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Predicting Print-thru for the Sub-scale Beryllium Mirror Demonstrator (SBMD)

This document presents a finite element method for predicting print-thru or quilting for a lightweight mirror in a low temperature environment. The mirror is represented with quadrilateral and triangular plate finite elements. The SBMD (Sub-scale Beryllium Mirror Demonstrator) is circular with a diameter of 50 cm and one flat side. The mirror structure is a thin-wall triangular cell core with a single facesheet. There is a 4 mm radius fillet between the facesheet and cell walls. It is made entirely of Beryllium. It is assumed that polishing the mirror surface creates a thin surface layer with different material properties. Finite element results are compared with measured values at cryogenic temperatures.

Craig, Larry↗

Spectral (Finite) Volume Method for Conservation Laws on Unstructured Grids II: Extension to Two Dimensional Scalar Equation

The framework for constructing a high-order, conservative Spectral (Finite) Volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids. Each triangular grid cell forms a spectral volume (SV), and the SV is further subdivided into polygonal control volumes (CVs) to supported high-order data reconstructions. Cell-averaged solutions from these CVs are used to reconstruct a high order polynomial approximation in the SV. Each CV is then updated independently with a Godunov-type finite volume method and a high-order Runge-Kutta time integration scheme. A universal reconstruction is obtained by partitioning all SVs in a geometrically similar manner. The convergence of the SV method is shown to depend on how a SV is partitioned. A criterion based on the Lebesgue constant has been developed and used successfully to determine the quality of various partitions. Symmetric, stable, and convergent linear, quadratic, and cubic SVs have been obtained, and many different types of partitions have been evaluated. The SV method is tested for both linear and non-linear model problems with and without discontinuities.

Wang, Z. J.↗

Eigenvalues of Rectangular Waveguide Using FEM With Hybrid Elements

A finite element analysis using hybrid triangular-rectangular elements is developed to estimate eigenvalues of a rectangular waveguide. Use of rectangular vector-edge finite elements in the vicinity of the PEC boundary and triangular elements in the interior region more accurately models the physical nature of the electromagnetic field, and consequently quicken the convergence.

Deshpande, Manohar D.↗

Numerical Differentiation for Adaptively Refined Finite Element Meshes

Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.

Borgioli, Andrea↗

Web Growth Used to Confine Screw Dislocations to Predetermined Lateral Positions in 4H-SiC Epilayers

Silicon-carbide- (SiC-) based power devices could enable substantial aerospace electronics benefits over today's silicon-based electronics. However, present-day SiC wafers contain electrically harmful dislocations (including micropipes) that are unpredictably distributed in high densities across all commercial 4H- and 6H-SiC wafers. The NASA Glenn Research Center recently demonstrated a crystal growth process that moves SiC wafer dislocations to predetermined lateral positions in epitaxial layers so that they can be reproducibly avoided during subsequent SiC electronic device fabrication. The process starts by reactive ion etching mesa patterns with enclosed trench regions into commercial on-axis (0001) 4H- or 6H-SiC substrates. An example of a pregrowth mesa geometry with six enclosed triangular-shaped trench regions is shown. After the etch mask is stripped, homoepitaxial growth is carried out in pure stepflow conditions that enable thin cantilevers to grow laterally from the tops of mesas whose pregrowth top surfaces are not threaded by substrate screw dislocations. The image in the bottom figure shows the postgrowth structure that forms after the lateral cantilevers expand to coalesce and completely roof over each of the six triangular trench regions. Atomic force microscope (AFM) measurements of the roof revealed that three elementary screw dislocation growth spirals, each shown in the AFM insets of the bottom image on the previous page, formed in the film roof at three respective points of cantilever film coalescence. The image above shows the structure following an etch in molten potassium hydroxide (KOH) that produced surface etch pits at the dislocation defects. The larger KOH etch pits--S1, S2, and S3--shown in this image correspond to screw dislocations relocated to the final points of cantilever coalescence. The smaller KOH etch pits are consistent with epilayer threading edge dislocations from the pregrowth substrate mesa (P1, P3, and P4) and a final cantilever coalescence point (P2). No defects (i.e., no etch pits) are observed in other cantilevered portions of the film surface. On the basis of the principle of dislocation Burgers vector conservation, we hypothesize that all vertically propagating substrate dislocations in an enclosed trench region become combined into a single dislocation in the webbed film roof at the point of final roof coalescence. The point of final roof coalescence, and therefore the lateral location of a webbed roof dislocation, can be designed into the pregrowth mesa pattern. Screw dislocations with predetermined lateral positions can then be used to provide the new growth steps necessary for growing a 4H/6H-SiC epilayer with a lower dislocation density than the substrate. Devices fabricated on top of such films can be positioned to avoid the preplaced dislocations.

Powell, J. Anthony↗

Fabrication and Deployment Testing of Solar Sail Quadrants for a 20-Meter Solar Sail Ground Test System Demonstration

A 20-meter Scalable Square Solar Sail (S(sup 4)) System was produced and successfully completed functional vacuum testing in NASA Glenn's Space Power Facility at Plum Brook Station Ohio in May 2005. The S(sup 4) system was designed and developed by ATK Space Systems, and the design and production of the Solar Sails for this system was carried out by SRS Technologies. The S(sup 4) system consists of a central structure with four deployable carbon fiber masts that support four triangular sails. SRS has developed an effective and efficient design for triangular sail quadrants that are supported at three points and provide a flat reflective surface with a high fill factor. This sail design is robust enough for deployments in a one atmosphere, one gravity environment and incorporates several advanced features including adhesiveless seaming of membrane strips, compliant edge borders to allow for film membrane cord strain mismatch without causing wrinkling and low mass (3% of total sail mass) ripstop. This paper will outline some of the sail design and fabrication processes and the mature production, packaging and deployment processes that have been developed. This paper will also detail the successful ambient and vacuum testing of the sails and the ATK spacecraft structure. Based on recent experience and testing, SRS is confidant that high Technology Readiness Level (TRL) 5-6 solar sails in the 40-120-meter size range with areal density in the 4-5 grams per square meters (sail minus structure) range can be produced with existing technology. Additional film production research will lead to further reductions in film thickness to less than 1 micron enabling production of sails with areal densities as low as 2.0 grams per square meters using the current design, resulting in a system areal densities as low as 5.3 grams per square meters (sail and structure). These areal densities are low enough to allow nearly all of the Solar Sail missions that have been proposed by the scientific community. The fundamental technologies required to produce these systems has been demonstrated on the 20-meter S(sup 4) sails that have recently completed ground testing demonstrating a mature and technology suitable for incorporation into future flight validation and future mission. Solar Sails can support NASA's Vision for Space Exploration by allowing communication satellite orbits that can maintain continuous communication with the polar regions of the Moon and Mars and to support solar weather monitoring to provide early warning of solar flares and storms that could threaten the safety of astronauts and other spacecraft.

Laue, Greg↗

Effect of Reinforcement Architecture on Fracture of Selectively Reinforced Metallic Compact Tension Specimens

A computer-based parametric study of the effect of reinforcement architectures on fracture response of aluminum compact-tension (CT) specimens is performed. Eleven different reinforcement architectures consisting of rectangular and triangular cross-section reinforcements were evaluated. Reinforced specimens produced between 13 and 28 percent higher fracture load than achieved with the non-reinforced case. Reinforcements with blunt leading edges (rectangular reinforcements) exhibited superior performance relative to the triangular reinforcements with sharp leading edges. Relative to the rectangular reinforcements, the most important architectural feature was reinforcement thickness. At failure, the reinforcements carried between 58 and 85 percent of the load applied to the specimen, suggesting that there is considerable load transfer between the base material and the reinforcement.

Abada, Christopher H.↗

Fracture Response Enhancement Of Aluminum Using In-Situ Selective Reinforcement

A computer-based parametric study of the effect of reinforcement architectures on fracture response of aluminum compact-tension (CT) specimens is performed. Eleven different reinforcement architectures consisting of rectangular and triangular cross-section reinforcements were evaluated. Reinforced specimens produced between 13 and 28 percent higher fracture load than achieved with the unreinforced case. Reinforcements with blunt leading edges (rectangular reinforcements) exhibited superior performance relative to the triangular reinforcements with sharp leading edges. Relative to the rectangular reinforcements, the most important architectural feature was reinforcement thickness. At failure, the reinforcements carried between 58 and 85 percent of the load applied to the specimen, suggesting that there is considerable load transfer between the base material and the reinforcement.

Abada, Christopher H.↗

Minimum mass design of large-scale space trusses subjected to thermal gradients

Lightweight, deployable trusses are commonly used to support space-borne instruments including RF reflectors, radar panels, and telescope optics. While in orbit, these support structures are subjected to thermal gradients that vary with altitude, location in orbit, and self-shadowing. Since these instruments have tight dimensional-stability requirements, their truss members are often covered with multi-layer insulation (MLI) blankets to minimize thermal distortions. This paper develops a radiation heat transfer model to predict the thermal gradient experienced by a triangular truss supporting a long, linear radar panel in Medium Earth Orbit (MEO). The influence of self-shadowing effects of the radar panel are included in the analysis, and the influence of both MLI thickness and outer covers/coatings on the magnitude of the thermal gradient are formed into a simple, two-dimensional analysis. This thermal model is then used to size and estimate the structural mass of a triangular truss that meets a given set of structural requirements.

thermal truss analysis↗

Method of fabricating lightweight honeycomb structures

A process is disclosed for fabricating lightweight honeycomb type structures out of material such as silicon carbide (SiC) and silicon (S). The lightweight structure consists of a core to define the shape and size of the structure. The core is coated with an appropriate deposit such as SiC or Si to give the lightweight structure strength and stiffness and for bonding the lightweight structure to another surface. The core is fabricated from extremely thin ribs of appropriately stiff and strong material such as graphite. First, a graphite core consisting of an outer hexagonal cell with six inner triangular cells is constructed from the graphite ribs. The graphite core may be placed on the back-up side of a SiC faceplate and then coated with SiC to produce a monolithic structure without the use of any bonding agent. Cores and methods for the fabrication thereof in which the six inner triangular cells are further divided into a plurality of cells are also disclosed.

Goela, Jitendra S.↗

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Diskin, Boris↗

Measuring Cyclic Error in Laser Heterodyne Interferometers

An improved method and apparatus have been devised for measuring cyclic errors in the readouts of laser heterodyne interferometers that are configured and operated as displacement gauges. The cyclic errors arise as a consequence of mixing of spurious optical and electrical signals in beam launchers that are subsystems of such interferometers. The conventional approach to measurement of cyclic error involves phase measurements and yields values precise to within about 10 pm over air optical paths at laser wavelengths in the visible and near infrared. The present approach, which involves amplitude measurements instead of phase measurements, yields values precise to about .0.1 microns . about 100 times the precision of the conventional approach. In a displacement gauge of the type of interest here, the laser heterodyne interferometer is used to measure any change in distance along an optical axis between two corner-cube retroreflectors. One of the corner-cube retroreflectors is mounted on a piezoelectric transducer (see figure), which is used to introduce a low-frequency periodic displacement that can be measured by the gauges. The transducer is excited at a frequency of 9 Hz by a triangular waveform to generate a 9-Hz triangular-wave displacement having an amplitude of 25 microns. The displacement gives rise to both amplitude and phase modulation of the heterodyne signals in the gauges. The modulation includes cyclic error components, and the magnitude of the cyclic-error component of the phase modulation is what one needs to measure in order to determine the magnitude of the cyclic displacement error. The precision attainable in the conventional (phase measurement) approach to measuring cyclic error is limited because the phase measurements are af-

Ryan, Daniel↗

Noncircular Cross Sections Could Enhance Mixing in Sprays

A computational study has shown that by injecting drops in jets of gas having square, elliptical, triangular, or other noncircular injection cross sections, it should be possible to increase (relative to comparable situations having circular cross section) the entrainment and dispersion of liquid drops. This finding has practical significance for a variety of applications in which it is desirable to increase dispersion of drops. For example, in chemical-process sprays, increased dispersion leads to increases in chemical- reaction rates; in diesel engines, increasing the dispersion of drops of sprayed fuel reduces the production of soot; and in household and paint sprays, increasing the dispersion of drops makes it possible to cover larger surfaces. It has been known for some years that single-phase fluid jets that enter flow fields through noncircular inlets entrain more fluid than do comparable jets entering through circular inlets. The computational study reported here was directed in part toward determining whether and how this superior mixing characteristic of noncircular single phase jets translates to a similar benefit in cases of two-phase jets (that is, sprays). The study involved direct numerical simulations of single- and two-phase free jets with circular, elliptical, rectangular, square, and triangular inlet cross sections. The two-phase jets consisted of gas laden with liquid drops randomly injected at the inlets. To address the more interesting case of evaporating drops, the carrier gas in the jets was specified to be initially unvitiated by the vapor of the liquid chemical species and the initial temperature of the drops was chosen to be smaller than that of the gas. The mathematical model used in the study was constructed from the conservation equations for the two-phase flow and included complete couplings of mass, momentum, and energy based on thermodynamically self-consistent specification of the enthalpy, internal energy, and latent heat of vaporization of the vapor.

Bellan, Josette↗

Structural Analysis of Lightning Protection System for New Launch Vehicle

This project includes the design and specification of a lightning protection system for Launch Complex 39 B (LC39B) at Kennedy Space Center, FL in support of the Constellation Program. The purpose of the lightning protection system is to protect the Crew Launch Vehicle (CLV) or Cargo Launch Vehicle (CaLV) and associated launch equipment from direct lightning strikes during launch processing and other activities prior to flight. The design includes a three-tower, overhead catenary wire system to protect the vehicle and equipment on LC39B as described in the study that preceded this design effort: KSC-DX-8234 "Study: Construct Lightning Protection System LC3 9B". The study was a collaborative effort between Reynolds, Smith, and Hills (RS&H) and ASRC Aerospace (ASRC), where ASRC was responsible for the theoretical design and risk analysis of the lightning protection system and RS&H was responsible for the development of the civil and structural components; the mechanical systems; the electrical and grounding systems; and the siting of the lightning protection system. The study determined that a triangular network of overhead catenary cables and down conductors supported by three triangular free-standing towers approximately 594 ft tall (each equipped with a man lift, ladder, electrical systems, and communications systems) would provide a level of lightning protection for the Constellation Program CLV and CaLV on Launch Pad 39B that exceeds the design requirements.

Cope, Anne↗

System and Method for Generating a Frequency Modulated Linear Laser Waveform

A system for generating a frequency modulated linear laser waveform includes a single frequency laser generator to produce a laser output signal. An electro-optical modulator modulates the frequency of the laser output signal to define a linear triangular waveform. An optical circulator passes the linear triangular waveform to a band-pass optical filter to filter out harmonic frequencies created in the waveform during modulation of the laser output signal, to define a pure filtered modulated waveform having a very narrow bandwidth. The optical circulator receives the pure filtered modulated laser waveform and transmits the modulated laser waveform to a target.

Pierrottet, Diego F.↗

Dividing the Concentrator Target From the Genesis Mission

The Genesis spacecraft, launched in 2001, traveled to a Lagrangian point between the Earth and Sun to collect particles from the solar wind and return them to Earth. However, during the return of the spacecraft in 2004, the parachute failed to open during descent, and the Genesis spacecraft crashed into the Utah desert. Many of the solar wind collectors were broken into smaller pieces, and the field team rapidly collected the capsule and collector pieces for later assessment. On each of the next few days, the team discovered that various collectors had survived intact, including three of four concentrator targets. Within a month, the team had imaged more than 10,000 fragments and packed them for transport to the Astromaterials Acquisition and Curation Office within the ARES Directorate at JSC. Currently, the Genesis samples are curated along with the other extraterrestrial sample collections within ARES. Although they were broken and dirty, the Genesis solar wind collectors still offered the science community the opportunity to better understand our Sun and the solar system as a whole. One of the more highly prized concentrator collectors survived the crash almost completely intact. The Genesis Concentrator was designed to concentrate the solar wind by a factor of at least 20 so that solar oxygen and nitrogen isotopes could be measured. One of these materials was the Diamond-on-Silicon (DoS) concentrator target. Unfortunately, the DoS concentrator broke on impact. Nevertheless, the scientific value of the DoS concentrator target was high. The Genesis Allocation Committee received a request for approximately 1 cm(sup 2) of the DoS specimen taken near the focal point of the concentrator for the analysis of solar wind nitrogen isotopes. The largest fragment, Genesis sample 60000, was designated for this allocation and needed to be precisely cut. The requirement was to subdivide the designated sample in a manner that prevented contamination of the sample and minimized the risk of losing or breaking the precious requested sample fragment. The Genesis curator determined that the use of laser scribing techniques to "cut" a precise line and subsequently cleave the sample (in a controlled break of the sample along that line) was the best method for accomplishing the sample subdivision. However, there were risks, including excess heating of the sample, that could cause some of the implanted solar wind to be lost via thermal diffusion. Accidentally breaking the sample during the handling and cleaving process was an additional risk. Early in fiscal year 2013, to address this delicate, complicated task, the ARES Directorate assembled its top scientists to develop a cutting plan that would ensure success when applied to the actual concentrator target wafer; i.e., to produce an approximately 1 cm(sup 2) piece from the requested area of the wafer. The team, subsequently referred to as the JSC Genesis Tiger Team, spent months researching and testing parameters and techniques related to scribing, cleaving, transporting, handling, and holding (i.e., mounting) the specimen. The investigation required considerable "thinking outside the box," and many, many trials using nonflight wafer analogs. After all preliminary testing, the following method was adopted as the final cutting plan. It was used in two final end-to-end practice runs before being used on the actual flight target wafer. The wafer was oriented on the laser cutting stage with the 100 and 010 directions of the wafer parallel to the corresponding X and Y directions of the cutting stage. The laser was programed to scribe 31 lines of the appropriate length along the Y stage direction. The programed scribe lines were separated by 5 micron in the X direction. The laser parameters were set as follows: (1) The laser power was 0.5 watts; (2) each line consisted of 50 passes, with the Z position being advanced 5 micron per pass; and (3) 30 s would elapse before the next line was scribed to allow for wafer cool down from any possible heating via the laser. The ablated material that "stuck" in the "scribe-cut" was removed from the "cut" using an ultrasonic micro-tool. After all the ablated silicon was removed from the wafer, the wafer was repositioned in exactly the same orientation on the laser stage. The laser was focused using the bottom of the wafer channel, and the 31-line scribing pattern described above was reprogrammed using the Z position of the groove bottom as the starting Z value instead of the top wafer surface, which was used previously. Upon completion of the second set of scribes, the ultrasonic micro-tool was again used to clean out the cut. The wafer was remounted on the stage in exactly the same orientation as before. The laser was again focused on the bottom of the groove. This time, however, the laser was.programed to scribe only one line down the exact center of the channel. The final scribe line consisted of 100 passes with a Z advance of 5 micron per pass and with the laser power set at 0.5 watts. As mentioned above, the final cutting plan was practiced in two end-to-end trials using non-flight, triangular-shaped silicon wafers similar in size and orientation to the actual DOS 60000 target sample. The actual scribing of the triangular-shaped wafers required scribing two lines and cleaving (i.e. scribe-cleave, then scribe-cleave) to obtain the piece requested for allocation. Early in December 2012, after many months of experiments and practicing and perfecting the techniques and procedures, the team successfully subdivided the Genesis DoS 60000 target sample, one of the most scientifically important samples from the Genesis mission (figure 2). On December 17, 2012, the allocated piece of concentrator target sample was delivered to the requesting principal investigator.The cutting plan developed for the subdivision of this sample will be used as the model for subdividing future requested Genesis flight wafers (appropriately modified for different wafer types).

Lauer, H. V., Jr.↗

Longitudinal Laminar Flow Between Cylinders Arranged in Regular Array

The increasing complexity of heat transfer and process situations which involve fluid flow has demanded the frequent use of flow passages of unusual geometrical configuration. The present investigation is concerned with one such novel configuration, namely the longitudinal flow between solid cylindrical rods which are arranged in regular array. A schematic diagram of the situation under study. The rods may be located either in triangular or square array. The flow will be taken to be laminar and fully developed. The aim of this analysis is to determine the pressure drop, shear stress, and velocity-distribution characteristics of the system. The starting point of this study is the basic law of momentum conservation. The resulting differential equation has been solved in an approximate, but almost exact, manner by the use of truncated trigonometric series. Results are obtained over a wide range of porosity values for both the triangular and square arrays. Heat transfer has not been considered. The configuration under investigation has potential application in compact heat exchangers for nuclear reactors and other situations. Further the results should also be of interest in the theory of flow through unconsolidated porous beds (ia, 9a). The only related analytical work known to the authors is that of Emersleben (S), who considered only the square array. His rather involved solution, based on complex zeta functions, appears to be valid only at high porosities. Experiments covering a porosity range of 0.093 to 0.984 have been made by Sullivan (4) using parallel-oriented fibers, most of the tests being for fibers in random array. These previous investigations will be compared with the present theory in a later section.

Sparrow, E. M.↗

System and Method for Generating a Frequency Modulated Linear Laser Waveform

A system for generating a frequency modulated linear laser waveform includes a single frequency laser generator to produce a laser output signal. An electro-optical modulator modulates the frequency of the laser output signal to define a linear triangular waveform. An optical circulator passes the linear triangular waveform to a band-pass optical filter to filter out harmonic frequencies created in the waveform during modulation of the laser output signal, to define a pure filtered modulated waveform having a very narrow bandwidth. The optical circulator receives the pure filtered modulated laser waveform and transmits the modulated laser waveform to a target.

Pierrottet, Diego F.↗