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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Rosen, I. G.↗
NASA NTRS1988

Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

Rosen, I. G.↗
NASA NTRS2006

Life Test Approach for Refractory Metal/Sodium Heat Pipes

Heat pipe life tests described in the literature have seldom been conducted on a systematic basis. Typically one or more heat pipes are built and tested for an extended period at a single temperature with simple condenser loading. This paper describes an approach to generate carefully controlled data that can conclusively establish heat pipe operating life with material-fluid combinations capable of extended operation. Approximately 10 years of operational life might be compressed into 3 years of laboratory testing through a combination of increased temperature and mass fluence. Two specific test series have been identified and include: investigation of long term corrosion rates based on the guidelines contained in ASTM G-68-80 (using 7 heat pipes); and investigation of corrosion trends in a cross correlation sequence at various temperatures and mass fluences based on a central composite test design (using 9 heat pipes). The heat pipes selected for demonstration purposes are fabricated from a Mo-44.5%Re alloy with a length of 0.3 meters and a diameter of 1.59 cm(to conserve material) with a condenser to evaporator length ratio of approximately 3. The wick is a crescent annular design formed from 400-mesh Mo-Re alloy material hot isostatically pressed to produce a final wick core of 20 microns or less.

Martin, James J.↗
NASA NTRS1991

Thermographic detection of cracks in thin sheets

A thermographic inspection technique for crack detection based on a 2D filter convolved with the thermal temperature images is presented. The filter is designed to approximate operating on the temperature images with a Laplacian operator. This operation yields an image which approximates changes in the heat flux in a thin plate. This filtering method results in an enhanced contrast due to the presence of cracks. Measurements have been performed on samples with fabricated electrical discharge machining (EDM) notches (both through-the-thickness and surface notches) and closed fatigue cracks around rivets. It is shown that the technique is effective for the detection of various crack lengths down to the resolution limits of the imager used.

Cramer, K. E.↗
NASA NTRS1994

On the convergence of local approximations to pseudodifferential operators with applications

We consider the approximation of a class pseudodifferential operators by sequences of operators which can be expressed as compositions of differential operators and their inverses. We show that the error in such approximations can be bounded in terms of L(1) error in approximating a convolution kernel, and use this fact to develop convergence results. Our main result is a finite time convergence analysis of the Engquist-Majda Pade approximants to the square root of the d'Alembertian. We also show that no spatially local approximation to this operator can be convergent uniformly in time. We propose some temporally local but spatially nonlocal operators with better long time behavior. These are based on Laguerre and exponential series.

Hagstrom, Thomas↗
NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. II.

Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.

Baxley, J. V.↗
NASA NTRS1948

Simulated Altitude Performance of Combustor of Westinghouse 19XB-1 Jet-Propulsion Engine

A 19XB-1 combustor was operated under conditions simulating zero-ram operation of the 19XB-1 turbojet engine at various altitudes and engine speeds. The combustion efficiencies and the altitude operational limits were determined; data were also obtained on the character of the combustion, the pressure drop through the combustor, and the combustor-outlet temperature and velocity profiles. At altitudes about 10,000 feet below the operational limits, the flames were yellow and steady and the temperature rise through the combustor increased with fuel-air ratio throughout the range of fuel-air ratios investigated. At altitudes near the operational limits, the flames were blue and flickering and the combustor was sluggish in its response to changes in fuel flow. At these high altitudes, the temperature rise through the combustor increased very slowly as the fuel flow was increased and attained a maximum at a fuel-air ratio much leaner than the over-all stoichiometric; further increases in fuel flow resulted in decreased values of combustor temperature rise and increased resonance until a rich-limit blow-out occurred. The approximate operational ceiling of the engine as determined by the combustor, using AN-F-28, Amendment-3, fuel, was 30,400 feet at a simulated engine speed of 7500 rpm and increased as the engine speed was increased. At an engine speed of 16,000 rpm, the operational ceiling was approximately 48,000 feet. Throughout the range of simulated altitudes and engine speeds investigated, the combustion efficiency increased with increasing engine speed and with decreasing altitude. The combustion efficiency varied from over 99 percent at operating conditions simulating high engine speed and low altitude operation to less than 50 percent at conditions simulating operation at altitudes near the operational limits. The isothermal total pressure drop through the combustor was 1.82 times as great as the inlet dynamic pressure. As expected from theoretical considerations, a straight-line correlation was obtained when the ratio of the combustor total pressure drop to the combustor-inlet dynamic pressure was plotted as a function of the ratio of the combustor-inlet air density to the combustor-outlet gas density. The combustor-outlet temperature profiles were, in general, more uniform for runs in which the temperature rise was low and the combustion efficiency was high. Inspection of the combustor basket after 36 hours of operation showed very little deterioration and no appreciable carbon deposits.

Childs, J. Howard↗
NASA NTRS2013

Data Compression Algorithm Architecture for Large Depth-of-Field Particle Image Velocimeters

A large depth-of-field particle image velocimeter (PIV) is designed to characterize dynamic dust environments on planetary surfaces. This instrument detects lofted dust particles, and senses the number of particles per unit volume, measuring their sizes, velocities (both speed and direction), and shape factors when the particles are large. To measure these particle characteristics in-flight, the instrument gathers two-dimensional image data at a high frame rate, typically >4,000 Hz, generating large amounts of data for every second of operation, approximately 6 GB/s. To characterize a planetary dust environment that is dynamic, the instrument would have to operate for at least several minutes during an observation period, easily producing more than a terabyte of data per observation. Given current technology, this amount of data would be very difficult to store onboard a spacecraft, and downlink to Earth. Since 2007, innovators have been developing an autonomous image analysis algorithm architecture for the PIV instrument to greatly reduce the amount of data that it has to store and downlink. The algorithm analyzes PIV images and automatically reduces the image information down to only the particle measurement data that is of interest, reducing the amount of data that is handled by more than 10(exp 3). The state of development for this innovation is now fairly mature, with a functional algorithm architecture, along with several key pieces of algorithm logic, that has been proven through field test data acquired with a proof-of-concept PIV instrument.

Bos, Brent↗
NASA NTRS1989

Design of a Versatile, Teleoperable, Towable Lifting Machine with Robotic Capabilities for Use in Nasa's Lunar Base Operations

The lifting machine will assist in lifting cargo off of landers sent to the Moon and in the construction of a lunar base. Three possible designs were considered for the overall configuration of the lifting machine: the variable angle crane, the tower crane, and the gantry crane. Alternate designs were developed for the major components of the lifting machine. A teleoperable, variable angle crane was chosen as its final design. The design consists of a telescoping boom mounted to a chassis that is supported by two conical wheels for towing and four outriggers for stability. Attached to the end of the boom is a seven degree of freedom robot arm for light, dexterous, lifting operations. A cable and hook suspends from the end of the boom for heavy, gross, lifting operations. Approximate structural sizes were determined for the lifter and its components. However, further analysis is needed to determine the optimum design dimensions. The design team also constructed a model of the design which demonstrates its features and operating principals.

Harris, Elizabeth↗
NASA NTRSDate not supplied

Analyzing Launch Operations using the Spaceport Throughput Analysis Resource (STAR)

NASA’s Kennedy Space Center (KSC) and Cape CanaveralSpace Force Station (CCSFS) are the world’s preeminent multi-user spaceport, providing facilities and launch capabilities to the agency, NASA’s commercial partners, and other government agencies. KSC works to ensure an environment in which NASA’s programs and other users can safely and effectively carry out their operations. Approximately 100 launches are expected to take place in 2024. KSC needs to meet the needs of customers who request launches based on their own schedules, but who may not be aware of KSC-wide resource limitations and external constraints on launch operations. KSC-wide resources include telecommunications, range tracking, commodities such as Helium and Nitrogen, and special equipment needed to support launches. External constraints include seasonal launch operations. Since space vehicles are complex and launch operations are uncertain, unexpected events can also cause delays in operations. The Spaceport Throughput AnalysisResource (STAR) assesses whether a specific set of pro-posed launches and associated activities can be performed given the resources KSC currently has available, and external constraints imposed on KSC operations. STAR integrates short-horizon scheduling and simulation of launches using a monte-carlo approach driven by configurable probabilities of different classes of event outcomes, including de-lays and worst-case use of resources. The resulting analyses inform stakeholders of key constraints preventing customers from being able to perform their missions as desired, and give insight into how to improve spaceport throughput. The rest of the paper is organized as follows. In 2 we de-scribe the problem STAR is intended to solve. In Section3 we formally describe the scheduling problem ingredients. In Section 4 we describe how manifests are simulated. InSection 5 we describe the constraints problem that is solved when rescheduling. In Section 6 we describe what information is recorded during manifest simulation in order to evaluate delays. In Section 7 we describe the specific problem solved for KSC. In Section 8 we describe the challenges of knowledge engineering for STAR.

Planning Scheduling Analysis↗
NASA NTRS2002

Dynamical Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations

This report summarizes the activities of NASA grant NAG5-11068, "Dynamicai Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations." The High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS) has been providing direct measurements of the Earth's horizontal wind field in the stratosphere, mesosphere and lower thermosphere. Mesospheric temperatures, ozone, and O((sup 1) D) densities, and stratospheric aerosol extinctions coefficients, are also retrieved. The goal of HRDI is to measure the vector winds in the stratosphere (10-40 km), mesosphere, and lower thermosphere (approximately 50-120 km) during the day, and the lower thermosphere at night (approximately 95 km) to an accuracy of 5 m/s. The horizontal wind vector is measured by observing the Doppler shift of rotational lines of molecular oxygen along two lines of sight. In addition to winds, temperatures and volume emission rates are determined in the mesosphere and lower thermosphere, from which ozone and O((sup 1) D) concentrations can be derived, and aerosol scattering coefficients are determined in the stratosphere. UARS was launched on September 12, 1991, into a 585-km circular orbit inclined 57 degrees to the equator HRDI was activated September 28, 1991 and following a period of checkout and adjustment of the instrument parameters, scientific observations began November 2, 199 1. HRDI operated nearly continuously from launch until April 1995. At that time the UARS solar array drive failed, forcing the instruments to time-share the available power. From July 1995 to July 1996 HRDI operated approximately 50% of the time. At that point, one of the three spacecraft batteries failed and from then until September 1998 the duty cycle was less than 20% per month, At that time it was determined that HRDI could operate during each daytime pass, which increased the daytime duty cycle to close to l00%, while nighttime operations were limited to about a week per month. In the fall of 1999, the second tape recorder failed requiring a real time contact with a TRDSS satellite to retrieve that data. This resulted in about 60% data collection efficiency. Finally, in the summer of 2000, the second star sensor failed requiring the spacecraft attitude to be controlled by a three axis magnetometer and sun sensor. This resulted in a loss of attitude knowledge but operations continue with the anticipation of correcting the attitude. A new method for determining the tide and mean structure from satellite data in conjunction with a new tidal model has been devised. For brevity, it shall be referred to as the TMAT or Tide-Mean Assimilation Technique. Most previous methods of tidal analysis are based on various ways of slicing the data set.

Skinner, Wilbert↗
NASA NTRS1985

The eigenvalues of the pseudospectral Fourier approximation to the operator sin (2x) d/dx

It is shown that the eigenvalues Z sub i of the pseudospectral Fourier approximation to the operator sin(2x) curly d/curly dx satisfy (R sub e) (Z sub i) = + or - 1 or (R sub e)(Z sub I) = 0. Whereas this does not prove stability for the Fourier method, applied to the hyperbolic equation U sub t = sin (2x)(U sub x) - pi x pi; it indicates that the growth in time of the numerical solution is essentially the same as that of the solution to the differential equation.

Tal-Ezer, H.↗
NASA NTRS1973

Ferrite logic reliability study

Development and use of digital circuits called all-magnetic logic are reported. In these circuits the magnetic elements and their windings comprise the active circuit devices in the logic portion of a system. The ferrite logic device belongs to the all-magnetic class of logic circuits. The FLO device is novel in that it makes use of a dual or bimaterial ferrite composition in one physical ceramic body. This bimaterial feature, coupled with its potential for relatively high speed operation, makes it attractive for high reliability applications. (Maximum speed of operation approximately 50 kHz.)

Baer, J. A.↗
NASA NTRS1973

Sputter erosion and deposition in the discharge chamber of a small mercury ion thruster

A 5 cm diameter mercury ion thruster similar to one tested for 9715 hours was operated approximately 400 hrs each at discharge voltages of 36.6, 39.6, and 42.6 V, with corresponding discharge propellant utilizations of 58, 68, and 70 percent. The observed sputter erosion rates of the internal thruster parts and the anode weight gain rate all rose rapidly with discharge voltage and were roughly in the ratio of 1:3:5 for the three voltages. The combined weight loss of the internal thruster parts nearly balanced the anode weight gain. Hg(+2) ion apparently caused most of the observed erosion.

Power, J. L.↗
NASA NTRS1973

Sputter erosion and deposition in the discharge chamber of a small mercury ion thruster

A 5-cm diameter mercury ion thruster similar to one tested for 9715 hours was operated approximately 400 hrs each at discharge voltages of 36.6, 39.6, and 42.6 V, with corresponding discharge propellant utilizations of 58, 68, and 70 percent. The observed sputter erosion rates of the internal thruster parts and the anode weight gain rate all rose rapidly with discharge voltage and were roughly in the ratio of 1:3:5 for the three voltages. The combined weight loss of the internal thruster parts nearly balanced the anode weight gain. Hg+2 ions apparently caused most of the observed erosion.

Power, J. L.↗
NASA NTRS1976

Investigation of applications for high-power, self-critical fissioning uranium plasma reactors

Analytical studies were conducted to investigate potentially attractive applications for gaseous nuclear cavity reactors fueled by uranium hexafluoride and its decomposition products at temperatures of 2000 to 6000 K and total pressures of a few hundred atmospheres. Approximate operating conditions and performance levels for a class of nuclear reactors in which fission energy removal is accomplished principally by radiant heat transfer from the high temperature gaseous nuclear fuel to surrounding absorbing media were determined. The results show the radiant energy deposited in the absorbing media may be efficiently utilized in energy conversion system applications which include (1) a primary energy source for high thrust, high specific impulse space propulsion, (2) an energy source for highly efficient generation of electricity, and (3) a source of high intensity photon flux for heating working fluid gases for hydrogen production or MHD power extraction.

Rodgers, R. J.↗