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NASA NTRS1995

Analytical and phenomenological studies of rotating turbulence

A framework, which combines mathematical analysis, closure theory, and phenomenological treatment, is developed to study the spectral transfer process and reduction of dimensionality in turbulent flows that are subject to rotation. First, we outline a mathematical procedure that is particularly appropriate for problems with two disparate time scales. The approach which is based on the Green's method leads to the Poincare velocity variables and the Poincare transformation when applied to rotating turbulence. The effects of the rotation are now reflected in the modifications to the convolution of a nonlinear term. The Poincare transformed equations are used to obtain a time-dependent analog of the Taylor-Proudman theorem valid in the asymptotic limit when the non-dimensional parameter mu is identical to Omega(t) approaches infinity (Omega is the rotation rate and t is the time). The 'split' of the energy transfer in both direct and inverse directions is established. Secondly, we apply the Eddy-Damped-Quasinormal-Markovian (EDQNM) closure to the Poincare transformed Euler/Navier-Stokes equations. This closure leads to expressions for the spectral energy transfer. In particular, an unique triple velocity decorrelation time is derived with an explicit dependence on the rotation rate. This provides an important input for applying the phenomenological treatment of Zhou. In order to characterize the relative strength of rotation, another non-dimensional number, a spectral Rossby number, which is defined as the ratio of rotation and turbulence time scales, is introduced. Finally, the energy spectrum and the spectral eddy viscosity are deduced.

Mahalov, Alex↗

NASA NTRS1998

Life and death in the microcirculation: a role for angiotensin II

OBJECTIVE: Angiotensin II (ANGII) plays a critical role in the maintenance of the microcirculation and in the anatomical loss of microvessels (rarefaction) that occurs in low renin forms of hypertension and in animals fed a high-salt diet. Elevations in sodium intake can trigger a series of hemodynamic and hormonal responses culminating in a substantial rarefaction of small arterioles and capillaries in both normal and reduced renal mass hypertensive rats. METHODS: Immunohistochemistry, Northern blot, and reverse transcription-polymerase chain reaction (RT-PCR) analysis of microdissected blood vessels were used to localize ANGII receptors in the microcirculation. Chronic infusion of ANGII and other physiologic and pharmacologic manipulations of the reninangiotensin system in rats was combined with morphologic and mathematical analysis of the network architecture. RESULTS: We have shown that rarefaction of the microcirculation can cause an increase in total peripheral resistance, reduced tissue perfusion, decreased oxygen delivery, and impaired organ function. Although the mechanisms by which this occurs are not well understood, a number of key observations point to a role for the renin-angiotensin system in this effect. First, ANGII infused systemically at subpressor levels, or locally into the skeletal muscle interstitium, can induce significant microvessel growth. Second, localization of ANGII receptor proteins by immunohistochemistry and Western blotting and RNA localization by RT-PCR confirm the presence of AT1 receptors, which are growth-stimulatory, and AT2 receptors, which are growth-inhibitory in the microcirculation. Third, maintenance of ANGII at normal levels during periods of hypertension or high-salt diet completely eliminates rarefaction. CONCLUSIONS: Taken together, these results support the hypothesis that ANGII acting through AT1- and AT2-receptor mechanisms modulate vessel density during high-salt diet and hypertension.

Review↗

NASA NTRS1974

Digital computer simulation of inductor-energy-storage dc-to-dc converters with closed-loop regulators

The simulation of converter-controller combinations by means of a flexible digital computer program which produces output to a graphic display is discussed. The procedure is an alternative to mathematical analysis of converter systems. The types of computer programming involved in the simulation are described. Schematic diagrams, state equations, and output equations are displayed for four basic forms of inductor-energy-storage dc to dc converters. Mathematical models are developed to show the relationship of the parameters.

Ohri, A. K.↗

NASA NTRS1973

Development of guidelines for the definition of the relavant information content in data classes

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Schmitt, E.↗

NASA NTRS1984

Fundamental remote science research program. Part 2: Status report of the mathematical pattern recognition and image analysis project

The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of he Earth from remotely sensed measurements of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inferences about the Earth. This report summarizes the progress that has been made toward this program goal by each of the principal investigators in the MPRIA Program.

Heydorn, R. P.↗

NASA NTRS1984

Fundamental remote sensing science research program. Part 1: Status report of the mathematical pattern recognition and image analysis project

The Mathematical Pattern Recognition and Image Analysis (MPRIA) Project is concerned with basic research problems related to the study of the Earth from remotely sensed measurement of its surface characteristics. The program goal is to better understand how to analyze the digital image that represents the spatial, spectral, and temporal arrangement of these measurements for purposing of making selected inference about the Earth.

Heydorn, R. D.↗

NASA NTRS1976

Transient analysis of unbalanced short circuits of the ERDA-NASA 100 kW wind turbine alternator

Unbalanced short-circuit faults on the alternator of the ERDA-NASA Mod-O100-kW experimental wind turbine are studied. For each case, complete solutions for armature, field, and damper-circuit currents; short-circuit torque; and open-phase voltage are derived directly by a mathematical analysis. Formulated results are tabulated. For the Mod-O wind turbine alternator, numerical calculations are given, and results are presented by graphs. Comparisons for significant points among the more important cases are summarized. For these cases the transients are found to be potentially severe. The effect of the alternator neutral-to-ground impedance is evaluated.

Hwang, H. H.↗

NASA NTRS2008

Crack Offset Measurement With the Projected Laser Target Device

The device and associated analysis methodology summarized in this report were developed for the purpose of estimating the size of discontinuities in the surface of the foam that covers the Space Shuttle External Tank. These surface offsets are thought to be due to subsurface cracks in the foam insulation. The mathematical analysis and procedure described here provide a method to quantity the dimensions of the crack offset in a direction perpendicular to the surface, making use of the projected laser target device (PLTD) tool and a laser line projector. The keys to the construction and use of the PLTD are the following geometrical design requirements: Laser dots are on a square grid: length on a side. Laser beams are perpendicular to projected surface. Beams are parallel out to the distance being projected. The PLTD can be used to (1) calibrate fixed cameras of unknown magnification and orientation (far-field solution); (2) provide equivalent calibration to multiple cameras, previously achieved only by the use of known target points, for example, in 3.D foreign-object debris tracking on a fixed launch platform; (3) compute scaling for conventional 2.D images, and depth of field for 3.D images (near-field solution); and (4) in conjunction with a laser line projector, achieve accurate measurements of surface discontinuity (cracks) in a direction perpendicular to the surface.

Source record↗

NASA NTRS1975

NASTRAN nonlinear vibration analysis of beam and frame structures

A capability for the nonlinear vibration analysis of beam and frame structures suitable for use with NASTRAN level 15.5 is described. The nonlinearity considered is due to the presence of axial loads induced by longitudinal end restraints and lateral displacements that are large compared to the beam height. A brief discussion is included of the mathematical analysis and the geometrical stiffness matrix for a prismatic beam (BAR) element. Also included are a brief discussion of the equivalent linearization iterative process used to determine the nonlinear frequency, the required modifications to subroutines DBAR and XMPLBD of the NASTRAN code, and the appropriate vibration capability, four example problems are presented. Comparisons with existing experimental and analytical results show that excellent accuracy is achieved with NASTRAN in all cases.

Mei, C.↗

NASA NTRS1984

Parabolic Dish Concentrator (PDC-1)

The design, construction, and installation of the Parabolic Dish Concentrator, Type 1 (PDC-1) has been one of the most significant JPL concentrator projects because of the knowledge gained about this type of concentrator and the development of design, testing, and analysis procedures which are applicable to all solar concentrator projects. The need for these procedures was more clearly understood during the testing period which started with the prototype panel evaluation and ended with the performance characterization of the completed concentrator. For each phase of the test program, practical test procedures were required and these procedures defined the mathematical analysis which was essential for successful concentrator development. The concentrator performance appears to be limited only by the distortions resulting from thermal gradients through the reflecting panels. Simple optical testing can be extremely effective, but comprehensive mechanical and optical analysis is essential for cost effective solar concentrator development.

Dennison, E. W.↗

NASA NTRS2002

Nonlinear Dynamic Models in Advanced Life Support

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Jones, Harry↗

NASA NTRS1995

Mission Success Driven Space System Sparing Analysis

Among the maintenance resources, the spare parts are the most difficult to predict. Items in the space systems are very different from the point of view of reliability, cost, weight, volume, etc. The different combinations of spares make different contribution to the: mission success, spare investment, volume occupied and weight. Hence, the selection of spares for a mission planned must take into account all of these features. This paper presents the generic mission success driven sparing model developed, for the complex space systems. The mathematical analysis used in the model enables the user to select the most suitable selection of the spare package for the mission planned. The illustrative examples presented clearly demonstrate the applicability and usefulness of the model introduced.

Knezevic, J.↗

NASA NTRS1993

Computer program for analysis of high speed, single row, angular contact, spherical roller bearing, SASHBEAN. Volume 2: Mathematical formulation and analysis

Spherical roller bearings have typically been used in applications with speeds limited to about 5000 rpm and loads limited for operation at less than about 0.25 million DN. However, spherical roller bearings are now being designed for high load and high speed applications including aerospace applications. A computer program, SASHBEAN, was developed to provide an analytical tool to design, analyze, and predict the performance of high speed, single row, angular contact (including zero contact angle), spherical roller bearings. The material presented is the mathematical formulation and analytical methods used to develop computer program SASHBEAN. For a given set of operating conditions, the program calculates the bearings ring deflections (axial and radial), roller deflections, contact areas stresses, depth and magnitude of maximum shear stresses, axial thrust, rolling element and cage rotational speeds, lubrication parameters, fatigue lives, and rates of heat generation. Centrifugal forces and gyroscopic moments are fully considered. The program is also capable of performing steady-state and time-transient thermal analyses of the bearing system.

Aggarwal, Arun K.↗

NASA NTRS1996

Test Outline for Flutter Analysis of Rectangular Panels in Rarefied Flow Conditions

Jet plume impingement forces acting on large flexible space structures may precipitate dynamically unstable behavior during space flights. Typical operating conditions in space involve rarefied gas flow regimes which are intrinsically distinct from continuum gas flow and are normally modeled using the kinetic theory of gas flow. Docking and undocking operations of the Space Shuttle with the Russian Mir space laboratory represent a scenario in which the stability boundaries of solar panels may be of interest. Extensive literature review of research work on the dynamic stability of rectangular panels in rarefied gas flow conditions indicated the lack of published reports dealing with this phenomenon. A recently completed preliminary study for NASA JSC dealing with the mathematical analysis of the stability of two-degree-of-freedom elastically supported rigid panels under the effect of rarefied gas flow was reviewed. A test plan outline is prepared for the purpose of conducting a series of experiments on four rectangular rigid test articles in a vacuum chamber under the effect of continuous and pulsating Nitrogen jet plumes. The purpose of the test plan is to gather enough data related to a number of key parameters to allow the validation of the two-degree-of-freedom mathematical model. The hardware required careful design to select a very lightweight material while satisfying rigidity and frequency requirements within the constraints of the test environment. The data to be obtained from the vacuum chamber tests can be compared with the predicted behavior of the theoretical two-degree-of-freedom model. Using the data obtained in this study, further research can identify the limitations of the mathematical model. In addition modifications to the mathematical model can be made, if warranted, to accurately predict the behavior of rigid panels under rarefied gas flow regimes.

Akl, Fred A.↗

NASA NTRS1988

SURE reliability analysis: Program and mathematics

The SURE program is a new reliability analysis tool for ultrareliable computer system architectures. The computational methods on which the program is based provide an efficient means for computing accurate upper and lower bounds for the death state probabilities of a large class of semi-Markov models. Once a semi-Markov model is described using a simple input language, the SURE program automatically computes the upper and lower bounds on the probability of system failure. A parameter of the model can be specified as a variable over a range of values directing the SURE program to perform a sensitivity analysis automatically. This feature, along with the speed of the program, makes it especially useful as a design tool.

Butler, Ricky W.↗

NASA NTRS1976

An analysis of satellite state vector observability using SST tracking data

Observability of satellite state vectors, using only SST tracking data was investigated by covariance analysis under a variety of satellite and station configurations. These results indicate very precarious observability in most short arc cases. The consequences of this are large variances on many state components, such as the downrange component of the relay satellite position. To illustrate the impact of observability problems, an example is given of two distinct satellite orbit pairs generating essentially the same data arc. The physical bases for unobservability are outlined and related to proposed TDRSS configurations. Results are relevant to any mission depending upon TDRSS to determine satellite state. The required mathematical analysis and the software used is described.

Englar, T. S., Jr.↗

NASA NTRS1985

Technical support for creating an artificial intelligence system for feature extraction and experimental design

Techniques for classifying objects into groups or clases go under many different names including, most commonly, cluster analysis. Mathematically, the general problem is to find a best mapping of objects into an index set consisting of class identifiers. When an a priori grouping of objects exists, the process of deriving the classification rules from samples of classified objects is known as discrimination. When such rules are applied to objects of unknown class, the process is denoted classification. The specific problem addressed involves the group classification of a set of objects that are each associated with a series of measurements (ratio, interval, ordinal, or nominal levels of measurement). Each measurement produces one variable in a multidimensional variable space. Cluster analysis techniques are reviewed and methods for incuding geographic location, distance measures, and spatial pattern (distribution) as parameters in clustering are examined. For the case of patterning, measures of spatial autocorrelation are discussed in terms of the kind of data (nominal, ordinal, or interval scaled) to which they may be applied.

Glick, B. J.↗

NASA NTRS1991

Impinging jets atomization

An analysis of the characteristics of the spray produced by an impinging-jet injector is presented. Predictions of the spray droplet size and distribution are obtained through studying the formation and disintegration of the liquid sheet formed by the impact of two cylindrical jets of the same diameter and momentum. Two breakup regimes of the sheet are considered depending on Weber number, with transition occurring at Weber numbers between 500 and 2000. In the lower Weber number regime, the breakup is due to Taylor cardioidal waves, while at Weber number higher than 2000, the sheet disintegration is by the growth of Kelvin-Helmholtz instability waves. Theoretical expressions to predict the sheet thickness and shape are derived for the low Weber number breakup regime. An existing mathematical analysis of Kelvin-Helmholtz instability of radially moving liquid sheets is adopted in the predictions of resultant drop sizes by sheet breakup at Weber numbers greater than 2000. Comparisons of present theoretical results with experimental measurements and empirical correlations reported in the literature reveal favorable agreement.

Ibrahim, E. A.↗