Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Hwang, Y. M.↗

Microstructure of Al2O3 scales formed on NiCrAl alloys

The structure of transient scales formed on pure and Y or Zr-doped Ni-15Cr-13Al alloys oxidized for 0.1 hr at 1100 C was studied by the use of transmission electron microscopy. Crystallographically oriented scales were found on all three alloys, but especially for the Zr-doped NiCrAl. The oriented scales consisted of alpha-(Al,Cr)2O3, Ni(Al,Cr)2O4 and gamma-Al2O3. They were often found in intimate contact with each other such that the close-packed planes and directions of one oxide phase were aligned with those of another. The prominent structural features of the oriented scales were approximately equal to micrometer subgrains; voids, antiphase domain boundaries and aligned precipitates were also prevalent. Randomly oriented alpha-Al2O3 was also found and was the only oxide ever observed at the immediate oxide metal interface. These approximately 0.15 micrometer grains were populated by intragranular voids which decreased in size and number towards the oxide metal interface. A sequence of oxidation was proposed in which the composition of the growing scale changed from oriented oxides rich in Ni and Cr to oriented oxides rich in Al. At the same time the structure changed from cubic spinels to hexagonal corundums with apparent precipitates of one phase in the matrix of the other. Eventually randomly oriented pure alpha-Al2O3 formed as the stable oxide with an abrupt transition: there was no gradual loss of orientation, no gradual compositional change or no gradual decrease in precipitate density.

Smialek, J. L.↗

Computation of Free-Free Transitions in Atomic Physics: Foundations

The amplitude T for "free-free" processes, such as bremsstrahlung or photo- absorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture, or the photo-effect, this expression contains an unphysical term, proportional to a delta-function and is not really the physical amplitude Tphys. This continues to be true for both the velocity and length form of the dipole approximation to the amplitude T. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude is modified by a long- distance cutoff, the modified form approaches Tphys as the cutoff is removed. The modified form then serves as a basis for the definition of a physical velocity dipole amplitude and this in turn leads to an equivalent length form of the dipole amplitude. This exercise provides a clear theoretical basis for many extant calculations in which cutoff factors are introduces somewhat ad hoc, as needed.

Bhatia, A. K.↗

Impact of Improvements in Volcanic Implementation on Atmospheric Chemistry and Climate in the GISS-E2 Model

The representation of volcanic eruptions in climate models introduces some of the largest errors when evaluating historical simulations, partly due to the crude model parameterizations. We will show preliminary results from the Goddard Institute for Space Studies (GISS)-E2 model comparing traditional highly parameterized volcanic implementation (specified Aerosol Optical Depth, Effective Radius) to deploying the full aerosol microphysics module MATRIX and directly emitting SO2 allowing us the prognosically determine the chemistry and climate impact. We show a reasonable match in aerosol optical depth, effective radius, and forcing between the full aerosol implementation and reconstructions/observations of the Mt. Pinatubo 1991 eruption, with a few areas as targets for future improvement. This allows us to investigate not only the climate impact of the injection of volcanic aerosols, but also influences on regional water vapor, O3, and OH distributions. With the skill of the MATRIX volcano implementation established, we explore (1) how the height of the injection column of SO2 influence atmospheric chemistry and climate response, (2) how the initial condition of the atmosphere influences the climate and chemistry impact of the eruption with a particular focus on how ENSO and QBO and (3) how the coupled chemistry could mitigate the climate signal for much larger eruptions (i.e. the 1258 eruption, reconstructed to be approximately 10x Pinatubo). During each sensitivity experiment we assess the impact on profiles of water vapor, O3, and OH, and assess how the eruption impacts the budget of each.

aerosols↗

Chondrule remelting: Evidence from coarse-grained chondrule rims and compound chondrules

The meteorites that best preserve the nebular record are the type 3 ordinary (OC) and carbonaceous chondrites; their major components include chondrules and chondrule fragments, refractory and mafic inclusions, FeO-rich silicate matrix material. Many chondrules are surrounded by nms; these can be divided into two major types: (1) fine-grained rims, which are composed of matrix material; and (2) igneous or coarse-grained rims, which have igneous textures and larger, less-ferroan mafic silicate grains. Fine-grained rims surround most of the chondrules in the least-equilibrated type 3 ordinary and carbonaceous chondrites. They were most likely derived via collapse of clumps of nebular dust that accreted around coarse objects such as chondrules and inclusions. Coarse-grined or igneous rims surround approximately 10% of the chondrules in type 3 OC and approximately 50% of the chondrules in CV3 chondrites as well as some chondrule fragments and isolated mineral grains. They probably formed by partly melting finer-grained dust-rich precursors and admixed chondrule fragments.

Rubin, A. E.↗

In Situ Location and Characterization of Carbon-bearing Phases in Carbonaceous Chondrites: Insights from Yamato 791198, a Weakly-altered CM2 Chondrite

Intense studies of carbonaceous chondrites have provided remarkable insights into the behavior of carbon during the earliest stages of our solar system. This research has demonstrated that carbonaceous meteorites contain a diverse array of organic compounds, whose origins are probably the result of multiple processes that occurred in different locations including interstellar space, the solar nebula and asteroidal parent bodies [1-3]. The most abundant organic carbon component in CI1 and CM2 carbonaceous chondrites is so-called macromolecular carbon, a high molecular weight material that has some affinities to terrestrial kerogen and constitutes approximately 60-70% of the organic material in these meteorites. Although recent studies e.g. [3] have radically improved our understanding of the structural and compositional characteristics of this material, a number of key questions remain to be addressed. In particular, our knowledge of where this macromolecular material is distributed at the fine-scale within carbonaceous chondrites is scant. [4] have shown that organic material is associated with phyllosilicate-rich matrix in CM chondrites, but the detailed mineralogical associations are not well-known. Over the past 2 years, we have begun to address this question by using energy filtered transmission electron microscopy (EFTEM) to locate carbon-bearing materials in situ, focusing specifically on the CM2s. To date we have reported data on the Murchison CM2 chondrite [5], a meteorite that has experienced a modest degree of aqueous alteration. To extend our observations to other CM2 chondrites, we have examined the occurrence of carbon-bearing phases in Yamato 791198. Our recent studies [5] have shown that Y-791198 is among the most weakly-altered CM chondrite currently known and hence is likely to preserve a quite primitive distribution of carbonaceous material. In this study, we present initial observations on the distribution of these materials in one fine-grained rim and compare them with our results from Murchison. Such information may provide important insights into the origins of the carbonaceous material and how it was distributed in nebular and perhaps presolar dust.

Brearley, Adrian J.↗

Thermal Inspection of a Composite Fuselage Section Using a Fixed Eigenvector Principal Component Analysis Method

A composite fuselage aircraft forward section was inspected with flash thermography. The fuselage section is 24 feet long and approximately 8 feet in diameter. The structure is primarily configured with a composite sandwich structure of carbon fiber face sheets with a Nomex(Trademark) honeycomb core. The outer surface area was inspected. The thermal data consisted of 477 data sets totaling in size of over 227 Gigabytes. Principal component analysis (PCA) was used to process the data sets for substructure and defect detection. A fixed eigenvector approach using a global covariance matrix was used and compared to a varying eigenvector approach. The fixed eigenvector approach was demonstrated to be a practical analysis method for the detection and interpretation of various defects such as paint thickness variation, possible water intrusion damage, and delamination damage. In addition, inspection considerations are discussed including coordinate system layout, manipulation of the fuselage section, and the manual scanning technique used for full coverage.

Zalameda, Joseph N.↗

Evaluation of the Trade Space Between UAS Maneuver Performance and SAA System Performance Requirements

A need exists to safely integrate Unmanned Aircraft Systems (UAS) into the National Airspace System. Replacing manned aircraft's see-and-avoid capability in the absence of an onboard pilot is one of the key challenges associated with safe integration. Sense-and-avoid (SAA) systems will have to achieve yet-to-be-determined required separation distances for a wide range of encounters. They will also need to account for the maneuver performance of the UAS they are paired with. The work described in this paper is aimed at developing an understanding of the trade space between UAS maneuver performance and SAA system performance requirements. An assessment of current manned and unmanned aircraft performance was used to establish potential UAS performance test matrix bounds. Then, nearterm UAS integration work was used to narrow down the scope. A simulator was developed with sufficient fidelity to assess SAA system performance requirements for a wide range of encounters. The simulator generates closest-point-of-approach (CPA) data from the wide range of UAS performance models maneuvering against a single intruder with various encounter geometries. The simulator is described herein and has both a graphical user interface and batch interface to support detailed analysis of individual UAS encounters and macro analysis of a very large set of UAS and encounter models, respectively. Results from the simulator using approximate performance data from a well-known manned aircraft is presented to provide insight into the problem and as verification and validation of the simulator. Analysis of climb, descent, and level turn maneuvers to avoid a collision is presented. Noting the diversity of backgrounds in the UAS community, a description of the UAS aerodynamic and propulsive design and performance parameters is included. Initial attempts to model the results made it clear that developing maneuver performance groups is required. Discussion of the performance groups developed and how to know in which group an aircraft belongs for a given flight condition and encounter is included. The groups are specific to airplane, flight condition, and encounter, rather than airplane-only specific. Results and methodology for developing UAS maneuver performance requirements are presented for each maneuver as well. Results for the vertical maneuver indicate that a minimum specific excess power value can assure a minimum CPA for a given time-to-go prediction. However, smaller values of specific excess power may achieve or exceed the same CPA if the UAS has sufficient speed to trade for altitude. Level turn results are less impacted by specific excess power and are presented as a function of turn rate. The effect of altitude is also discussed for the turns. Next steps and future work are discussed. Future studies will lead to better quantification of the preliminary results and cover the remainder of the proposed test matrix. It is anticipated that this will be done in conjunction with RTCA SC-228 over the next few months.

Jack, Devin P.↗

Carbide coated fibers in graphites-aluminum composites

Research activities are described for a NASA-supported program at the Los Alamos Scientific Laboratory to develop graphite fiber-aluminum matrix composites. A chemical vapor deposition apparatus was constructed for continuously coating graphite fibers with TiC. As much as 150 meters of continuously coated fibers were produced. Deposition temperatures were varied from 1365 K to about 1750 K, and deposition time from 6 to 150 seconds. The 6 sec deposition time corresponded to a fiber feed rate of 2.54 m/min through the coater. Thin, uniform, adherent TiC coats, with thicknesses up to approximately 0.1 micrometer were produced on the individual fibers of Thornel 50 graphite yarns without affecting fiber strength. Although coat properties were fairly uniform throughout a given batch, more work is needed to improve the batch-to-batch reproducibility. Samples of TiC-coated Thornel 50 fibers were infiltrated with an aluminum alloy and hot-pressed in vacuum to produce small composite bars for flexure testing. Strengths as high as 90% of the rule-of-mixtures strength were achieved. Results of the examination of the fracture surfaces indicate that the bonding between the aluminum and the TiC-coated fibers is better than that achieved in a similar, commercially infiltrated material made with fibers having no observable surface coats. Several samples of Al-infiltrated, TiC-coated Thornel 50 graphite yarns, together with samples of the commercially infiltrated, uncoated fibers, were heated for 100 hours at temperatures near the alloy solidus. The TiC-coated samples appear to undergo less reaction than do the uncoated samples. Photomicrographs are shown.

Imprescia, R. J.↗

A model of the thermal-spike mechanism in graphite/epoxy laminates

The influence of a thermal spike on a moisture-saturated graphite/epoxy composite was studied in detail. A single thermal spike from 25 C to 132 C was found to produce damage as evidenced by a significant increase in the level of moisture saturation in the composite. Approximately half of this increase remained after a vacuum anneal at 150 C for 7 days, suggesting the presence of an irreversible damage component. Subsequent thermal spikes created less and less additional moisture absorption, with the cumulative effect being a maximum or limiting moisture capacity of the composite. These observations are explained in terms of a model previously developed to explain the reverse thermal effect of moisture absorption in epoxy and epoxy matrix composites. This model, based on the inverse temperature dependence of free volume, contributes an improved understanding of thermal-spike effects in graphite/epoxy composites.

Adamson, M. J.↗

New acousto-ultrasonic techniques applied to aerospace materials

The use of an NdYAG pulsed laser for generating ultrasonic waves for NDE in resin matrix composites was investigated. A study was conducted of the use of the 1.064 micron wavelength NdYAG pulsed laser with the neat, unreinforced resin as well as graphite fiber/polymer composite specimens. In the case of the neat resins it was found that, at normal incidence, about 25 percent of the laser pulse energy was reflected at the incident surface. An attenuation coefficient for the polyimide resin, PMR-15 was determined to be approximately 5.8 np/cm. It was found in energy balance studies that graphite fiber/polymer specimens attenuate the laser beam more than do neat resins. The increase absorption is in the graphite fibers. The occurrence of laser induced surface damage was also studied. For the polymer neat resin, damage appears as pit formation over a small fraction of the pulse impact area and discoloration over a larger part of the area. A damage threshold was inferred from observed damage as a function of pulse energy. The 600 F cured PMR-15 and PMR-11 exhibit about the same amount of damage for a given laser pulse energy. The damage threshold is between 0.06 and 0.07 J/sq cm.

Kautz, Harold E.↗

Progress in navigation filter estimate fusion and its application to spacecraft rendezvous

A new derivation of an algorithm which fuses the outputs of two Kalman filters is presented within the context of previous research in this field. Unlike other works, this derivation clearly shows the combination of estimates to be optimal, minimizing the trace of the fused covariance matrix. The algorithm assumes that the filters use identical models, and are stable and operating optimally with respect to their own local measurements. Evidence is presented which indicates that the error ellipsoid derived from the covariance of the optimally fused estimate is contained within the intersections of the error ellipsoids of the two filters being fused. Modifications which reduce the algorithm's data transmission requirements are also presented, including a scalar gain approximation, a cross-covariance update formula which employs only the two contributing filters' autocovariances, and a form of the algorithm which can be used to reinitialize the two Kalman filters. A sufficient condition for using the optimally fused estimates to periodically reinitialize the Kalman filters in this fashion is presented and proved as a theorem. When these results are applied to an optimal spacecraft rendezvous problem, simulated performance results indicate that the use of optimally fused data leads to significantly improved robustness to initial target vehicle state errors. The following applications of estimate fusion methods to spacecraft rendezvous are also described: state vector differencing, and redundancy management.

Carpenter, J. Russell↗

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Kreider, Kevin L.↗

Testing of DLR C/C-SiC for HIFiRE 8 Scramjet Combustor

Ceramic Matrix Composites (CMCs) have been proposed for hot structures in scramjet combustors. Previous studies have calculated significant weight savings by utilizing CMCs (active and passive) versus actively cooled metallic scramjet structures. Both a C/C and a C/C-SiC material system fabricated by DLR (Stuttgart, Germany) are being considered for use in a passively cooled combustor design for HIFiRE 8, a joint Australia / AFRL hypersonic flight program, expected to fly at Mach 7 for approximately 30 sec, at a dynamic pressure of 55 kPa. Flat panels of the DLR C/C and the C/C-SiC were tested in the NASA Langley Direct Connect Rig (DCR) at Mach 5 and Mach 6 enthalpy for several minutes. Gaseous hydrogen fuel was used to fuel the scramjet combustor. The test panels were instrumented with embedded Type K and Type S thermocouples. Zirconia felt insulation was used in some of the tests to increase the surface temperature of the C/C-SiC panel for approximately 350degF. The final C/C-SiC panel was tested for 3 cycles totaling over 135 sec at Mach 6 enthalpy. Slightly more erosion was observed on the C/C panel than the C/C-SiC panels, but both material systems demonstrated acceptable recession performance for the HIFiRE 8 flight.

Glass, David E.↗

The coupled states approximation for scattering of two diatoms

The paper presents a detailed development of the coupled-states approximation for the general case of two colliding diatomic molecules. The high-energy limit of the exact Lippman-Schwinger equation is applied, and the analysis follows the Shimoni and Kouri (1977) treatment of atom-diatom collisions where the coupled rotor angular momentum and projection replace the single diatom angular momentum and projection. Parallels to the expression for the differential scattering amplitude, the opacity function, and the nondiagonality of the T matrix are reported. Symmetrized expressions and symmetrized coupled equations are derived. The present correctly labeled coupled-states theory is tested by comparing its calculated results with other computed results for three cases: H2-H2 collisions, ortho-para H2-H2 scattering, and H2-HCl.

Heil, T. G.↗

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗

Single-Scattering Properties of Ellipsoidal Dust Aerosols Constrained By Measured Dust Shape Distributions

Most global aerosol models approximate dust as spherical particles, whereas most remote sensing retrieval algorithms approximate dust as spheroidal particles with a shape distribution that conflicts with measurements. These inconsistent and inaccurate shape assumptions generate biases in dust single-scattering properties. Here, we obtain dust single-scattering properties by approximating dust as triaxial ellipsoidal particles with observationally constrained shape distributions. We find that, relative to the ellipsoidal dust optics obtained here, the spherical dust optics used in most aerosol models underestimate dust single-scattering albedo, mass extinction efficiency, and asymmetry parameter for almost all dust sizes in both the shortwave and longwave spectra. We further find that the ellipsoidal dust optics are in substantially better agreement with observations of the scattering matrix and linear depolarization ratio than the spheroidal dust optics used in most retrieval algorithms. However, relative to observations, the ellipsoidal dust optics overestimate the lidar ratio by underestimating the backscattering intensity by a factor of ∼2. This occurs largely because the computational method used to simulate ellipsoidal dust optics (i.e., the improved geometric optics method) underestimates the backscattering intensity by a factor of ∼2 relative to other computational methods (e.g., the physical geometric optics method). We conclude that the ellipsoidal dust optics with observationally constrained shape distributions can help improve global aerosol models and possibly remote sensing retrieval algorithms that do not use the backscattering signal.

Dust↗

A conceptual model of the thermal-spike mechanism in graphte/epoxy laminates

The influence of a thermal spike on a moisture-saturated graphite/epoxy composite was studied in detail. A single thermal spike from 25 to 132 C was found to produce damage, as evidenced by a significant increase in the level of moisture saturation in the composite. Approximately half of this increase remained after a vacuum-anneal at 150 C for seven days, suggesting the presence of an irreversible damage component. Subsequent thermal spikes created less and less additional moisture absorption, with the cumulative effect being a maximum or limiting moisture capacity of the composite. These observations are explained in terms of a model previously developed to explain the reverse thermal effect of moisture absorption in epoxy and epoxy-matrix composites. This model, based on the inverse temperature dependence of free volume, improves current understanding of thermal spike effects in graphite/epoxy composites.

Adamson, M. J.↗