the south, it has a non-impact (i.e., volcanic) source. PDF in quartz were commonly obscured by secondary overgrowths on the surfaces of quartz grains, presumably from diagenetic reprecipitation of silica dissolved from opaline radiolarian tests that are common in these sediments. However, careful examination revealed that most grains had multiple sets of PDF. Of the 133 quartz grains greater than 30 micrometers analyzed, 62 percent showed evidence of shock. The largest shocked grain recovered to date had a maximum diameter of 160 micrometers, consistent with other sites in the Pacific.

Bostwick, Jennifer A.↗

NASA NTRS2001

The Effect of Stochastic Perturbation of Fuel Distribution on the Criticality of a One Speed Reactor and the Development of Multi-Material Multinomial Line Statistics

The effect of random fuel redistribution on the eigenvalue of a one-speed reactor is investigated. An ensemble of such reactors that are identical to a homogeneous reference critical reactor except for the fissile isotope density distribution is constructed such that it meets a set of well-posed redistribution requirements. The average eigenvalue, , is evaluated when the total fissile loading per ensemble element, or realization, is conserved. The perturbation is proven to increase the reactor criticality on average when it is uniformly distributed. The various causes of the change in reactivity, and their relative effects are identified and ranked. From this, a path towards identifying the causes. and relative effects of reactivity fluctuations for the energy dependent problem is pointed to. The perturbation method of using multinomial distributions for representing the perturbed reactor is developed. This method has some advantages that can be of use in other stochastic problems. Finally, some of the features of this perturbation problem are related to other techniques that have been used for addressing similar problems.

Jahshan, S. N.↗

NASA NTRS2015

2nd-Order CESE Results For C1.4: Vortex Transport by Uniform Flow

The Conservation Element and Solution Element (CESE) method was used as implemented in the NASA research code ez4d. The CESE method is a time accurate formulation with flux-conservation in both space and time. The method treats the discretized derivatives of space and time identically and while the 2nd-order accurate version was used, high-order versions exist, the 2nd-order accurate version was used. In regards to the ez4d code, it is an unstructured Navier-Stokes solver coded in C++ with serial and parallel versions available. As part of its architecture, ez4d has the capability to utilize multi-thread and Messaging Passage Interface (MPI) for parallel runs.

Space-time CE/SE method↗

NASA NTRSDate not supplied

Bistable Deployable Composite Booms With Parabolic Cross-Sections

This paper investigates how stable equilibrium states in the extended and coiled configurations can be predicted in thin-shelled composite booms with parabolic cross-sections. These conic shapes potentially offer greater stiffness properties when compared to circular cross-sections, which is critical for improving the load bearing performance of deployed booms. Inducing bistability through the choice of composite shell layups in parabolic booms would allow for controllable self-deployment due to a less energetic coiled state when compared to monostable booms. An inextensional analytical model is used to predict the stable coiled diameters of tape spring and Collapsible Tubular Mast (CTM) booms with parabolic cross-sections. The parabolic section is discretized into circular segments using biarc spline interpolation, which allows them to be integrated into the strain energy minimization procedure used to obtain the equilibrium states. When the parabolic booms are parametrically compared against circular booms with identical layups, flattened height, and mass, the former are found to generally have better stiffness performance while being less efficient in stowed volume as evidenced by larger coiled diameters. Analytical coiled diameters and their strain energy are verified with finite element simulations for optimal parabolic tape spring and CTM booms.

Andrew J. Lee↗

NASA NTRS1980

Light scattering by randomly oriented spheroidal particles

A study of the light scattering properties of randomly oriented, identical spheroidal particles is presented. A computation method was developed to integrate the Asano and Yamomoto solution (1975) for scattering from a homogeneous spheroid over all particle orientations; the extinction and scattering cross-sections, the asymmetry factor, and scattering matrix elements are calculated for randomly oriented prolate and oblate spheroids and compared with the calculations for spheres and laboratory measurements. The angular scattering behavior of spheroids is found to be different from that of the spheres for side scattering to backscattering directions, and prolate and oblate spheroids of the same shape parameter have similar angular scattering patterns.

Asano, S.↗

NASA NTRS1982

Elastic-plastic finite-element analyses of thermally cycled single-edge wedge specimens

Elastic-plastic stress-strain analyses were performed for single-edge wedge alloys subjected to thermal cycling in fluidized beds. Three cases (NASA TAZ-8A alloy under one cycling condition and 316 stainless steel alloy under two cycling conditions) were analyzed by using the MARC nonlinear, finite-element computer program. Elastic solutions from MARC showed good agreement with previously reported solutions that used the NASTRAN and ISO3DQ computer programs. The NASA TAZ-8A case exhibited no plastic strains, and the elastic and elastic-plastic analyses gave identical results. Elastic-plastic analyses of the 316 stainless steel alloy showed plastic strain reversal with a shift of the mean stresses in the compressive direction. The maximum equivalent total strain ranges for these cases were 13 to 22 percent greater than that calculated from elastic analyses.

Kaufman, A.↗

NASA NTRS1982

Optimal turning climb-out and descent of commercial jet aircraft

Optimal turning climb-out and descent flight-paths from and to runway headings are derived to provide the missing elements of a complete flight-path optimization for minimum fuel consumption. The paths are derived by generating a field of extremals, using the necessary conditions of optimal control. Results show that the speed profiles for straight and turning flight are essentially identical, except for the final horizontal accelerating or decelerating turn. The optimal turns, which require no abrupt maneuvers, could easily be integrated with present climb-cruise-descent fuel-optimization algorithms.

Neuman, F.↗

NASA NTRS2004

High Temperature Propulsion System Structural Seals for Future Space Launch Vehicles

Durable, flexible sliding seals are required in advanced hypersonic engines to seal the perimeters of movable engine ramps for efficient, safe operation in high heat flux environments at temperatures of 2000 to 2500 F. Current seal designs do not meet the demanding requirements for future engines, so NASA s Glenn Research Center is developing advanced seals and preloading devices to overcome these shortfalls. An advanced ceramic wafer seal design and two types of seal preloading devices were evaluated in a series of compression, scrub, and flow tests. Silicon nitride wafer seals survived 2000 in. 1000 cycles) of scrubbing at 1600 F against an Inconel 625 rub surface with no chips or signs of damage. Flow rates measured for the wafers before and after scrubbing were almost identical and were up to 32 times lower than those recorded for the best braided rope seal flow blockers. Canted coil springs and silicon nitride compression springs showed promise conceptually as potential seal preloading devices to help maintain seal resiliency. A finite element model of the canted coil spring revealed that it should be possible to produce a spring out of high temperature materials for applications at 2000+ F.

Dunlap, Patrick H., Jr.↗

NASA NTRS2013

Performance Measurement of Advanced Stirling Convertors (ASC-E3)

NASA Glenn Research Center (GRC) has been supporting development of the Advanced Stirling Radioisotope Generator (ASRG) since 2006. A key element of the ASRG project is providing life, reliability, and performance testing data of the Advanced Stirling Convertor (ASC). The latest version of the ASC (ASC-E3, to represent the third cycle of engineering model test hardware) is of a design identical to the forthcoming flight convertors. For this generation of hardware, a joint Sunpower and GRC effort was initiated to improve and standardize the test support hardware. After this effort was completed, the first pair of ASC-E3 units was produced by Sunpower and then delivered to GRC in December 2012. GRC has begun operation of these units. This process included performance verification, which examined the data from various tests to validate the convertor performance to the product specification. Other tests included detailed performance mapping that encompassed the wide range of operating conditions that will exist during a mission. These convertors were then transferred to Lockheed Martin for controller checkout testing. The results of this latest convertor performance verification activity are summarized here.

Stirling Cycle↗