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Results for “weighted residual methods”

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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Supercomputer implementation of finite element algorithms for high speed compressible flows

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

Thornton, E. A.↗
DOE OSTI2023

Assessment and Non-Destructive Evaluation of the Influence of Residual Solvent on a Two-Part Epoxy-Based Adhesive Using Ultrasonics

Polymers are increasingly being used in higher demanding applications due to their ability to tailor the properties of structures while allowing for a weight and cost reduction. Solvents play an important role in the manufacture of polymeric structures since they allow for a reduction in the polymer’s viscosity or assist with the dispersion of fillers into the polymer matrix. However, the incorrect removal of the solvent affects both the physical and chemical properties of polymeric materials. The presence of residual solvent can also negatively affect the curing kinetics and the final quality of polymers. Destructive testing is mainly performed to characterize the properties of these materials. However, this type of testing involves using lab-type equipment that cannot be taken in-field to perform in situ testing and requires a specific sample preparation. Here, a method is presented to non-destructively evaluate the curing process and final viscoelastic properties of polymeric materials using ultrasonics. In this study, changes in longitudinal sound speed were detected during the curing of an aerospace epoxy adhesive as a result of variations in polymer chemistry. To simulate the presence of residual solvent, samples containing different weight percentages of isopropyl alcohol were manufactured and tested using ultrasonics. Thermogravimetric analysis was used to show changes in the decomposition of the adhesive due to the presence of IPA within the polymer structure. Adding 2, 4, and 6 wt.% of IPA decreased the adhesive’s lap shear strength by 40, 58, and 71%, respectively. Ultrasonics were used to show how the solvent influenced the curing process and the final sound speed of the adhesive. Young’s modulus and Poisson’s ratio were determined using both the longitudinal and shear sound speeds of the adhesive. Using ultrasonics has the potential to non-invasively characterize the quality of polymers in both an in-field and manufacturing settings, ensuring their reliability during use in demanding applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Automated shaker placement and regularized input estimation for MIMO testing.

Multi-input, multi-output (MIMO) testing is used in component qualification to reproduce operational responses in the laboratory. It is often preferred to single-input and base-shake testing because of the potential for equivalent or better tests using smaller actuators and shorter test suites. Given a target response, two key steps in MIMO test design are selecting actuator locations and solving for input loads. Actuator locations are often manually selected using expert judgment. If an automatic method is used, locations are usually determined by simulating the vibration control problem and minimizing a combination of the input energy and control residuals. To select a configuration, the relative importance of input energy and residuals must be specified. Specifying relative weights is, in general, a manual and subjective process. This paper develops an objective function that compares actuator configurations based on control accuracy and required input energy without any manual parameter tuning. The objective function uses an optimally selected tradeoff parameter for each candidate configuration. To choose actuator locations using the new objective function, a pivoting algorithm for integer programming problems is developed. Starting with an initial configuration (such as the one generated by a greedy algorithm), the pivoting algorithm guarantees an objective function decrease in each iteration until convergence is reached. In a simulation featuring a structure excited by a diffuse acoustic field, electrodynamic shaker locations and regularized inputs are solved for without any analyst-specified parameters. Simulations are performed in MIMO configurations where the number of target responses is less than, equal to, and greater than the number of actuators.

Multi-input multi-output↗
NASA NTRS1976

Structural design of supersonic cruise aircraft

The major efforts leading to an efficient structural design include: (1) the analysis methods used to improve the structural model optimization and compare the structural concepts, (2) the analysis and description of the fail-safe, crack growth, and residual strength studies and tests, (3) baseline structural trade studies to determine optimum structural weights including effects of geometry changes, strength, fail-safety, aeroelastics and flutter, 6AL-4V annealed titanium in structural efficiency after 70,000 hours at temperature, (5) the study of three structural models for aircraft at 2.0 Mach, 2.2 Mach, and 2.4 Mach cruise speeds, (6) the study of many structural concepts to determine their weight efficiencies; and (7) the determination of the requirements for large-scale structural development testing.

Fischler, J. E.↗
NASA NTRS2014

Novel Epoxy Particulate Composites for Mitigation of Insect Residue Adhesion on Future Aircraft Surfaces

Drag is reduced significantly for airflow over surfaces when laminar flow can be maintained over greater chord lengths, the distance from the leading edge of an airfoil.1 However, surface imperfections, such as chipped paint, scratches, and events that change topography on a microscopic scale can introduce airflow instabilities resulting in premature transition to turbulent flow.1 Although many of these surface imperfections can be avoided with proper maintenance, advanced materials, and advanced manufacturing practices, topographical surface anomalies arising during flight from insect impacts cannot be controlled and can influence laminar flow stability. Practical solutions to this operational challenge need to be developed for future aircraft to have full advantage of laminar flow designs that improve fuel efficiency.2 Researchers have investigated various methods to mitigate insect residue adhesion for decades.3 Although several techniques have demonstrated efficacy including mechanical scrapers, active liquid discharge systems, and sacrificial paper coatings, they have not been commercially implemented due to increased manufacturing and operational complexity, environmental impact, and weight penalties. Coatings offer a simple route for passive insect residue adhesion prevention without many of the challenges associated with maintenance of laminar flow.4 In our previous work, we determined that most commercially available materials were not effective at insect residue adhesion.5 We also identified improvements when both surface energy could be controlled by surface modifying agents and the topography could be altered through the use of micron-sized and nanometer-sized filler materials.6 In this work, these general principles were applied to an epoxy system to evaluate the behavior of the surface modifying agent, a fluorinated alkyl ether oligomer, on surface energy and insect residue adhesion properties.

Wohl, Christopher J.↗
DOE OSTI2020

Physico-chemical properties of lignin fractions from acid pretreated corn stover and their effects on enzymatic hydrolysis of microcrystalline cellulose

Lignin has been shown to be a recalcitrance factor in many biomass conversion studies. To better understand the effects of lignin on cellulose conversion, different lignin fractions were extracted from the same dilute acid pretreated corn stover by three sequential isolation methods, namely ethanol extraction, dioxane extraction, and enzyme purification. The physicochemical properties of each lignin fraction including molecular weight distribution, surface area, surface charge, and other structural features varied, depending on the isolation methods. All three lignin fractions had negative surface charges, and ethanol-extracted lignin carried the highest surface charges, followed by dioxane-extracted lignin and cellulase-purified residual lignin. These physicochemical properties of lignin fractions also resulted in different extent of inhibitory effects on enzymatic hydrolysis of microcrystalline cellulose (MCC). Dioxane-extracted lignin exhibited the highest inhibitory effect on glucose release from MCC, followed by the cellulase-purified residual lignin fraction and ethanol-extracted lignin. Furthermore, lignin fractions with higher contents of syringyl (S) substructure and β-O-4 aryl ether interunit linkages showed a stronger negative effect on cellulase hydrolysis of MCC.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1990

Multi-disciplinary optimization of aeroservoelastic systems

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Karpel, Mordechay↗
NASA NTRS1992

Multidisciplinary optimization of aeroservoelastic systems using reduced-size models

Efficient analytical and computational tools for simultaneous optimal design of the structural and control components of aeroservoelastic systems are presented. The optimization objective is to achieve aircraft performance requirements and sufficient flutter and control stability margins with a minimal weight penalty and without violating the design constraints. Analytical sensitivity derivatives facilitate an efficient optimization process which allows a relatively large number of design variables. Standard finite element and unsteady aerodynamic routines are used to construct a modal data base. Minimum State aerodynamic approximations and dynamic residualization methods are used to construct a high accuracy, low order aeroservoelastic model. Sensitivity derivatives of flutter dynamic pressure, control stability margins and control effectiveness with respect to structural and control design variables are presented. The performance requirements are utilized by equality constraints which affect the sensitivity derivatives. A gradient-based optimization algorithm is used to minimize an overall cost function. A realistic numerical example of a composite wing with four controls is used to demonstrate the modeling technique, the optimization process, and their accuracy and efficiency.

Karpel, Mordechay↗
NASA NTRS1996

First-Order System Least Squares for Velocity-Vorticity-Pressure Form of the Stokes Equations, with Application to Linear Elasticity

In this paper, we study the least-squares method for the generalized Stokes equations (including linear elasticity) based on the velocity-vorticity-pressure formulation in d = 2 or 3 dimensions. The least squares functional is defined in terms of the sum of the L(exp 2)- and H(exp -1)-norms of the residual equations, which is weighted appropriately by by the Reynolds number. Our approach for establishing ellipticity of the functional does not use ADN theory, but is founded more on basic principles. We also analyze the case where the H(exp -1)-norm in the functional is replaced by a discrete functional to make the computation feasible. We show that the resulting algebraic equations can be uniformly preconditioned by well-known techniques.

Cai, Zhiqiang↗
NASA NTRS2000

The Sugar Model: Catalytic Flow Reactor Dynamics of Pyruvaldehyde Synthesis from Triose Catalyzed by Poly-L-Lysine Contained in a Dialyzer

The formation of pyruvaldehyde from triose sugars was catalyzed by poly-L-lysine contained in a small dialyzer (100 MWCO) suspended in a much larger triose substrate reservoir. The polylysine confined in the dialyzer functioned as a catalytic flow reactor that constantly brought in triose from the substrate reservoir by diffusion to offset the drop in triose concentration within the reactor caused by its conversion to pyruvaldehyde. A 400 mM solution of poly-L-lysine contained in a 0.35 ml dialyzer placed in a 120 ml solution of triose substrate (pH 5.5, 40 C) generated pyruvaldehyde 11 -times faster than an a control reaction without the catalytic dialyzer. However, since the catalytic dialyzer's volume was 343-times smaller than the control reaction, the synthetic intensity (rate/volume) of pyruvaldehyde synthesis within the catalytic dialyzer was 3400-times greater than that of the control reaction and substrate solution. A similar result was obtained using a dialyzer with a 500 MWCO value. Acting as a catalytic flow reactor the polylysine catalytic dialyzer synthesized about 3.5 molecules of pyruvaldehyde per lysine residue in 7 days -- an amount of triose equal to twice the weight of the catalyst. At 7 days the catalytic activity of polylysine was 16% of its initial value, a result indicating catalyst-poisoning caused by reaction of pyruvaldehyde with the e-amino groups of polylysine. The dialyzer method of catalyst containment was selected it provides a simple, flexible, and easily manipulated experimental system for studying the dynamics and evolutionary development of confined autocatalytic processes related to the origin of life under anaerobic conditions.

Weber, Arthur L.↗
NASA NTRS2017

Wind Tunnel Strain-Gage Balance Calibration Data Analysis Using a Weighted Least Squares Approach

A new approach is presented that uses a weighted least squares fit to analyze wind tunnel strain-gage balance calibration data. The weighted least squares fit is specifically designed to increase the influence of single-component loadings during the regression analysis. The weighted least squares fit also reduces the impact of calibration load schedule asymmetries on the predicted primary sensitivities of the balance gages. A weighting factor between zero and one is assigned to each calibration data point that depends on a simple count of its intentionally loaded load components or gages. The greater the number of a data point's intentionally loaded load components or gages is, the smaller its weighting factor becomes. The proposed approach is applicable to both the Iterative and Non-Iterative Methods that are used for the analysis of strain-gage balance calibration data in the aerospace testing community. The Iterative Method uses a reasonable estimate of the tare corrected load set as input for the determination of the weighting factors. The Non-Iterative Method, on the other hand, uses gage output differences relative to the natural zeros as input for the determination of the weighting factors. Machine calibration data of a six-component force balance is used to illustrate benefits of the proposed weighted least squares fit. In addition, a detailed derivation of the PRESS residuals associated with a weighted least squares fit is given in the appendices of the paper as this information could not be found in the literature. These PRESS residuals may be needed to evaluate the predictive capabilities of the final regression models that result from a weighted least squares fit of the balance calibration data.

calibration analysis↗
NASA NTRS1989

Optimum data weighting and error calibration for estimation of gravitational parameters

A new technique was developed for the weighting of data from satellite tracking systems in order to obtain an optimum least-squares solution and an error calibration for the solution parameters. Data sets from optical, electronic, and laser systems on 17 satellites in GEM-T1 Goddard Earth Model-T1 (GEM-T1) were employed toward application of this technique for gravity field parameters. Also GEM-T2 (31 satellites) was recently computed as a direct application of the method and is summarized. The method employs subset solutions of the data associated with the complete solution to agree with their error estimates. With the adjusted weights the process provides for an automatic calibration of the error estimates for the solution parameters. The data weights derived are generally much smaller than corresponding weights obtained from nominal values of observation accuracy or residuals. Independent tests show significant improvement for solutions with optimal weighting. The technique is general and may be applied to orbit parameters, station coordinates, or other parameters than the gravity model.

Lerch, Francis J.↗
NASA NTRS2012

Methods for Decontamination of a Bipropellant Propulsion System

Most propulsion systems are designed to be filled and flown, draining can be done but decontamination may be difficult. Transport of these systems may be difficult as well because flight weight vessels are not designed around DOT or UN shipping requirements. Repairs, failure analysis work or post firing inspections may be difficult or impossible to perform due to the hazards of residual propellants being present.

McClure, Mark B.↗
NASA NTRS1994

ASTM and VAMAS activities in titanium matrix composites test methods development

Titanium matrix composites (TMC's) are being considered for a number of aerospace applications ranging from high performance engine components to airframe structures in areas that require high stiffness to weight ratios at temperatures up to 400 C. TMC's exhibit unique mechanical behavior due to fiber-matrix interface failures, matrix cracks bridged by fibers, thermo-viscoplastic behavior of the matrix at elevated temperatures, and the development of significant thermal residual stresses in the composite due to fabrication. Standard testing methodology must be developed to reflect the uniqueness of this type of material systems. The purpose of this paper is to review the current activities in ASTM and Versailles Project on Advanced Materials and Standards (VAMAS) that are directed toward the development of standard test methodology for titanium matrix composites.

Johnson, W. S.↗
NASA NTRS1986

New methodology for shaft design based on life expectancy

The design of power transmission shafting for reliability has not historically received a great deal of attention. However, weight sensitive aerospace and vehicle applications and those where the penalties of shaft failure are great, require greater confidence in shaft design than earlier methods provided. This report summarizes a fatigue strength-based, design method for sizing shafts under variable amplitude loading histories for limited or nonlimited service life. Moreover, applications factors such as press-fitted collars, shaft size, residual stresses from shot peening or plating, corrosive environments can be readily accommodated into the framework of the analysis. Examples are given which illustrate the use of the method, pointing out the large life penalties due to occasional cyclic overloads.

Loewenthal, S. H.↗
NASA NTRS1993

Steady induction effects in geomagnetism. Part 1C: Geomagnetic estimation of steady surficial core motions: Application to the definitive geomagnetic reference field models

In the source-free mantle/frozen-flux core magnetic earth model, the non-linear inverse steady motional induction problem was solved using the method presented in Part 1B. How that method was applied to estimate steady, broad-scale fluid velocity fields near the top of Earth's core that induce the secular change indicated by the Definitive Geomagnetic Reference Field (DGRF) models from 1945 to 1980 are described. Special attention is given to the derivation of weight matrices for the DGRF models because the weights determine the apparent significance of the residual secular change. The derived weight matrices also enable estimation of the secular change signal-to-noise ratio characterizing the DGRF models. Two types of weights were derived in 1987-88: radial field weights for fitting the evolution of the broad-scale portion of the radial geomagnetic field component at Earth's surface implied by the DGRF's, and general weights for fitting the evolution of the broad-scale portion of the scalar potential specified by these models. The difference is non-trivial because not all the geomagnetic data represented by the DGRF's constrain the radial field component. For radial field weights (or general weights), a quantitatively acceptable explication of broad-scale secular change relative to the 1980 Magsat epoch must account for 99.94271 percent (or 99.98784 percent) of the total weighted variance accumulated therein. Tolerable normalized root-mean-square weighted residuals of 2.394 percent (or 1.103 percent) are less than the 7 percent errors expected in the source-free mantle/frozen-flux core approximation.

Voorhies, Coerte V.↗
NASA NTRS1993

Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction

Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.

Sockol, Peter M.↗
DOE OSTI2025

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗