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 523 records · Page 29

Thermographic imaging for high-temperature composite materials: A defect detection study

The ability of a thermographic imaging technique for detecting flat-bottom hole defects of various diameters and depths was evaluated in four composite systems (two types of ceramic matrix composites, one metal matrix composite, and one polymer matrix composite) of interest as high-temperature structural materials. The holes ranged from 1 to 13 mm in diameter and 0.1 to 2.5 mm in depth in samples approximately 2-3 mm thick. The thermographic imaging system utilized a scanning mirror optical system and infrared (IR) focusing lens in conjunction with a mercury cadmium telluride infrared detector element to obtain high resolution infrared images. High intensity flash lamps located on the same side as the infrared camera were used to heat the samples. After heating, up to 30 images were sequentially acquired at 70-150 msec intervals. Limits of detectability based on depth and diameter of the flat-bottom holes were defined for each composite material. Ultrasonic and radiographic images of the samples were obtained and compared with the thermographic images.

Roth, Don J.↗

Mineralogy and Ar-39 - Ar-40 of an old pristine basalt: Thermal history of the HED parent body

Previous investigations of mineral chemistry and Rb-Sr and Sm-Nd ages indicated that clast,84 from eucrite Yamato 75011 had preserved the pristine nature of its initial crystallization during an early stage of the HED parent body. Microscale mineralogy and Ar-39-Ar-40 ages of this clast, however, revealed local disturbance of microtextures and partially reset ages. This evidence suggests that, in addition to initial crystallization and rapid cooling, the Y75011,84 clast experienced shock deformation, reheating of short duration at higher temperature, and brecciation. These characteristics suggest two or more impact events. Fe-rich olivine filling fractures in pyroxene may have been introduced during the accompanying shock fracturing. The inferred Ar-39-Ar-40 degassing ages for Y75011 matrix and clast, 84 are 3.94 +/- 0.04 Ga and 3.98 +/- 0.03 Ga, respectively. The suggested degassing age for a clast from Y790020, believed to be paired with Y75011, is approximately 4.03 Ga, but could be younger. We consider it likely that all three samples experienced a common degassing event 3.95 +/- 0.05 Ga ago, but we cannot rule out two or more events spaced over a approximately 0.1 Ga interval. Higher temperature extractions of the two clast samples show significantly older apparent ages up to approximately 4.5 Ga and suggest that the time/temperature regime of this event was not sufficient to degas Ar totally. Most likely, the K-Ar ages were reset by thermal metamorphism associated with one or more impact events associated with shock fracturing, formation of Fe-rich olivine veins, and/or meteorite brecciation. The pyroxene annealing that commonly occurs in many eucrites is likely to be a much earlier process than the impact-produced textural changes and reset K-Ar ages observed in these meteorites. The existence of mineralogical and chronological evidence for metamorphism in an otherwise pristine eucrite suggests that the HED parent body experienced an extensive degree of early cratering.

Takeda, Hiroshi↗

On the synthesis of resonance lines in dynamical models of structured hot-star winds

We examine basic issues involved in synthesizing resonance-line profiles from 1-D, dynamical models of highly structured hot-star winds. Although these models exhibit extensive variations in density as well as velocity, the density scale length is still typically much greater than the Sobolev length. The line transfer is thus treated using a Sobolev approach, as generalized by Rybicki & Hummer (1978) to take proper account of the multiple Sobolev resonances arising from the nonmonotonic velocity field. The resulting reduced-lambda-matrix equation describing nonlocal coupling of the source function is solved by iteration, and line profiles are then derived from formal solution integration using this source function. Two more approximate methods that instead use either a stationary or a structured, local source function yield qualitatively similar line-profiles, but are found to violate photon conservation by 10% or more. The full results suggest that such models may indeed be able to reproduce naturally some of the qualitative properties long noted in observed UV line profiles, such as discrete absorption components in unsaturated lines, or the blue-edge variability in saturated lines. However, these particular models do not yet produce the black absorption troughs commonly observed in saturated lines, and it seems that this and other important discrepancies (e.g., in acceleration time scale of absorption components) may require development of more complete models that include rotation and other 2-D and/or 3-D effects.

Puls, J.↗

Aero-Heating of Shallow Cavities in Hypersonic Freestream Flow

The purpose of these experiments and analysis was to augment the heating database and tools used for assessment of impact-induced shallow-cavity damage to the thermal protection system of the Space Shuttle Orbiter. The effect of length and depth on the local heating disturbance of rectangular cavities tested at hypersonic freestream conditions has been globally assessed using the two-color phosphor thermography method. These rapid-response experiments were conducted in the Langley 31-Inch Mach 10 Tunnel and were initiated immediately prior to the launch of STS-114, the initial flight in the Space Shuttle Return-To-Flight Program, and continued during the first week of the mission. Previously-designed and numerically-characterized blunted-nose baseline flat plates were used as the test surfaces. Three-dimensional computational predictions of the entire model geometry were used as a check on the design process and the two-dimensional flow assumptions used for the data analysis. The experimental boundary layer state conditions were inferred using the measured heating distributions on a no-cavity test article. Two test plates were developed, each containing 4 equally-spaced spanwise-distributed cavities. The first test plate contained cavities with a constant length-to-depth ratio of 8 with design point depth-to-boundary-layer-thickness ratios of 0.1, 0.2, 0.35, and 0.5. The second test plate contained cavities with a constant design point depth-to-boundary-layer-thickness ratio of 0.35 with length-to-depth ratios of 8, 12, 16, and 20. Cavity design parameters and the test condition matrix were established using the computational predictions. Preliminary results indicate that the floor-averaged Bump Factor (local heating rate nondimensionalized by upstream reference) at the tested conditions is approximately 0.3 with a standard deviation of 0.04 for laminar-in/laminar-out conditions when the cavity length-to-boundary-layer thickness is between 2.5 and 10 and for cavities in the depth-to-boundary-layer-thickness range of 0.3 to 0.8. Over this same range of conditions and parameters, preliminary results also indicate that the maximum Bump Factor on the cavity centerline falls between 2.0 and 2.75, as long as the cavity-exit conditions remain laminar. Cavities with length-to-boundary-layer-thickness ratio less than 2.5 can not be easily classified with this approach and require further analysis.

Everhart, Joel L.↗

Thermal Conductivity and Erosion Durability of Composite Two-Phase Air Plasma Sprayed Thermal Barrier Coatings

To enhance efficiency of gas turbines, new thermal barrier coatings (TBCs) must be designed which improve upon the thermal stability limit of 7 wt% yttria stabilized zirconia (7YSZ), approximately 1200 C. This tenant has led to the development of new TBC materials and microstructures capable of improved high temperature performance. This study focused on increasing the erosion durability of cubic zirconia based TBCs, traditionally less durable than the metastable t' zirconia based TBCs. Composite TBC microstructures composed of a low thermal conductivity/high temperature stable cubic Low-k matrix phase and a durable t' Low-k secondary phase were deposited via APS. Monolithic coatings composed of cubic Low-k and t' Low-k were also deposited, in addition to a 7YSZ benchmark. The thermal conductivity and erosion durability were then measured and it was found that both of the Low-k materials have significantly reduced thermal conductivities, with monolithic t' Low-k and cubic Low-k improving upon 7YSZ by approximately 13 and approximately 25%, respectively. The 40 wt% t' Low-k composite (40 wt% t' Low-k - 60 wt% cubic Low-k) showed a approximately 22% reduction in thermal conductivity over 7YSZ, indicating even at high levels, the t' Low-k secondary phase had a minimal impact on thermal in the composite coating. It was observed that a mere 20 wt% t' Low-k phase addition can reduce the erosion of a cubic Low-k matrix phase composite coating by over 37%. Various mixing rules were then investigated to assess this non-linear composite behavior and suggestions were made to further improve erosion durability.

Rare earth zirconia↗

Modified Coulomb-Dipole Theory for 2e Photoionization

In the light of recent experiment on 2e photoionization of Li near threshold, we have considered a modification of the Coulomb-dipole theory, retaining the basic assumption that the threshold is dominated by asymmetric events in phase space [implies r(sub 1), k(sub 1)) greater than or equal to 2(r(sub 2), k(sub )]. In this region [in a collinear model, 2/r(sub 12) approached + 2/(r(sub 1)+r(sub 2)] the interaction reduces to V(rIsub 1) is greater than or equal to 2r(sub 2) is identically equal to [(-Z/r(sub 2)-(A-1)/r(sub 1)] + [(-2r(sub 2)/r(sub 1 exp 2)] is identically equal to V(sub c)+[V(sub d)]. For two electron emission Z = 2, thus both electrons see a Coulomb potential (V(sub c)) asymptotically, albeit each seeing a different charge. The residual potential (V(sub d)) is dipole in character. Writing the total psi = psi (sub c) + psi(sub d) = delta psi, and noting that. (T+V(sub c)-E)psy(sub c) = 0 and (T+V(sub c))psi(sub d) = 0 can be solved exactly, we find, substituting psi into the complete Schrod. Eq., that delta psi = -(H-E)(exp -1)(V(sub d) psi(sub 0)+V(sub c psi (sub 1). Using the fact that the absolute value of V(sub c) is much more than the absolute value of V(sub d) in almost all of configuration space, we can replace H by H(sub 0) in 9H-E)(exp -1) to obtain an improved approximation psi (improved) = psi(sub c) + psi(sub d) -(H(sub 0)-E)(exp -1) (V(sub c) psi (sub 0) + V(sub c) psi(sub 1). Here's the Green's function (H(sub 0)-E)(exp -1), can be exhibited explicitly, but the last term in psi (improved) is small, compared to the first two terms. Inserting them into the transition matrix element, which one handles in the usual way, we obtain in the limit E approaches 0, the threshold law: Q(E) alpha E + M(E)E(exp 5/4) + higher order (Eq. 1a). The modulation function, M(E), is a well-defined (but very non-trivial integral, but it is expected to be well approximated by a sinusoidal function containing a dipole phase term (M(E) = c sin[alpha log (E) + micron] (Eq. 1b). Experimental results show definite modulations, and are well fitted by Eqs (1).

Source record↗

Properties of silicon carbide fiber-reinforced silicon nitride matrix composites

The mechanical properties of NASA Lewis developed SiC/RBSN composites and their thermal and environmental stability havd been studied. The composites consist of nearly 30 vol pct of aligned 142 micron diameter chemically vapor-deposited SiC fibers in a relatively porous silicon nitride matrix. In the as-fabricated condition, the unidirectional and 2-D composites exhibited metal-like stress-strain behavior, graceful failure, and showed improved properties when compared with unreinforced matrix of comparable density. Furthermore, the measured room temperature tensile properties were relativley independent of tested volume and were unaffected by artifical notches normal to the loading direction or by thermal shocking from temperatures up to 800 C. The four-point bend strength data measured as a function of temperature to 1400 C in air showed that as-fabricated strength was maintained to 1200 C. At 1400 C, however, nearly 15 pct loss in strength was observed. Measurement of room temperature tensile strength after 100 hr exposure at temperatures to 1400 C in a nitrogen environment indicated no loss from the as-fabricated composite strength. On the other hand, after 100 hr exposure in flowing oxygen at 1200 and 1400 C, the composites showed approximately 40 pct loss from their as-fabricated ultimate tensile strength. Those exposed between 400 to 1200 C showed nearly 60 pct strength loss. Oxidation of the fiber/matrix interface as well as internal oxidation of the porous Si3N4 matrix are likely mechanisms for strength degradation. The excellent strength reproducibility, notch insensitivity, and high temperature strength of the composite makes it an ideal candidate for advanced heat engine applications provided coating or densification methods are developed to avoid internal oxidation attack.

Bhatt, Ramakrishna T.↗

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗

Nonlinear filtering for spacecraft attitude estimation

Nonlinear filtering techniques are applied to spacecraft attitude estimation using quaternion parameterization for the attitude kinematics. By replacing the angular velocity vector by the gyro output vector, a state dependent noise vector is introduced in the seven-dimensional system equations. The resulting conditional probability density function from the Ito differential rule is governed by the Fokker Planck partial differential equation which is approximated by the second order mean and covariance differential equations. In order to minimize computer loading, the covariance propagation is carried out in six-dimensional state space using a matrix transformation. The star tracker data is used to update the covariance matrix in the seven-dimensional space. The algorithm is simulated for an earth pointing spacecraft mission, using Monte Carlo samples of gyro and star measurements. The performance of the second order filter is compared with the extended Kalman Filter through several simulation runs and drift rates have been identified.

Vathsal, S.↗

Integrated structural-aerodynamic design optimization

This paper focuses on the processes of simultaneous aerodynamic and structural wing design as a prototype for design integration, with emphasis on the major difficulty associated with multidisciplinary design optimization processes, their enormous computational costs. Methods are presented for reducing this computational burden through the development of efficient methods for cross-sensitivity calculations and the implementation of approximate optimization procedures. Utilizing a modular sensitivity analysis approach, it is shown that the sensitivities can be computed without the expensive calculation of the derivatives of the aerodynamic influence coefficient matrix, and the derivatives of the structural flexibility matrix. The same process is used to efficiently evaluate the sensitivities of the wing divergence constraint, which should be particularly useful, not only in problems of complete integrated aircraft design, but also in aeroelastic tailoring applications.

Haftka, R. T.↗

Matrix elements in the coupled-cluster approach - With application to low-lying states in Li

A procedure is suggested for evaluating matrix elements of an operator between wavefunctions in the coupled-cluster form. The use of the exponential ansatz leads to compact exponential expressions also for matrix elements. Algorithms are developed for summing all effects of one-particle clusters and certain chains of two-particle clusters (containing the well-known random-phase approximation as a subset). The treatment of one-particle perturbations in single valence states is investigated in detail. As examples the oscillator strength for the 2s-2p transition in Li as well as the hyperfine structure for the two states are studied and compared to earlier work.

Martensson-Pendrill, Ann-Marie↗

SXRF determination of trace elements in chondrule rims in the unequilibrated CO3 chondrite, ALH A77307

The concentrations of Ni, Cu, Zn, Ga, Ge, and Se in five chondrule rims in the CO3 chondrite ALH A77307 (3.0) using the synchrotron x-ray fluorescence (SXRF) microprobe at Brookhaven National Laboratory were determined. The data show that the trace element chemistry of rims on different chondrules is remarkably similar, consistent with data obtained for the major elements by electron microprobe. These results support the idea that rims are not genetically related to individual chondrules, but all sampled the same reservoir of homogeneously mixed dust. Of the trace elements analyzed Zn and Ga show depletions relative to CI chondrite values, but in comparison with bulk CO chondrites all the elements are enriched by approximately 1.5 to 3.5 x CO. The high concentrations of the highly volatile elements Se and Ga and moderately volatile Zn (1.5 to 2 x CO) in rims show that matrix is the major reservoir of volatile elements in ALH A77307.

Brearley, Adrian J.↗

A noniterative improvement of Guyan reduction

In determining the natural modes and frequencies of a linear elastic structure, Guyan reduction is often used to reduce the size of the mass and stiffness matrices and the solution of the reduced system is obtained first. The reduced system modes are then expanded to the size of the original system by using a static transformation linking the retained degrees of freedom to the omitted degrees of freedom. In the present paper, the transformation matrix of Guyan reduction is modified to include additional terms from a series accounting for the inertial effects. However, the inertial terms are dependent on the unknown frequencies. A practical approximation is employed to compute the inertial terms without any iteration. This new transformation is implemented in NASTRAN using a DMAP sequence alter. Numerical examples using a cantilever beam illustrate the necessary condition for allowing a large number of additional terms in the proposed series correction of Guyan reduction. A practical example of a large model of the Plasma Motor Generator module to be flown on a Delta launch vehicle is also presented.

Ganesan, N.↗

Atmospheric Probe Model: Construction and Wind Tunnel Tests

The material contained in this document represents a summary of the results of a low speed wind tunnel test program to determine the performance of an atmospheric probe at low speed. The probe configuration tested consists of a 2/3 scale model constructed from a combination of hard maple wood and aluminum stock. The model design includes approximately 130 surface static pressure taps. Additional hardware incorporated in the baseline model provides a mechanism for simulating external and internal trailing edge split flaps for probe flow control. Test matrix parameters include probe side slip angle, external/internal split flap deflection angle, and trip strip applications. Test output database includes surface pressure distributions on both inner and outer annular wings and probe center line velocity distributions from forward probe to aft probe locations.

Vogel, Jerald M.↗

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗

Computing the effective elasticity of anisotropic porous media from X-ray computed micro-tomography images

Development and optimization of composite materials designed for thermal protection of NASA’s spacecraft requires the understanding of their physical response to high-enthalpy environments. To predict their macro-scale properties and behavior, high-fidelity 3D simulations are performed at the micro-scale on realistic representations of these composites. The digital micro-structures are generated either synthetically or through X-ray micro-tomography reconstructions. One of the main challenges in the prediction of heatshield material structural response is the computation of the effective elasticity of the fibrous composite, as well as the understanding of the deformation and stresses generated at the micro-scale. These are driven by the fiber layout within the micro-structure and the distribution of the infused matrix. In this effort, the micro-mechanical linear elastic behavior of fibrous ablators is modeled through the use of a numerical method based on the Multi-Point Stress Approximation (MPSA) finite volume scheme. The MPSA, a generalization of the more commonly used Multi-Point Flux Approximation (MPFA), was discussed in a previous presentation at the 15th USCCN and in reference. To predict the behavior of fibrous and woven architectures, algorithms that compute the local fiber orientation are used. The implementation of the MPSA was verified using analytical solutions, engineering test cases and compared against legacy Finite Element Analysis (FEA) software. The stress analysis models were then applied to real geometries used by NASA in thermal protection systems such as fibrous preforms and woven materials and the results were compared to experimental data.

Federico Semeraro↗

Dynamics of Gaps Created By Burning in Florida Oak-Saw Palmetto (Quercus, Fagaceae-Serenoa repens, Arecaceae) Scrub

Sandy gaps in the shrub matrix of oak (Quercus L.)-saw palmetto (Serenoa repens (W. Bartram) Small) scrub are created by fire but typically close quickly because of rapid regrowth. Such gaps are important habitat features for rare scrub flora and fauna and appear to have been more common in the historical landscape. We followed, from 1993 to 2016, the dynamics of 12 gaps (32.2-98.1 sq m) created by burning slash piles as part of restoration of long-unburned scrub. Gaps closed slowly, primarily by canopy spread of oaks around the gaps. In the absence of subsequent fire, gaps closed within approximately 12 yr. When burned a second or third time, gap area increased to near the initial after-burn size but then declined in area more rapidly than after the initial fire. Vegetation that reestablished in gaps differed from that of the scrub matrix in having less cover of scrub oaks, less cover of S. repens. > 0.5 m, greater cover of native shrubs and forbs. > 0.5 m, and more bare ground. Soil heating from slash-pile burning killed the roots and rhizomes from which scrub oaks, Serenoa, and ericaceous shrubs sprout; this altered and slowed the after-fire recovery.

Serenoa↗

Software for Processing Flight and Simulated Data of the ATIC Experiment

ATIC (Advanced Thin Ionization Calorimeter) is a balloon borne experiment designed to measure the cosmic ray composition for elements from hydrogen to iron and their energy spectra from approx.50 GeV to near 100 TeV. It consists of a Si-matrix detector to determine the charge of a CR particle, a scintillator hodoscope for tracking, carbon interaction targets and a fully active BGO calorimeter. ATIC had its first flight from McMurdo, Antarctica from 28/12/2000 to 13/01/2001. The ATIC flight collected approximately 25 million events. A C++-class library for building different programs for processing flight and simulated data of the ATIC balloon experiment is described. This library is compatible with the ROOT-system and includes classes and methods for solving a number of problems as the following: Reading data files in different formats (raw-data format, ROOT-format, ASCII-format, different formats for simulated data); Transferring all these formats to the only inner format of the library; Reconstruction of trajectories of primary particles with BGO calorimeter only. The Monte-Carlo simulations with GEANT code were used to obtain the basic tables for computing error corridors and chi(sup 2)-values for the trajectories. Obtaining error corridors for searching for signal of primary particle in the Si-matrix; Searching for hit of primary particle in the Si-matrix with using of error corridor and other criteria (chi(sup 2)-values, agreement between signals in Si-matrix and in the upper layer of scintillator and others); Determination of charge of primary particle; Determination of energy deposit in BGO calorimeter.

Panov, A. D.↗