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NASA NTRS1993

Preconditioning and the limit to the incompressible flow equations

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

Turkel, E.↗

NASA NTRS1995

Pseudo-time methods for constrained optimization problems governed by PDE

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

Taasan, Shlomo↗

NASA NTRS2006

Kalman Filter for Calibrating a Telescope Focal Plane

The instrument-pointing frame (IPF) Kalman filter, and an algorithm that implements this filter, have been devised for calibrating the focal plane of a telescope. As used here, calibration signifies, more specifically, a combination of measurements and calculations directed toward ensuring accuracy in aiming the telescope and determining the locations of objects imaged in various arrays of photodetectors in instruments located on the focal plane. The IPF Kalman filter was originally intended for application to a spaceborne infrared astronomical telescope, but can also be applied to other spaceborne and ground-based telescopes. In the traditional approach to calibration of a telescope, (1) one team of experts concentrates on estimating parameters (e.g., pointing alignments and gyroscope drifts) that are classified as being of primarily an engineering nature, (2) another team of experts concentrates on estimating calibration parameters (e.g., plate scales and optical distortions) that are classified as being primarily of a scientific nature, and (3) the two teams repeatedly exchange data in an iterative process in which each team refines its estimates with the help of the data provided by the other team. This iterative process is inefficient and uneconomical because it is time-consuming and entails the maintenance of two survey teams and the development of computer programs specific to the requirements of each team. Moreover, theoretical analysis reveals that the engineering/ science iterative approach is not optimal in that it does not yield the best estimates of focal-plane parameters and, depending on the application, may not even enable convergence toward a set of estimates.

Kang, Bryan↗

NASA NTRS2012

Modifications Of Discrete Ordinate Method For Computations With High Scattering Anisotropy: Comparative Analysis

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as an anisotropic part. The TMS method uses Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside of the aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.

Korkin, Sergey V.↗

NASA NTRS2015

Technology Candidates for Air-to-Air and Air-to-Ground Data Exchange

Technology Candidates for Air-to-Air and Air-to-Ground Data Exchange is a two-year research effort to visualize the U. S. aviation industry at a point 50 years in the future, and to define potential communication solutions to meet those future data exchange needs. The research team, led by XCELAR, was tasked with identifying future National Airspace System (NAS) scenarios, determining requirements and functions (including gaps), investigating technical and business issues for air, ground, & air-to-ground interactions, and reporting on the results. The project was conducted under technical direction from NASA and in collaboration with XCELAR's partner, National Institute of Aerospace, and NASA technical representatives. Parallel efforts were initiated to define the information exchange functional needs of the future NAS, and specific communication link technologies to potentially serve those needs. Those efforts converged with the mapping of each identified future NAS function to potential enabling communication solutions; those solutions were then compared with, and ranked relative to, each other on a technical basis in a structured analysis process. The technical solutions emerging from that process were then assessed from a business case perspective to determine their viability from a real-world adoption and deployment standpoint. The results of that analysis produced a proposed set of future solutions and most promising candidate technologies. Gap analyses were conducted at two points in the process, the first examining technical factors, and the second as part of the business case analysis. In each case, no gaps or unmet needs were identified in applying the solutions evaluated to the requirements identified. The future communication solutions identified in the research comprise both specific link technologies and two enabling technologies that apply to most or all specific links. As a result, the research resulted in a new analysis approach, viewing the underlying architecture of ground-air and air-air communications as a whole, rather than as simple "link to function" paired solutions. For the business case analysis, a number of "reference architectures" were developed for both the future technologies and the current systems, based on three typical configurations of current aircraft. Current and future costs were assigned, and various comparisons made between the current and future architectures. In general, it was assumed that if a future architecture offers lower cost than the current typical architecture, while delivering equivalent or better performance, it is likely that the future solution will gain industry acceptance. Conversely, future architectures presenting higher costs than their current counterparts must present a compelling benefit case in other areas or risk a lack of industry acceptance. The business case analysis consistently indicated lower costs for the proposed future architectures, and in most cases, significantly so. The proposed future solutions were found to offer significantly greater functionality, flexibility, and growth potential over time, at lower cost, than current systems. This was true for overall, fleet-wide equipage for domestic and oceanic air carriers, as well as for single, General Aviation (GA) aircraft. The overall research results indicate that all identified requirements can be met by the proposed solutions with significant capacity for future growth. Results also illustrate that the majority of the future communication needs can be met using currently allocated aviation RF spectrum, if used in more effective ways than it is today. A combination of such optimized aviation-specific links and commercial communication systems meets all identified needs for the 50-year future and beyond, with the caveat that a new, overall function will be needed to manage all information exchange, individual links, security, cost, and other factors. This function was labeled "Delivery Manager" (DM) within this research. DM employs a distributed client/server architecture, for both airborne and ground communications architectures. Final research results included identifying the most promising candidate technologies for the future system, conclusions and recommendations, and identifying areas where further research should be considered.

Communications↗

NASA NTRS2012

Influence of Finite Element Size in Residual Strength Prediction of Composite Structures

The sensitivity of failure load to the element size used in a progressive failure analysis (PFA) of carbon composite center notched laminates is evaluated. The sensitivity study employs a PFA methodology previously developed by the authors consisting of Hashin-Rotem intra-laminar fiber and matrix failure criteria and a complete stress degradation scheme for damage simulation. The approach is implemented with a user defined subroutine in the ABAQUS/Explicit finite element package. The effect of element size near the notch tips on residual strength predictions was assessed for a brittle failure mode with a parametric study that included three laminates of varying material system, thickness and stacking sequence. The study resulted in the selection of an element size of 0.09 in. X 0.09 in., which was later used for predicting crack paths and failure loads in sandwich panels and monolithic laminated panels. Comparison of predicted crack paths and failure loads for these panels agreed well with experimental observations. Additionally, the element size vs. normalized failure load relationship, determined in the parametric study, was used to evaluate strength-scaling factors for three different element sizes. The failure loads predicted with all three element sizes provided converged failure loads with respect to that corresponding with the 0.09 in. X 0.09 in. element size. Though preliminary in nature, the strength-scaling concept has the potential to greatly reduce the computational time required for PFA and can enable the analysis of large scale structural components where failure is dominated by fiber failure in tension.

Satyanarayana, Arunkumar↗

NASA NTRS1972

Buckling and vibration analysis for stiffened orthotropic shells of revolution.

Development of a numerical method, using the multistep integration approach, in which the buckling and vibration analyses are formulated as a succession of linear eigenvalue problems. The method does not require an estimate of the eigenvector, and once an eigenvalue has been converged good estimates for other eigenvalues are automatically available. This is accomplished through the use of an in-core Householder scheme for solution of the eigenvalue problem. Furthermore, since the method uses an eigenvalue solution, the possibility of missing modes is eliminated.

Svalbonas, V.↗

NASA NTRS1984

An investigation of the transient thermal analysis of spur gears

A finite element computer program is developed for evaluating the transient behavior of surface temperature in high performance spur gears. The time dimension is implemented using two and three point finite difference schemes. The different schemes are provided for the purpose of numerical stability and convergence studies. A detailed explanation of the gear cooling process leading to the establishment of a modified Blok model is also included. Other conventional models for approximating the heat transfer coefficients are available for comparison. Preliminary results are given showing snap shots of gear temperature contours at the initial stages of tooth engagement.

El-Bayoumy, L. E.↗

NASA NTRS1984

Transonic cascade flow analysis using viscous/inviscid coupling concepts

Transonic two-dimensional cascade flows have been analyzed using viscous/inviscid coupling concepts. A full potential cascade code is coupled with an inverse integral boundary layer/wake method that permits calculation of separated laminar or turbulent flow. The semi-inverse coupling method of Wigton converges slowly in the case of a strong shock in the region between the shock and the trailing edge. The location of a strong shock is not well predicted by the coupling method, which indicates the need for an entropy correction in the potential code or the inclusion of a shock-boundary layer interaction module.

Olling, C. R.↗

NASA NTRS1985

An investigation of the transient thermal analysis of spur gears

El-Bayoumy, L. E.↗

NASA NTRS1979

ATLAS, an integrated structural analysis and design system. Volume 6: Design module theory

The automated design theory underlying the operation of the ATLAS Design Module is decribed. The methods, applications and limitations associated with the fully stressed design, the thermal fully stressed design and a regional optimization algorithm are presented. A discussion of the convergence characteristics of the fully stressed design is also included. Derivations and concepts specific to the ATLAS design theory are shown, while conventional terminology and established methods are identified by references.

Backman, B. F.↗

NASA NTRS1980

The solution of variable-step implicit difference equations for dynamic systems analysis

A semi-implicit iterative technique is given for the solution of implicit matrix difference equations which arise in variable-step direct time integration of dynamic systems equations. For all practical purposes, the technique avoids repeated refactoring of the stepsize-dependent solution matrix and achieves the solution convergence for engineering accuracy requirements within a permissible number of iterations. Extension of the present method to nonlinear problems treated by the pseudo-force procedure is straightforward. For nonlinear solution procedures based on the tangent modulus formulation, the technique requires modification to make use of the tangent stiffness matrix. It is noted that the question of whether to include the nonlinear terms within the iteration loop has not yet been resolved.

Park, K. C.↗

NASA NTRS1982

Application of a finite element algorithm for the solution of steady transonic Euler equations

A finite element algorithm for the solution of two-dimensional, steady Euler equations is presented which, through a Clebsch-type transformation for the velocity vector, solves the conservation of mass equation with one primary variable and two additional equations for the convection of two new variables. The accuracy and efficiency of this scheme is discussed, and the second-order accuracy attained in the analysis of the convection of the vorticity is demonstrated together with the efficient treatment of rotational and irrotational flow subregions. A sample problem is used to show the accuracy of the numerical scheme and its convergence characteristics.

Akay, H. U.↗

NASA NTRS1989

Rotordynamic coefficients for stepped labyrinth gas seals

The basic equations are derived for compressible flow in a stepped labyrinth gas seal. The flow is assumed to be completely turbulent in the circumferential direction where the friction factor is determined by the Blasius relation. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order pressure distribution is found by satisfying the leakage equation while the circumferential velocity distribution is determined by satisfying the momentum equations. The first order equations are solved by a separation of variables solution. Integration of the resultant pressure distribution along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The results of this analysis are presented in the form of a parametric study, since there are no known experimental data for the rotordynamic coefficients of stepped labyrinth gas seals. The parametric study investigates the relative rotordynamic stability of convergent, straight and divergent stepped labyrinth gas seals. The results show that, generally, the divergent seal is more stable, rotordynamically, than the straight or convergent seals. The results also show that the teeth-on-stator seals are not always more stable, rotordynamically, then the teeth-on-rotor seals as was shown by experiment by Childs and Scharrer (1986b) for a 15 tooth seal.

Scharrer, Joseph K.↗

NASA NTRS1997

Digital storage and analysis of color Doppler echocardiograms

Color Doppler flow mapping has played an important role in clinical echocardiography. Most of the clinical work, however, has been primarily qualitative. Although qualitative information is very valuable, there is considerable quantitative information stored within the velocity map that has not been extensively exploited so far. Recently, many researchers have shown interest in using the encoded velocities to address the clinical problems such as quantification of valvular regurgitation, calculation of cardiac output, and characterization of ventricular filling. In this article, we review some basic physics and engineering aspects of color Doppler echocardiography, as well as drawbacks of trying to retrieve velocities from video tape data. Digital storage, which plays a critical role in performing quantitative analysis, is discussed in some detail with special attention to velocity encoding in DICOM 3.0 (medical image storage standard) and the use of digital compression. Lossy compression can considerably reduce file size with minimal loss of information (mostly redundant); this is critical for digital storage because of the enormous amount of data generated (a 10 minute study could require 18 Gigabytes of storage capacity). Lossy JPEG compression and its impact on quantitative analysis has been studied, showing that images compressed at 27:1 using the JPEG algorithm compares favorably with directly digitized video images, the current goldstandard. Some potential applications of these velocities in analyzing the proximal convergence zones, mitral inflow, and some areas of future development are also discussed in the article.

NASA Discipline Cardiopulmonary↗

NASA NTRS1999

Analysis of the ST-T complex of the electrocardiogram using the Karhunen--Loeve transform: adaptive monitoring and alternans detection

The Karhunen-Loeve transform (KLT) is applied to study the ventricular repolarisation period as reflected in the ST-T complex of the surface ECG. The KLT coefficients provide a sensitive means of quantitating ST-T shapes. A training set of ST-T complexes is used to derive a set of KLT basis vectors that permits representation of 90% of the signal energy using four KLT coefficients. As a truncated KLT expansion tends to favor representation of the signal over any additive noise, a time series of KLT coefficients obtained from successive ST-T complexes is better suited for representation of both medium-term variations (such as ischemic changes) and short-term variations (such as ST-T alternans) than discrete parameters such as the ST level or other local indices. For analysis of ischemic changes, an adaptive filter is described that can be used to estimate the KLT coefficient, yielding an increase in the signal-to-noise ratio of 10 dB (u = 0.1), with a convergence time of about three beats. A beat spectrum of the unfiltered KLT coefficient series is used for detection of ST-T alterans. These methods are illustrated with examples from the European ST-T Database. About 20% of records revealed quasi-periodic salvos of ischemic ST-T change episodes and another 20% exhibit repetitive, but not clearly periodic patterns of ST-T change episodes. About 5% of ischemic episodes were associated with ST-T alterans.

NASA Discipline Cardiopulmonary↗

NASA NTRS2014

Compositional Solution Space Quantification for Probabilistic Software Analysis

Probabilistic software analysis aims at quantifying how likely a target event is to occur during program execution. Current approaches rely on symbolic execution to identify the conditions to reach the target event and try to quantify the fraction of the input domain satisfying these conditions. Precise quantification is usually limited to linear constraints, while only approximate solutions can be provided in general through statistical approaches. However, statistical approaches may fail to converge to an acceptable accuracy within a reasonable time. We present a compositional statistical approach for the efficient quantification of solution spaces for arbitrarily complex constraints over bounded floating-point domains. The approach leverages interval constraint propagation to improve the accuracy of the estimation by focusing the sampling on the regions of the input domain containing the sought solutions. Preliminary experiments show significant improvement on previous approaches both in results accuracy and analysis time.

Monte Carlo Methods↗

NASA NTRS1995

Precision Cleaning Verification of Fluid Components by Air/Water Impingement and Total Carbon Analysis

NASA personnel at Kennedy Space Center's Material Science Laboratory have developed new environmentally sound precision cleaning and verification techniques for systems and components found at the center. This technology is required to replace existing methods traditionally employing CFC-113. The new patent-pending technique of precision cleaning verification is for large components of cryogenic fluid systems. These are stainless steel, sand cast valve bodies with internal surface areas ranging from 0.2 to 0.9 m(exp 2). Extrapolation of this technique to components of even larger sizes (by orders of magnitude) is planned. Currently, the verification process is completely manual. In the new technique, a high velocity, low volume water stream impacts the part to be verified. This process is referred to as Breathing Air/Water Impingement and forms the basis for the Impingement Verification System (IVS). The system is unique in that a gas stream is used to accelerate the water droplets to high speeds. Water is injected into the gas stream in a small, continuous amount. The air/water mixture is then passed through a converging-diverging nozzle where the gas is accelerated to supersonic velocities. These droplets impart sufficient energy to the precision cleaned surface to place non-volatile residue (NVR) contaminants into suspension in the water. The sample water is collected and its NVR level is determined by total organic carbon (TOC) analysis at 880 C. The TOC, in ppm carbon, is used to establish the NVR level. A correlation between the present gravimetric CFC-113 NVR and the IVS NVR is found from experimental sensitivity factors measured for various contaminants. The sensitivity has the units of ppm of carbon per mg-ft(exp 2) of contaminant. In this paper, the equipment is described and data are presented showing the development of the sensitivity factors from a test set including four NVR's impinged from witness plates of 0.05 to 0.75 m(exp 2).

Barile, Ronald G.↗