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At least 685 records · Page 38

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. Previous derivations of these matrices have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The present work derives differentiating matrices on grids with arbitrarily spaced points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids through the expedient of including 'near boundary' points. Use of the differentiating matrix as an operator in the solution of problems involving ordinary differential equations is also considered.

Lakin, W. D.↗

Polarimetric clutter modeling: Theory and application

The two-layer anisotropic random medium model is used to investigate fully polarimetric scattering properties of earth terrain media. The polarization covariance matrices for the untilted and tilted uniaxial random medium are evaluated using the strong fluctuation theory and distorted Born approximation. In order to account for the azimuthal randomness in the growth direction of leaves in tree and grass fields, an averaging scheme over the azimuthal direction is also applied. It is found that characteristics of terrain clutter can be identified through the analysis of each element of the covariance matrix. Theoretical results are illustrated by the comparison with experimental data provided by MIT Lincoln Laboratory for tree and grass fields.

Kong, J. A.↗

Analysis of Modified SMI Method for Adaptive Array Weight Control

An adaptive array is used to receive a desired signal in the presence of weak interference signals which need to be suppressed. A modified sample matrix inversion (SMI) algorithm controls the array weights. The modification leads to increased interference suppression by subtracting a fraction of the noise power from the diagonal elements of the covariance matrix. The modified algorithm maximizes an intuitive power ratio criterion. The expected values and variances of the array weights, output powers, and power ratios as functions of the fraction and the number of snapshots are found and compared to computer simulation and real experimental array performance. Reduced-rank covariance approximations and errors in the estimated covariance are also described.

Dilsavor, Ronald Louis↗

On polynomial preconditioning for indefinite Hermitian matrices

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Freund, Roland W.↗

Modeling of Electromagnetic Scattering by Discrete and Discretely Heterogeneous Random Media by Using Numerically Exact Solutions of the Maxwell Equations

In this paper, we discuss some aspects of numerical modeling of electromagnetic scattering by discrete random medium by using numerically exact solutions of the macroscopic Maxwell equations. Typical examples of such media are clouds of interstellar dust, clouds of interplanetary dust in the Solar system, dusty atmospheres of comets, particulate planetary rings, clouds in planetary atmospheres, aerosol particles with numerous inclusions and so on. Our study is based on the results of extensive computations of different characteristics of electromagnetic scattering obtained by using the superposition T-matrix method which represents a direct computer solver of the macroscopic Maxwell equations for an arbitrary multisphere configuration. As a result, in particular, we clarify the range of applicability of the low-density theories of radiative transfer and coherent backscattering as well as of widely used effective-medium approximations.

Dlugach, Janna M.↗

Lightweight Metal Matrix Composite Segmented for Manufacturing High-Precision Mirrors

High-precision mirrors for space applications are traditionally manufactured from one piece of material, such as lightweight glass sandwich or beryllium. The purpose of this project was to develop and test the feasibility of a manufacturing process capable of producing mirrors out of welded segments of AlBeMet(Registered Trademark) (AM162H). AlBeMet(Registered Trademark) is a HIP'd (hot isostatic pressed) material containing approximately 62% beryllium and 38% aluminum. As a result, AlBeMet shares many of the benefits of both of those materials for use in high performance mirrors, while minimizing many of their weaknesses.

Vudler, Vladimir↗

Eutectic equilibria in the quaternary system Fe-Cr-Mn-C

The constitution of the quaternary system, Fe-Cr-Mn-C and to a lesser extent of the quinary system, Fe-Cr-Mn-Al-C were examined for in situ composite alloy candidates. Multivariant eutectic compositions were determined from phase equilibria studies wherein M7C3 carbides (approximately 30% by volume) formed from the melt within gamma iron. An extended field of the hexagonal carbide, (Cr, Fe, Mn)7 C3, was found without undergoing transformation to the orthorhombic structure. Increasing stability for this carbide was found for higher ratios of Cr/Fe(+) Cr + Mn. Aluminum additions promoted a ferritic matrix while manganese favored the desired gamma austenitic matrix. In coexistence with the matrix phase, chromium enters preferentially the carbide phase while manganese distributes equally between the gamma matrix and the M7C3 carbide. The composition and lattice parameters of the carbide and matrix phases were determined to establish their respective stabilities.

Nowotny, H.↗

The solution of radiative transfer problems in molecular bands without the LTE assumption by accelerated lambda iteration methods

An iterative method based on the use of approximate transfer operators, which was designed initially to solve multilevel NLTE line formation problems in stellar atmospheres, is adapted and applied to the solution of the NLTE molecular band radiative transfer in planetary atmospheres. The matrices to be constructed and inverted are much smaller than those used in the traditional Curtis matrix technique, which makes possible the treatment of more realistic problems using relatively small computers. This technique converges much more rapidly than straightforward iteration between the transfer equation and the equations of statistical equilibrium. A test application of this new technique to the solution of NLTE radiative transfer problems for optically thick and thin bands (the 4.3 micron CO2 band in the Venusian atmosphere and the 4.7 and 2.3 micron CO bands in the earth's atmosphere) is described.

Kutepov, A. A.↗

Biological removal of gaseous ammonia in biofilters: space travel and earth-based applications

Gaseous NH3 removal was studied in laboratory-scale biofilters (14-L reactor volume) containing perlite inoculated with a nitrifying enrichment culture. These biofilters received 6 L/min of airflow with inlet NH3 concentrations of 20 or 50 ppm, and removed more than 99.99% of the NH3 for the period of operation (101, 102 days). Comparison between an active reactor and an autoclaved control indicated that NH3 removal resulted from nitrification directly, as well as from enhanced absorption resulting from acidity produced by nitrification. Spatial distribution studies (20 ppm only) after 8 days of operation showed that nearly 95% of the NH3 could be accounted for in the lower 25% of the biofilter matrix, proximate to the port of entry. Periodic analysis of the biofilter material (20 and 50 ppm) showed accumulation of the nitrification product NO3- early in the operation, but later both NO2- and NO3- accumulated. Additionally, the N-mass balance accountability dropped from near 100% early in the experiments to approximately 95 and 75% for the 20- and 50-ppm biofilters, respectively. A partial contributing factor to this drop in mass balance accountability was the production of NO and N2O, which were detected in the biofilter exhaust.

NASA Discipline Life Support Systems↗

Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure

One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.

Ooijevaar, T. H.↗

A triangular thin shell finite element: Linear analysis

The formulation of the linear stiffness matrix for a doubly-curved triangular thin shell element, using a modified potential energy principle, is described. The strain energy component of the potential energy is expressed in terms of displacements and displacement gradients by use of consistent Koiter strain-displacement equations. The element inplane and normal displacement fields are approximated by complete cubic polynomials. The interelement displacement admissibility conditions are met in the global representation by imposition of constraint conditions on the interelement boundaries; the constraints represent the modification of the potential energy. Errors due to the nonzero strains under rigid body motion are shown to be of small importance for practical grid refinements through performance of extensive comparison analyses.

Thomas, G. R.↗

A transfer matrix approach to vibration localization in mistuned blade assemblies

A study of mode localization in mistuned bladed disks is performed using transfer matrices. The transfer matrix approach yields the free response of a general, mono-coupled, perfectly cyclic assembly in closed form. A mistuned structure is represented by random transfer matrices, and the expansion of these matrices in terms of the small mistuning parameter leads to the definition of a measure of sensitivity to mistuning. An approximation of the localization factor, the spatially averaged rate of exponential attenuation per blade-disk sector, is obtained through perturbation techniques in the limits of high and low sensitivity. The methodology is applied to a common model of a bladed disk and the results verified by Monte Carlo simulations. The easily calculated sensitivity measure may prove to be a valuable design tool due to its system-independent quantification of mistuning effects such as mode localization.

Ottarson, Gisli↗

Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation

In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.

Kouatchou, Jules↗

Evidence for Methane Segregation at the Surface of Pluto

In May 1995, a set of spectrophotometric curves of the system Pluto-Charon was recorded with the UKIRT telescope equipped with the spectrometer CGS4. As for the previous observations, the spectra cover a part of the near infrared range, between 1.4 and 2.55 micrometers, but with a higher resolution of approximately 700. In both the 1992 and 1995 data, the existence of solid methane is confirmed by numerous absorption bands, and the carbon monoxide and the nitrogen ices are identified by their respective signatures at 2.35 and 2.15 um. The solid nitrogen seems to be the principal icy component and forms a matrix in which the CH4 and CO molecules are diluted. However a spectroscopic analysis of the 1995 observations indicates that pure methane may coexist with its diluted phase in N2. In order to derive the horizontal and vertical distribution of these different species and to obtain some quantitative information about their characteristics, we have modeled the spectrum of May 15 that corresponds to the maximum of Pluto's visible light curve. This was achieved by means of a radiative transfer algorithm dealing with compact and stratified media. Among the various representations we have tested to describe the surface of Pluto, only a geographical mixture of three distinct units explains all the significant structures of the analyzed spectrum. The first unit is a thin granular layer of pure CH4 covering a compact polycrystalline substratum of N2-CH4-CO, which are in a molecular mixture (concentrations of and CO of the order of 0.45%, 0.1-0.2% respectively). It covers about 70% of the observed area and corresponds to volatile deposits that are sublimating under solar illumination. The second unit is either (a) a single thick layer of pure granular methane or (b) a unit similar to the first unit but with the two components inverted (i.e. with CH4 forming a substratum and the N2-CH4-CO mixture a superficial layer of fine grains). Covering 20% of the surface, it represents some old surfaces that have been sublimated for a long time, and eventually recovered later by very small amounts of fresh deposits of the molecular mixture N2-CH4-CO. Finally, the third unit may result from the condensation of very fine grains of nearly pure N2. It covers the remainder of the surface (about 10%). All these results allow a better understanding of the processes of deposition, metamorphism, sublimation and transport affecting the different ices detected on Pluto during its climatic cycles.

Doute, S.↗

Stochastic Optimal Control via Bellman's Principle

This paper presents a method for finding optimal controls of nonlinear systems subject to random excitations. The method is capable to generate global control solutions when state and control constraints are present. The solution is global in the sense that controls for all initial conditions in a region of the state space are obtained. The approach is based on Bellman's Principle of optimality, the Gaussian closure and the Short-time Gaussian approximation. Examples include a system with a state-dependent diffusion term, a system in which the infinite hierarchy of moment equations cannot be analytically closed, and an impact system with a elastic boundary. The uncontrolled and controlled dynamics are studied by creating a Markov chain with a control dependent transition probability matrix via the Generalized Cell Mapping method. In this fashion, both the transient and stationary controlled responses are evaluated. The results show excellent control performances.

Crespo, Luis G.↗

Completion of Dragonfly PPF Testing in the NFAC 80x120-Foot Wind Tunnel

The Dragonfly entry, descent, and landing team (JHU-APL, NASA Langley Research Center, NASA Ames Research Center, Sikorsky Aircraft) recently completed testing in the National Full-Scale Aerodynamics Complex (NFAC) 80x120-Foot Wind Tunnel. The facility is located at NASA Ames Research Center and is operated by the U.S. Air Force's Arnold Engineering Development Complex. The test was designed to simulate conditions of Preparation for Powered (PPF), an approximately 10-minute period during which the Lander is posed in front of the Backshell at low subsonic airspeeds, all under the main parachute, and the rotors are used to null residual Lander yaw rates prior to release i. e. de-spin. The Lander (approximately 50% scale) that previously was tested in the NASA Langley 14x22 Wind Tunnel in 2023 was used for the NFAC test with a new Backshell designed and fabricated specifically for NFAC. This memorandum summarizes execution of the test: objective, facility and models, instrumentation and data products, test procedure, and completed test matrix. Other future documents will include a test report (JHU-APL) and documentation of data processing/analysis and computational fluid dynamics (CFD) comparisons to test data (Sikorsky).

Dragonfly↗

AERoBOND Project Summary

Under NASA’s Convergent Aeronautics Solutions (CAS) project, the Adhesive-Free Bonding of Complex Composites (AERoBOND) project investigated off-stoichiometric epoxy polymers for fast, reliable assembly of epoxy matrix composite structures. The project goal was to demonstrate feasibility of the AERoBOND joining method by demonstrating mechanical properties greater than 80% of conventional co-cured materials while reducing structure weight by 1%. The project consisted of three convergent research areas: material and process development, systems analysis, and material and process modeling. Material and process development was the largest component of AERoBOND with approximately 6 FTE and 1WYE of support to formulate and characterize new resins, prepare carbon fiber prepregs, fabricate laminates, measure mechanical properties, analyze failure results, and select material and process improvements. The systems analysis activity estimated the potential reduction in part count and aircraft weight by comparing models of composite wing boxes with no fasteners (co-cured structure), fasteners in major joints (co-cured stringers), and fasteners in all joints. The materials and process modeling activity included a molecular model of the AERoBOND materials system to predict mechanical properties of resins with offset stoichiometry and a process model to predict the effect of resin formulation and processing conditions on the extent of mixing and degree of cure in a finished joint. As the number of airline passenger trips doubles in the next 20 years (IATA/Tourism Economics Air Passenger Forecasts, April 2019), the increased demand for new commercial aircraft is now the single greatest technical challenge to the airframe manufacturing industry. To meet efficiency requirements, new aircraft must be fabricated primarily from high performance structural composites, but manufacturing processes are inherently slow with the largest bottleneck attributed to assembly and installation of fasteners (NASA/TM–2019-220428). Manufactures of commercial transport aircraft are compelled to install more than 100,000 redundant fasteners into bonded joints to prevent failures due to unpredictable weak bonds. In structural adhesive bonds, the interface between adherend and adhesive is nearly two-dimensional making it susceptible to minute quantities of contamination, which can cause weak bonds. Currently, bond strength assessment is only possible through destructive testing (i.e., breaking the joint). For these reasons, regulatory organizations such as the Federal Aviation Administration (FAA) often require redundant load paths in secondary-bonded, primary-structures to alleviate concerns with bond performance. The AERoBOND process enables reflow of matrix resin during assembly to eliminate the material discontinuity at the interface, thereby eliminating the dependence of mechanical performance on interfacial adhesion. The AERoBOND joint is equivalent to the interlaminar region obtained during a co-cure process, so joint performance depends on the cohesive properties of the matrix resin. Conventional co-cured structures, although too costly and complex for large-scale manufacturing, are trusted by manufacturers and regulators, and are certified for flight with few or no redundant fasteners.Systems analysis performed on a composite wing model at the scale of a single-aisle commercial transport aircraft indicated that >20,000 redundant fasteners per wing could be eliminated by implementing the AERoBOND joining method. A total weight reduction of 15% was predicted in a wing box by eliminating fasteners and thinning components that must no longer support localized fastener loads and accommodate fastener dimensions. Interlaminar shear fracture toughness measured by the end-notched flexure test was greater than 1 kJ/m2 (nearly 140% of the co-cured benchmark property), which is greatly in excess of the project goals for mechanical properties. Testing was planned to measure interlaminar tensile fracture toughness as well as interlaminar tensile and shear strengths using the same AERoBOND configuration, but was delayed due to closure of LaRC facilities during the COVID-19 pandemic. The AERoBOND process model is partially validated and available for experimental use. It allows the user to input AERoBOND process parameters such as material composition, laminate configuration, and cure cycle to predict the final cure state of the AERoBOND joint. A preliminary, multi-scale material model was developed to predict AERoBOND joint mechanical properties (stiffness and strength) based on the cure state of the joint provided by the process model. The timing for transition of this technology within NASA is excellent as NASA initiates new enduring projects to address composites manufacturing rate challenges. AERoBOND technology is well suited to AAVP/AATT objectives for rapid manufacturing of a composite wing. A minimal effort (1 FTE/$15k procurement/0 WYE) is proposed in FY21 to continue a minor mechanical testing effort and maintain a SAA with ASX composites to develop commercial quality prepreg material. An RFI with the composites industry is suggested to quantify the technology gap between the current TRL and the TRL needed for transition to industry. A moderate effort [3-4 FTE/$150k/1 WYE (~$115k)] is proposed in FY22 for the “high rate composites manufacturing” project currently in planning. The partnership with ASX Composites will be expanded to produce material for sub-element/element-scale “panel-off” activities. Industry partnerships with airframe manufacturers is an expected component to explore damage tolerance and environmental stability. Further development of multi-scale modeling tools (process model, meso-scale model, and molecular model) is planned to enhance and deliver tools for rapid manufacturing infusion.

Frank Louis Palmieri↗

Research on output feedback control of systems with ill-conditioned dynamics

The accuracy of a two time scale approach to the output feedback regulator design problem is examined. An approximate quadratic performance index which reflects a two time scale decomposition of the system dynamics is developed. A sequential numerical algorithm is defined which obtains output feedback gains minimizing a broad class of performance indices, including the standard LQ case. A procedure for optimally zeroing selected gain elements in an output feedback gain matrix is developed and demonstrated. A summary of conference and journal publications from this research is also provided.

Calise, A. J.↗