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NASA NTRS1976

Polynominal Interpolation Methods for Viscous Flow Calculations

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.

Rubin, S. G.↗

NASA NTRS1988

Recursive inversion of externally defined linear systems

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problems of system identification and compensation.

Bach, Ralph E., Jr.↗

NASA NTRS1988

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Lerch, F. J.↗

NASA NTRS1991

Application of a two-point exponential approximation method in optimizing rotorcraft airframe structures

The Fadel (1990) two-point exponential approximation technique for rotorcraft airframe structural optimization is presently examined by comparing its results with the well established linear and hybrid first-order methods. Attention is given to both the elastic-line and FEM models of an AH-1G airframe. The Direct Matrix Abstraction Programming Language is used to compute sensitivity derivatives and motivate the CONMIN optimizer to produce the design change.

Sareen, Ashish K.↗

NASA NTRS1993

The effect of grid aspect ratio on convergence

Vector stability theory and computational experiments are used to examine the effects of high aspect ratio grids on algorithm convergence. Emphasis is placed on identifying the degree of convergence deterioration that ADI schemes experience as grid aspect ratio increases and on deriving methods for circumventing this problem. Approximately factored implicit schemes are found to experience convergence deterioration because of nonoptimum local time stepping procedures and the increased need for viscous preconditioning. An enhanced algorithm is devised on the basis of improved selection of the local time step, appropriate definition of viscous preconditioning matrix, and proper implementation of boundary conditions. The novel algorithm provides uniformly efficient convergence at all aspect ratios for both Euler and Navier-Stokes computations for a variety of test problems.

Buelow, P. E. O.↗

NASA NTRS2004

High-Performance SiC/SiC Ceramic Composite Systems Developed for 1315 C (2400 F) Engine Components

As structural materials for hot-section components in advanced aerospace and land-based gas turbine engines, silicon carbide (SiC) ceramic matrix composites reinforced by high performance SiC fibers offer a variety of performance advantages over current bill-of-materials, such as nickel-based superalloys. These advantages are based on the SiC/SiC composites displaying higher temperature capability for a given structural load, lower density (approximately 30- to 50-percent metal density), and lower thermal expansion. These properties should, in turn, result in many important engine benefits, such as reduced component cooling air requirements, simpler component design, reduced support structure weight, improved fuel efficiency, reduced emissions, higher blade frequencies, reduced blade clearances, and higher thrust. Under the NASA Ultra-Efficient Engine Technology (UEET) Project, much progress has been made at the NASA Glenn Research Center in identifying and optimizing two highperformance SiC/SiC composite systems. The table compares typical properties of oxide/oxide panels and SiC/SiC panels formed by the random stacking of balanced 0 degrees/90 degrees fabric pieces reinforced by the indicated fiber types. The Glenn SiC/SiC systems A and B (shaded area of the table) were reinforced by the Sylramic-iBN SiC fiber, which was produced at Glenn by thermal treatment of the commercial Sylramic SiC fiber (Dow Corning, Midland, MI; ref. 2). The treatment process (1) removes boron from the Sylramic fiber, thereby improving fiber creep, rupture, and oxidation resistance and (2) allows the boron to react with nitrogen to form a thin in situ grown BN coating on the fiber surface, thereby providing an oxidation-resistant buffer layer between contacting fibers in the fabric and the final composite. The fabric stacks for all SiC/SiC panels were provided to GE Power Systems Composites for chemical vapor infiltration of Glenn designed BN fiber coatings and conventional SiC matrices. Composite panels with system B were heat treated at Glenn, and the pores that remained open were filled by silicon melt infiltration (MI). Panels with system A and the other SiC/SiC systems were not heat treated, and remaining open pores in these systems were filled with SiC slurry and silicon MI.

DiCarlo, James A.↗

NASA NTRS2006

Tunable Fiber Bragg Grating Ring Lasers using Macro Fiber Composite Actuators

The research reported herein includes the fabrication of a tunable optical fiber Bragg grating (FBG) fiber ring laser (FRL)1 from commercially available components as a high-speed alternative tunable laser source for NASA Langley s optical frequency domain reflectometer (OFDR) interrogator, which reads low reflectivity FBG sensors. A Macro-Fiber Composite (MFC) actuator invented at NASA Langley Research Center (LaRC) was selected to tune the laser. MFC actuators use a piezoelectric sheet cut into uniaxially aligned rectangular piezo-fibers surrounded by a polymer matrix and incorporate interdigitated electrodes to deliver electric fields along the length of the piezo-fibers. This configuration enables MFC actuators to produce displacements larger than the original uncut piezoelectric sheet. The FBG filter was sandwiched between two MFC actuators, and when strained, produced approximately 3.62 nm of wavelength shift in the FRL when biasing the MFC actuators from 500 V to 2000 V. This tunability range is comparable to that of other tunable lasers and is adequate for interrogating FBG sensors using OFDR technology. Three different FRL configurations were studied. Configuration A examined the importance of erbium-doped fiber length and output coupling. Configuration B demonstrated the importance of the FBG filter. Configuration C added an output coupler to increase the output power and to isolate the filter. Only configuration C was tuned because it offered the best optical power output of the three configurations. Use of Plastic Optical Fiber (POF) FBG s holds promise for enhanced tunability in future research.

Geddis, Demetris L.↗

NASA NTRS1993

Post-translational control of collagen fibrillogenesis in mineralizing cultures of chick osteoblasts

Cultured osteoblasts from chick embryo calvaria were used as a model system to investigate the post-translational extracellular mechanisms controlling the macroassembly of collagen fibrils. The results of these studies demonstrated that cultured osteoblasts secreted a collagenous extracellular matrix that assembled and mineralized in a defined temporal and spatial sequence. The assembly of collagen occurred in a polarized fashion, such that successive orthogonal arrays of fibrils formed between successive cell layers proceeding from the culture surface toward the media. Mineralization followed in the same manner, being observed first in the deepest and oldest fibril layers. Collagen fibrillogenesis, the kinetics of cross-link formation, and collagen stability in the extracellular matrix of the cultures were examined over a 30 day culture period. Between days 8 and 12 in culture, collagen fibril diameters increased from < 30 nm to an average of 30-45 nm. Thereafter, diameters ranged in size from 20 to 200 nm. Quantitation of the collagen cross-linking residues, hydroxylysyl pyridinoline (HP) and lysyl pyridinoline (LP), showed that these mature cross-links increased from undetectable levels to concentrations found in normal chick bone. Analysis of the kinetics of their formation by pulse-chase labeling the cultures with [3H]lysine showed a doubling time of approximately 5 days. The relationships between cross-link formation, fibrillogenesis, and collagen stability were examined in cultures treated with beta-aminopropionitrile (beta-APN), a potent inhibitor of lysyl oxidase and cross-link formation. In beta-APN-treated cultures, total collagen synthesis was increased twofold, with no change in mRNA levels for type I collagen, whereas the amount of collagen accumulated in the cell layer was decreased by 50% and mineral deposition was reduced. The rate of collagen retention in the matrix was assessed by pulse-chase analysis of [3H]proline over a 16 day period in control and beta-APN-treated cultures. In control cultures, about 20% of the labeled collagen was lost from the cell layers over a 16 day period compared with > 80% in the presence of beta-APN. The beta-APN-treated cultures also showed a wider diversity of fibril diameters with a median in the > 45-60 nm range. In summary, these data suggest that cross-linking and assembly of collagen fibrils secreted by osteoblasts in vitro occur in a fashion similar to that found in vivo. The rate of cross-link formation is relatively constant and may be correlated with increasing collagen mass.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Musculoskeletal↗

NASA NTRS1977

On the stability of Galerkin methods for initial-boundary value problems for hyperbolic systems

The stability of approximating the solution of mixed initial-boundary value problems for hyperbolic systems by semidiscrete Galerkin methods is studied. It is shown that a particular straightforward Galerkin method yields an unstable approximation, and that this numerical instability is caused by an improper treatment of the boundary. Stable schemes are then presented, one of which differs from the unstable scheme only insofar as the treatment of the boundary is concerned. These stable schemes make use of a particular matrix which symmetrizes the differential system. It is therefore shown that the use of this matrix is crucial to the stability of the computations as well as for obtaining a priori bounds on the energy of the continuous system. This symmetrizing matrix is also related to the diagonalizing matrix for the system of hyperbolic equations and to the Liapunov matrix for the system of ordinary differential equations resulting from the application of Galerkin's method.

Gunzburger, M. D.↗

NASA NTRS1989

Recursive inversion of externally defined linear systems by FIR filters

The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.

Bach, Ralph E., Jr.↗

NASA NTRS1994

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗

NASA NTRS1998

Development and Characterization of SiC)/ MoSi2-Si3N4(p) Hybrid Composites

Intermetallic compound MoSi2 has long been known as a high temperature material that has excellent oxidation resistance and electrical/thermal conductivity. Also its low cost, high melting point (2023 C), relatively low density (6.2 g/cu cm versus 9 g/cu cm for current engine materials), and ease of machining, make it an attractive structural material. However, the use of MoSi2 has been hindered due to its poor toughness at low temperatures, poor creep resistance at high temperatures, and accelerated oxidation (also known as 'pest' oxidation) at temperatures between approximately 450 and 550 C. Continuous fiber reinforcing is very effective means of improving both toughness and strength. Unfortunately, MoSi2 has a relatively high coefficient of thermal expansion (CTE) compared to potential reinforcing fibers such as SiC. The large CTE mismatch between the fiber and the matrix resulted in severe matrix cracking during thermal cycling. Addition of about 30 to 50 vol % of Si3N4 particulate to MoSi2 improved resistance to low temperature accelerated oxidation by forming a Si2ON2 protective scale and thereby eliminating catastrophic 'pest failure'. The Si3N4 addition also improved the high temperature creep strength by nearly five orders of magnitude, doubled the room temperature toughness and significantly lowered the CTE of the MoSi2 and eliminated matrix cracking in SCS-6 reinforced composites even after thermal cycling. The SCS-6 fiber reinforcement improved the room temperature fracture toughness by seven times and impact resistance by five times. The composite exhibited excellent strength and toughness improvement up to 1400 C. More recently, tape casting was adopted as the preferred processing of MoSi2-base composites for improved fiber spacing, ability to use small diameter fibers, and for lower cost. Good strength and toughness values were also obtained with fine diameter Hi-Nicalon tow fibers. This hybrid composite remains competitive with ceramic matrix composites as a replacement for Ni-base superalloys in aircraft engine applications.

Hebsur, Mohan G.↗

NASA NTRS2007

Electron-Molecule Col1isions: Quantitative Approaches, and the Legacy of Aaron Temkin

This article, on electron-molecule collisions, is dedicated to the legacy of my good friend and sometime collaborator, Aaron Temkin on his retirement from the NASA-Goddard Space Flight Center after many years of work at the highest intellectual level in the theoretical treatment of electron-atom and electron-molecule scattering. Aaron's contributions to the manner in which we think about electron-molecule collisions is clear to all of us who have worked in this field. I doubt that the great progress that has occurred in the computational treatment of such complex collision problems could have happened without these contributions. For a brief historical account, see the discussion of Temkin's contribution to electron-molecule scattering in the first article of this volume by Dr. A. K. Bhatia. In this article, I will concentrate on the application of the so called, non-adiabatic R-matrix theory, to vibrational excitation and dissociative attachment, although I will also present some results applying the Linear Algebraic and Kohn-Variational methods to vibrational excitation. As a starting point for almost all computationally effective approaches to electron-molecule collisions, is the fixed nuclei approximation. That is, one recognizes, just as one does with molecular bound states, that there is a separation of electronic(fast) and nuclear(s1ow) degrees of freedom. This separation makes it possible to "freeze" the nuclei in space, calculate the collision parameters for the frozen molecule and then, somehow to add back the vibrations and rotations. The manner in which this is done, depends on the details of the collision problem. It is the work of Aaron and a number of other researchers that has provided the guidance necessary to resolve these issues.

Schneider, B.I.↗

NASA NTRS2002

Origins of Solar Systems Program

O'D. Alexander, Conel↗

NASA NTRS2003

Final Summary of Research Report to the National Aeronautics and Space Administration Origins of Solar Systems Program

The chondrites are aggregates of components (e.g. chondrules, chondrule rims and matrix) that formed in the nebula but, at present, there is no consensus on how any of these components formed or whether their formation produced or post dated the chemical fractionations between the chondrites. Chondrites are, at present, the most primitive Solar System objects available for laboratory study and the conditions under which their principle components formed would provide the most direct constraints for models of nebula formation and evolution. The conditions under which chondrules formed is of particular importance because, if their relative abundance in chondrites approximates that in the nebula, they are the products of one of the most energetic and pervasive processes that operated in the early Solar System. The goal of this proposal was to combine theoretical modeling with a comprehensive study of the elemental and isotopic compositions of the major components in unequilibrated ordinary chondrites (UOCs), with the aim of determining the conditions in the nebula at the time of their formation. The isotopes of volatile and moderately volatile elements should be particularly revealing of conditions during chondrule formation, as evaporation under most conditions would lead to isotopic mass fractionation. Modeling of chondrule and matrix formation requires the development of a kinetic model of evaporation and condensation, and calibration of this model against experiments. Cosmic spherules present an opportunity to test our evaporation models under flash heating conditions that would be difficult to simulate experimentally. However, there is surprisingly little known about the isotopic compositions of silicate cosmic spherules, and a number of questions need to be addressed. Is the range of compositions they exhibit due to evaporation? If they are, are the relative volatilities consistent with the models/experiments and are the isotopic fractionations consistent with Rayleigh conditions? For instance, do the alkalis and S evaporate prior to significant melting so that conditions did not meet the Rayleigh criteria of rapid diffusion? If so, their isotopic fractionation might be considerably suppressed. Could this mechanism of K loss apply to chondrule formation? The Fe isotopic fractionation during evaporation of silicates has not been measured, so cosmic spherules might provide a clue to whether FeO diffusion is fast enough to maintain Rayleigh conditions during evaporation. And so on.

O'D. Alexander, Conel↗

NASA NTRS1987

Effective collision strengths for electron impact excitations in S II

Electron impact collision strengths for forbidden, semiforbidden, and allowed transitions in S II calculated using the R-matrix method are presented. Configuration interaction wave functions are used to represent the six target states included in the calculation. At low impact energies the collision strengths are dominated by resonances for several transitions. The contribution from higher partial waves is obtained in the close-coupling approximation with exchange terms omitted. Results are presented for the effective collision strengths over a wide temperature range (5000-150,000 K) of astrophysical interest. The present results for the 4S(0) yields 2P(0) transition are 20-30 percent lower than previous calculations, while for the 4S(0) yields 2D(0) transition they are in good agreement. The results are approximately 30 percent higher than those of Ho and Henry (1983) for the 4S(0) yields 2P(0) transition at 80,000 K, and the difference between the two results increases with decreasing temperatures (under 80,000 K).

Tayal, S. S.↗

NASA NTRS1987

A versatile and low order hybrid stress element for general shell geometry

A hybrid stress general shell element is developed based on the Hellinger-Reissner principle modified for relaxed element compatibility conditions. The element is based on a consistent first order thin shell theory with Love Kirchhoff hypotheses. It is of quadrilateral shape with only four corner nodes and five degrees of freedom per node. The geometry of the element is approximated through a bi-cubic polynomial surface patch. Numerical examples consist of torsion-loaded slit cylinder and pinched cylinder with open ends and rigid diaphragmed ends. Also, the representation of the rigid body motion is studied by series of parametric eigenvalue analysis of the stiffness matrix.

Kang, David S.↗

NASA NTRS1991

Transonic adaptive flutter suppression using approximate unsteady time domain aerodynamics

A digital adaptive controller is applied to the active flutter suppression problem of a wing under time varying flight conditions in subsonic and transonic flow. Linear quadratic controller gain at each time step is obtained using an iterative Riccati solver. The digital adaptive optimal controller is robust with respect to the unknown external loads. Flutter and divergence instabilities are simultaneously suppressed using a trailing-edge control surface and displacement sensing. A new transonic unsteady aerodynamic approximation methodology is developed which enables one to carry out the rapid calculation required for transonic aeroservoelastic applications. This approximation is based on a combination of unsteady subsonic aerodynamics combined with a transonic correction procedure. Aeroservoelastic transient time response is obtained using Roger's approximation, state transition matrices and an iterative time marching algorithm. The aeroservoelastic system in the time domain is modeled using a deterministic ARMA model together with a parameter estimator. Transonic flutter boundaries of a wing structure are computed, in the time domain, using an estimated aeroelastic system matrix and are in good agreement with experimental data for the low transonic Mach number range.

Pak, Chan-Gi↗