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NASA NTRS2005

Monte Carlo Simulation of Markov, Semi-Markov, and Generalized Semi- Markov Processes in Probabilistic Risk Assessment

A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.

English, Thomas↗

NASA NTRS1997

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program.

Deng, Xiaomin↗

NASA NTRS2005

Depth-Penetrating Luminescence Thermography of Thermal- Barrier Coatings

A thermographic method has been developed for measuring temperatures at predetermined depths within dielectric material layers . especially thermal-barrier coatings. This method will help satisfy a need for noncontact measurement of through-the-thickness temperature gradients for evaluating the effectiveness of thermal- barrier coatings designed to prevent overheating of turbine blades, combustor liners, and other engine parts. Heretofore, thermography has been limited to measurement of surface and near-surface temperatures. In the thermographic method that is the immediate predecessor of the present method, a thermographic phosphor is applied to the outer surface of a thermal barrier coating, luminescence in the phosphor is excited by illuminating the phosphor at a suitable wavelength, and either the time dependence of the intensity of luminescence or the intensities of luminescence spectral lines is measured. Then an emissivity-independent surface-temperature value is computed by use of either the known temperature dependence of the luminescence decay time or the known temperature dependence of ratios between intensities of selected luminescence spectral lines. Until now, depth-penetrating measurements have not been possible because light of the wavelengths needed to excite phosphors could not penetrate thermal-barrier coating materials to useful depths. In the present method as in the method described above, one exploits the temperature dependence of luminescence decay time. In this case, the phosphor is incorporated into the thermal-barrier coat at the depth at which temperature is to be measured. To be suitable for use in this method, a phosphor must (1) exhibit a temperature dependence of luminescence decay time in the desired range, (2) be thermochemically compatible with the thermal-barrier coating, and (3) exhibit at least a minor excitation spectral peak and an emission spectral peak, both peaks being at wavelengths at which the thermal-barrier coating is transparent or at least translucent. Conventional thermographic phosphors are not suitable because they are most efficiently excited by ultraviolet light, which does not penetrate thermal- barrier coating materials. (Typical thermal-barrier coating materials include or consist of various formulations of yttria-stabilized zirconia.) Only a small fraction of phosphor candidates have significant excitation at wavelengths long enough (>500 nm) for sufficient penetration of thermal-barrier coatings. One suitable phosphor material . yttria doped with europium (Y2O3:Eu) . has a minor excitation peak at 532 nm and an emission peak at 611 nm. In experiments, this material was incorporated beneath a 100-microns-thick thermal-barrier coating and subjected to excitation and measurement by the luminescence-decay-time technique. These experiments were found to yield reliable temperature values up to 1,100 C. At the time of reporting the information for this article, a search for suitable phosphors other than (Y2O3:Eu) was continuing.

Eldridge, Jeffrey↗

NASA NTRS1983

Finite Element Analysis of a Deployable Space Structure

The dynamic characteristics of the Solar Array Flight Experiment (SAFE) structure during deployment and retraction are investigated. The SAFE structure consists of a deployable mast with an attached solar blanket designed with accordion type folds to permit packaging in a small volume. The planar form of the blanket geometry during deployment is maintained by a blanket tension/guidewire system. Structurally, the mast is modeled as an Euler beam column with inplane and out of plane bending and finite torsional stiffness. For out of plane motion, the blanket is modeled as a distributed mass uniformly supported by the three guidewires. For inplane motion the blanket displacements are assumed to vary linearly from the mast base to the mast tip. The mathematical model uses a virtual work formulation, required because the axial loading on the mast is nonconservative, combined with assumed beam modes to derive the differential equations of motion. Consideration of the time dependent boundary conditions results in an infinite set of ODE with time dependent coefficients. Finally, correlation of mast tip accelerations to mast base bending moments for specified modal motions are indicated.

Weeks, G. E.↗

NASA NTRS1990

False-vacuum decay in generalized extended inflation

False-vacuum decay was studied in context of generalized extended inflationary theories, and the bubble nucleation rates was computed for these theories in the limit of G(sub N) yields 0. It was found that the time dependence of the nucleation rate can be exponentially strong through the time dependence of the Jordan-Brans-Dicke field. This can have a pronounced effect on whether extended inflation can be successfully implemented.

Holman, Richard↗

NASA NTRS2000

Systems Analysis of Life Support for Long-Duration Missions

Work defining advanced life support (ALS) technologies and evaluating their applicability to various long-duration missions has continued. Time-dependent and time-invariant costs have been estimated for a variety of life support technology options, including International Space Station (ISS) environmental control and life support systems (ECLSS) technologies and improved options under development by the ALS Project. These advanced options include physicochemical (PC) and bioregenerative (BIO) technologies, and may in the future include in-situ resource utilization (ISRU) in an attempt to reduce both logistics costs and dependence on supply from Earth. PC and bioregenerative technologies both provide possibilities for reducing mission equivalent system mass (ESM). PC technologies are most advantageous for missions of up to several years in length, while bioregenerative options are most appropriate for longer missions. ISRU can be synergistic with both PC and bioregenerative options.

IN SITU RESOURCES UTILIZATION↗

NASA NTRS1985

The cosmic ray interplanetary radial gradient from 1972 - 1985

It is now established that the solar modulation of cosmic rays is produced by turbulent magnetic fields propagated outward by the solar wind. Changes in cosmic ray intensity are not simultaneous throughout the modulation region, thus requiring time dependent theories for the cosmic ray modulation. Fundamental to an overall understanding of this observed time dependent cosmic ray modulation is the behavior of the radial intensity gradient with time and heliocentric distance over the course of a solar modulation cycle. The period from 1977 to 1985 when data are available from the cosmic ray telescopes on Pioneer (P) 10, Voyager (V) 1 and 2, and IMP 8 spacecraft is studied. Additional data from P10 and other IMP satellites for 1972 to 1977 can be used to determine the gradient at the minimum in the solar modulation cycle and as a function of heliocentric distance. All of these telescopes have thresholds for protons and helium nuclei of E 60 MeV/nucleon.

Webber, W. R.↗

NASA NTRS1993

The WINCOF-I code: Detailed description

The performance of an axial-flow fan-compressor unit is basically unsteady when there is ingestion of water along with the gas phase. The gas phase is a mixture of air and water vapor in the case of a bypass fan engine that provides thrust power to an aircraft. The liquid water may be in the form of droplets and film at entry to the fan. The unsteadiness is then associated with the relative motion between the gas phase and water, at entry and within the machine, while the water undergoes impact on material surfaces, centrifuging, heat and mass transfer processes, and reingestion in blade wakes, following peal off from blade surfaces. The unsteadiness may be caused by changes in atmospheric conditions and at entry into and exit from rain storms while the aircraft is in flight. In a multi-stage machine, with an uneven distribution of blade tip clearance, the combined effect of various processes in the presence of steady or time-dependent ingestion is such as to make the performance of a fan and a compressor unit time-dependent from the start of ingestion up to a short time following termination of ingestion. The original WINCOF code was developed without accounting for the relative motion between gas and liquid phases in the ingested fluid. A modification of the WINCOF code was developed and named WINCOF-1. The WINCOF-1 code can provide the transient performance of a fan-compressor unit under a variety of input conditions.

Murthy, S. N. B.↗

NASA NTRS1972

The challenge to unify treatment of high-temperature fatigue - A partisan proposal based on strainrange partitioning

The strainrange partitioning concept divides the imposed strain into four basic ranges involving time-dependent and time-independent components. It is shown that some of the results presented at the symposium can be better correlated on the basis of this concept than by alternative methods. It is also suggested that methods of data generation and analysis can be helpfully guided by this approach. Potential applicability of the concept to the treatment of frequency and hold-time effects, environmental influence, crack initiation and growth, thermal fatigue, and code specifications are briefly considered. A required experimental program is outlined.

Manson, S. S.↗

NASA NTRS1973

The application of holography as a real-time three-dimensional motion picture camera

A historical introduction to holography is presented, as well as a basic description of sideband holography for stationary objects. A brief theoretical development of both time-dependent and time-independent holography is also provided, along with an analytical and intuitive discussion of a unique holographic arrangement which allows the resolution of front surface detail from an object moving at high speeds. As an application of such a system, a real-time three-dimensional motion picture camera system is discussed and the results of a recent demonstration of the world's first true three-dimensional motion picture are given.

Kurtz, R. L.↗

NASA NTRS1972

The challenge to unify treatment of high-temperature fatigue - A partisan proposal based on strainrange partitioning.

The strainrange partitioning concept divides the imposed strain into four basic ranges involving time-dependent and time-independent components. It is shown that some of the results presented at the Symposium can be better correlated on the basis of this concept than by alternative methods. It is also suggested that methods of data generation and analysis can be helpfully guided by this approach. Potential applicability of the concept to the treatment of frequency and hold-time effects, environmental influence, crack initiation and growth, thermal fatigue, and code specifications are then briefly considered. A required experimental program is outlined.

Manson, S. S.↗

NASA NTRS1973

Computational problems in three and four dimensional boundary layer theory

It is shown that three-dimensional and time-dependent boundary layer flows can be calculated in a reasonable amount of time with the current generation of computers. The physical problems used to illustrate this have a wide application, and are the following: (1) oscillating flows over cylinders with both the wall and the inviscid flow oscillating, and (2) time-dependent and three-dimensional flow over a rotating airfoil in forward flight.

Dwyer, H. A.↗

NASA NTRS1981

Semi-actuator disk theory for compressor choke flutter

A mathematical anaysis predict the unsteady aerodynamic utilizing semi actuator theory environment for a cascade of airfoils harmonically oscillating in choked flow was developed. A normal shock is located in the blade passage, its position depending on the time dependent geometry, and pressure perturbations of the system. In addition to shock dynamics, the model includes the effect of compressibility, interblade phase lag, and an unsteady flow field upstream and downstream of the cascade. Calculated unsteady aerodynamics were compared with isolated airfoil wind tunnel data, and choke flutter onset boundaries were compared with data from testing of an F100 high pressure compressor stage.

Micklow, J.↗

NASA NTRS1982

A parameterized model for the evolution of isotopic heterogeneities in a convecting system

It is experimentally shown that, although steady convective flows are efficient means to heterogeneity within a single cell, they do not produce a dispersal of heterogeneous material over scales that are large by comparison to their depth, which requires that the flow be time-dependent on a time scale comparable to the overturn time. Convection in an internally heated layer does possess this property, and numerical solutions are presently used to study the way in which it disperses a set of neutrally bouyant particles initially confined to a small space. The derived concept of effective diffusivity is applied to the isotopic evolution of the Sm-Nd and Rb-Sr systems, with spatial variations generated by horizontal variations in degree of melting 1.8 billion years ago.

Richter, F. M.↗

NASA NTRS1985

Unified constitutive material models for nonlinear finite-element structural analysis

Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine components with particular application to isotropic materials used for high-pressure stage turbine blades and vanes. Forms or combinations of models independently proposed by Bodner and Walker were considered. These theories combine time-dependent and time-independent aspects of inelasticity into a continuous spectrum of behavior. This is in sharp contrast to previous classical approaches that partition inelastic strain into uncoupled plastic and creep components. Predicted stress-strain responses from these models were evaluated against monotonic and cyclic test results for uniaxial specimens of two cast nickel-base alloys, B1900+Hf and Rene' 80. Previously obtained tension-torsion test results for Hastelloy X alloy were used to evaluate multiaxial stress-strain cycle predictions. The unified models, as well as appropriate algorithms for integrating the constitutive equations, were implemented in finite-element computer codes.

Kaufman, A.↗

NASA NTRS1985

Unified constitutive material models for nonlinear finite-element structural analysis

Unified constitutive material models were developed for structural analyses of aircraft gas turbine engine components with particular application to isotropic materials used for high-pressure stage turbine blades and vanes. Forms or combinations of models independently proposed by Bodner and Walker were considered. These theories combine time-dependent and time-independent aspects of inelasticity into a continuous spectrum of behavior. This is in sharp contrast to previous classical approaches that partition inelastic strain into uncoupled plastic and creep components. Predicted stress-strain responses from these models were evaluated against monotonic and cyclic test results for uniaxial specimens of two cast nickel-base alloys, B1900+Hf and Rene 80. Previously obtained tension-torsion test results for Hastelloy X alloy were used to evaluate multiaxial stress-strain cycle predictions. The unified models, as well as appropriate algorithms for integrating the constitutive equations, were implemented in finite-element computer codes.

Kaufman, A.↗

NASA NTRS1992

The steady part of the secular variation of the Earth's magnetic field

The secular variation of the Earth's magnetic field results from the effects of magnetic induction in the fluid outer core and from the effects of magnetic diffusion in the core and the mantle. Adequate observations to map the magnetic field at the core-mantle boundary extend back over three centuries, providing a model of the secular variation at the core-mantle boundary. Here we consider how best to analyze this time-dependent part of the field. To calculate steady core flow over long time periods, we introduce an adaptation of our earlier method of calculating the flow in order to achieve greater numerical stability. We perform this procedure for the periods 1840-1990 and 1690-1840 and find that well over 90 percent of the variance of the time-dependent field can be explained by simple steady core flow. The core flows obtained for the two intervals are broadly similar to each other and to flows determined over much shorter recent intervals.

Bloxham, Jeremy↗

NASA NTRS1995

Tidal influence on O(1S) airglow emission rate distributions at the geographic equator as observed by WINDII

WINDII, the Wind Imaging Interferometer on the Upper Atmosphere Research Satellite, observes winds, temperatures and emission rates in the upper mesosphere and thermosphere. In this paper we report on nighttime observations of the vertical distribution of the O(1S) 557.7 nm emission near the geographic equator for March/April, 1993. The airglow volume emission rate distribution is found to be strongly dependent on local time. Beginning at dusk, an intense airglow emission layer descends from a mean altitude of 95 km, reaching 89 km by midnight after which the emission rapidly decays. Shortly after midnight it reappears weakly at a higher altitude and remains at this level as the emission rate gradually increases towards dawn. This strong local time dependence leads us to conclude that the effect is tidally driven. Comparison with the Forbes (1982a,b) model suggest that total density perturbations and changes in the atomic oxygen mixing ratio may the cause of the changes in emission rate distribution between dusk and midnight. The reappearance of the emission after midnight may be caused by downward winds bringing oxygen-rich air from above.

Shephere, G. G.↗