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 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fluid-like shock compression of dilute polymer nanocomposites

The shock Hugoniot of heterogenous mixtures of discrete particles has been experimentally investigated for porous agglomerates and fluids, while the study of full-density solids has been primarily limited to compressed powders and high-dimensional composites. By dispersing ceria nanoparticles in a polyethylene matrix, we are able to examine the hydrodynamic behavior of a nonporous, heterogenous solid in thermal equilibrium during weak shock compression. Phase-driven discontinuities in the Hugoniot particle velocity–shock velocity (u−D) relationship of pure polyethylene are replicated in the nanocomposites but are shifted to lower velocity and to higher pressure with higher particle concentration. The results are explained using an isothermal, two-velocity fluid model under the hydrodynamic approximation. The model, which assumes a theoretical equation-of-state for ceria and either a low-order or high-order fit to the measured polyethylene Hugoniot, reasonably predicts the Hugoniot for two different polyethylene/ceria nanocomposites. Using the model, the mixture Hugoniot is shown to be insensitive to the Hugoniot of the stiffer constituent when the moduli are sufficiently disparate, while dependence on particle density and volume fraction is preserved through fluid-like motion.

Moore, Nathan W. [Sandia National Laboratories (SN↗
NASA NTRS1976

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.↗
NASA NTRS1982

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.↗
NASA NTRS1988

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.↗
NASA NTRS1994

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↗
NASA NTRS1996

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.↗
NASA NTRS2013

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.↗
DOE OSTI2024

Quasiclassical Gluon Fields and Low’s Soft Theorem at Small Momentum-Fraction x

In the high-energy limit, soft gluons can be approximately described by quasiclassical gluon fields. It is well known that the gluon field is a pure gauge field on the transverse plane at eikonal order. We derived the complete next-to-eikonal order solutions of the classical Yang-Mills equations for soft gluons in the dense nuclear regime. Utilizing these solutions, it is shown that Low’s soft theorem at small x can be obtained by considering off-diagonal matrix elements of quasiclassical chromoelectric field between single-gluon states in the dilute regime. We further propose on extending Low’s soft theorem at small x to incorporate the effects of gluon saturation in the dense regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Tailoring Carbide Dispersed Steels: A Path to Increased Strength and Hydrogen Tolerance

The use of transition metal carbides is reported for use as a hydrogen trapping mechanism for ferritic and austenitic steel materials. The program combined computational modeling and simulations to guide experiments towards candidate metal carbide traps, both for interfacial and interior trapping. It was found that interfacial trapping is less effective than interior trapping, with the group IVB transition metal carbides being the most effect internal traps with a loss of carbon. The sub-stoichiometric rocksalt structure accommodate the hydrogen atoms in its octahedral interstices. Using percolation theory, carbon loss of approximately 25% or more was sufficient to ensure an interconnected network of vacancies for such trapping from the surface to the internal sites within the carbide. Using this as a guide, the program developed a means to provide a uniform dispersion of ZrC nanoparticles with either Fe or 304L micron-scale powders which was then consolidated by direct current sintering. Electrolytic hydrogen diffusivity studies confirmed the reduction of hydrogen diffusion in the matrix with increasing ZrC content, which was a linear response over the sample range studied (0.01 to 1.0 wt.%). The consolidated material was micro-tensile tested in either a non-hydrogen or hydrogen charge condition and compared to a control with no carbides. Additions up to 0.05 wt.% ZrC increased the yield strength with no loss in ductility in either the non-hydrogen or hydrogen tested condition. ZrC concentrations above this amount further increased the yield strength at the expense of ductility. While these samples had a lower absolute ductility value prior to failure, the relative change in ductility between the non-hydrogen and hydrogen charge states was less for the carbides than that of the control. Metal-rich ZrC nanoparticles were fabricated through a conformal coating process yielding ZrC0.66 particles that were then incorporated into a metal matrix. Notch fatigue testing in a hydrogen environment was conducted where the number of cycles to failure was found to be less in the control than that of the carbide addition. However, the spread in experimental data and the number of samples tested limits a conclusive outcome based on defects noticed in the gauge section of all the powder processed samples. The collective outcomes of this report provide further insight into the mechanisms by which carbides act as hydrogen traps; a means to process such carbides through powder metallurgy; and their associated mechanical performance in either a non-hydrogen or hydrogen-charged condition.

08 HYDROGEN↗
NASA NTRS1978

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.↗
NASA NTRS1994

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.↗
NASA NTRS2023

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↗
NASA NTRS1983

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.↗
DOE OSTI2022

Preprocessing of municipal solid waste towards thermal insulating material

Municipal solid waste (MSW) is one of the significant challenges in today’s world. A continuous surge in population, increasing living standards, and rapid urbanization are generating an enormous quantity of MSW. For example, the Environmental Protection Agency (EPA) reported that the total generation of MSW in the United States in 2018 was 292.4 million tons. Improper management of this MSW often leads to the release of greenhouse gases, emission of particulate matters, and formation of dioxins, which all ultimately contributes to climate change. Recycling these wastes via landfills with gas recovery and/or energy and material production via thermal and chemical conversions could be viable options to manage these challenges. Depending on the inherent chemical and structural properties of unrecycled wastes, the carbon structures can be tailored for processing and reuse in manufacturing of structural composites, building materials such as insulation, carbon dense reactant materials such as activated carbon, and so on. According to the EPA’s estimation, MSW in the United States is approximately 23% paper and paperboard, 12% plastics, 6% wood and 6% is textiles. Thus, this research focused on the feasibility of using the MSW as insulation material for the construction sector. The goal of this work was to determine the range of particle sizes, consolidation ratios, and component blends that can achieve insulation R-values within at least 70% that of traditional blown cellulose fiber. To achieve this goal, we designed the testing matrix based on five different component blends, three different particle sizes, and three different compaction level. An American Society for Testing and Materials (ASTM) method (C-739) was used to measure the R-value of the insulation material. Results showed that, adding more paper component in addition to smaller particle size and loose compaction made the insulation similar to the traditional blown cellulose fiber insulation as the R-value was within a range of 2.5-3.0 per inch.

42 ENGINEERING↗
NASA NTRS1987

Addition polymers from 1,4,5,8-tetrahydro-1,4;5,8-diepoxyanthracene and Bis-dienes: Processable resins for high temperature application

1,4,5,8-Tetrahydro-1,4;5,8-diepoxyanthracene reacts with various anthracene endcapped polyimide oligomers to form Diels-Alder cycloaddition copolymers. The polymers are soluble in common organic solvents, and have molecular weights of approximately 21,000 to 32,000. Interestingly, these resins appear to be more stable in air then in nitrogen. This is shown to be due to a unique dehydration (loss of water ranges from 2 to 5 percent) at temperatures of 390 to 400 C to give thermo-oxidatively stable pentiptycene units along the polymer backbone. Because of their high softening points and good thermo-oxidative stability, the polymers have potential as processible, matrix resins for high temperature composite applications.

Meador, Mary Ann B.↗
NASA NTRS1946

Numerical procedures for the calculation of the stresses in monocoques III : calculation of the bending moments in fuselage frames

This report deals with the calculation of the bending moments in and the distortions of fuselage rings upon which known concentrated and distributed loads are acting. In the procedure suggested, the ring is divided into a number of beams each having a constant radius of curvature. The forces and moments caused in the end sections of the beams by individual unit displacements of the end sections are listed in a table designated as the operations table in conformity with Southwell's nomenclature. The operations table and the external loads are equivalent to a set of linear equations. For their solution the following three procedures are presented: 1) Southwell's method of systematic relaxations. This is a step-by-step approximation procedure guided by the physical interpretation of the changes in the values of the unknown. 2) The growing unit procedure in which the individual beams are combined successively into beams of increasing length until finally the entire ring becomes a single beam. In each step of the procedure a set of not more than three simultaneous linear equations is solved. 3) Solution of the entire set of simultaneous equations by the methods of the matrix calculus. In order to demonstrate the manner in which the calculations may be carried out, the following numerical examples are worked out: 1) Curved beam with both its end sections rigidly fixed. The load is a concentrated force. 2) Egg-shape ring with symmetric concentrated loads. 3) Circular ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 4) Same with V-braces incorporated in the ring. 5) Egg-shape ring with antisymmetric concentrated loads and shear flow (torsion of the fuselage). 6) Same with V-braces incorporated in the ring. The results of these calculations are checked, whenever possible, by calculations carried out according to known methods of analysis. The agreement is found to be good. The amount of work necessary for the solution of ring problems by the methods described in the present report is practically independent of the degree of redundancy of the structure. For this reason the methods are recommended for use particularly in problems of rings having one or more internal bracing elements.

LOADS - FUSELAGES↗
NASA NTRS1994

Dynamic analysis of Space Shuttle/RMS configuration using continuum approach

The initial assembly of Space Station Freedom involves the Space Shuttle, its Remote Manipulation System (RMS) and the evolving Space Station Freedom. The dynamics of this coupled system involves both the structural and the control system dynamics of each of these components. The modeling and analysis of such an assembly is made even more formidable by kinematic and joint nonlinearities. The current practice of modeling such flexible structures is to use finite element modeling in which the mass and interior dynamics is ignored between thousands of nodes, for each major component. The model characteristics of only tens of modes are kept out of thousands which are calculated. The components are then connected by approximating the boundary conditions and inserting the control system dynamics. In this paper continuum models are used instead of finite element models because of the improved accuracy, reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural and control system dynamics in the same system of equations. Dynamic analysis of linear versions of the model is performed and compared with finite element model results. Additionally, the transfer matrix to continuum modeling is presented.

Ramakrishnan, Jayant↗
NASA NTRS2002

C/sic Life Prediction for Propulsion Applications

Accurate life prediction is critical to successful use of ceramic matrix composites (CMC). The tools to accomplish this are immature and not oriented toward the behavior of carbon fiber reinforced silicon carbide (C/SiC), the primary system of interest for many reusable and single mission launch vehicle propulsion and airframe applications. This paper describes an approach and process made to satisfy the need to develop an integrated life prediction system that addresses mechanical durability and environmental degradation of C/SiC. Issues such as oxidation, steam and hydrogen effects on material behavior are discussed. Preliminary tests indicate that steam will aggressively remove SiC seal coat and matrix in line with past experience. The kinetics of water vapor reaction with carbon fibers is negligible at 600 C, but comparable to air attack at 1200 C. The mitigating effect of steam observed in fiber oxidation studies has also been observed in stress rupture tests. Detailed microscopy of oxidized specimens is being carried out to develop the oxidation model. Carbon oxidation kinetics are reaction controlled at intermediate temperatures and diffusion controlled at high temperatures (approximately 1000 C). Activation energies for T-300 and interface pyrolytic carbon were determined as key inputs to the oxidation model. Crack opening as a function of temperature and stress was calculated. Mechanical property tests to develop and verify the probabilistic life model are very encouraging except for residual strength prediction. Gage width is a key variable governing edge oxidation of seal coated specimens. Future efforts will include architectural effects, enhanced coatings, biaxial tests, and LCF. Modeling will need to account for combined effects.

Levine, Stanley R.↗