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NASA NTRS1986

Advances in numerical and applied mathematics

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

South, J. C., Jr.↗

NASA NTRS1995

Comparison of spatial numerical operators for duct-nozzle acoustics

A production Navier-Stokes/Euler CFD code, NASTD, developed for aircraft flowfield analysis has been modified to analyze acoustic fields associated with propulsion exhaust systems. The modified code has been applied to the Category 5 nozzle problem using six different spatial discretization schemes combined with a third-order, compact storage Runge-Kutta time integration. NASTD was found capable of tracking pressure disturbances normalized by the freestream value of order 10(exp -6), even with lower-order schemes, for the benchmark problem.

Cain, A. B.↗

NASA NTRS1993

Noniterative implicit method for tracking particles in mixed Lagrangian-Eulerian formulations

The existing implicit methods for the current initial value problems (IVPs) concerning particle-laden flows are complicated and iterative in nature. This paper presents a noniterative implicit method which can be used with pressure-based as well as with density-based algorithms. The method is illustrated by analyzing a dilute dispersion of noninteracting solid particles in an isothermal flow in a passage bounded by one straight wall and one wavy wall, in which all particles are spherical and have a finite velociy relative to the continuum phase at the inflow boundary.

Shih, T. I.-P.↗

NASA NTRS1999

Tracking the Relative Motion of Four Space Payloads Launched from a Sub-Orbital NASA Rocket

One problem, which is comparatively new in the field of GPS (Global Positioning System) applications, is the determination of the relative trajectories of space vehicles. Applications include the docking of spacecraft, collision avoidance in the area of space stations, and trajectory reconstruction of multiple payloads. The required precision in any of these applications will vary, according to the requirements of the task and abilities of GPS to cope with the environment and the dynamics. This paper describes the post-mission reconstruction of the relative trajectories of four GPS receivers attached to four payloads jettisoned from a Black Brant XII rocket. This vehicle was launched by the National Aeronautics and Space Administration (NASA) in January 1999 from the Poker Flats Research Range near Fairbanks, Alaska. The Black Brant XII is a sub-orbital rocket designed to carry payloads of 100 to 500 kg into the upper atmosphere. Flight time is generally in the order of 10 - 20 minutes.

Bull, Barton↗

NASA NTRS1999

Tracking the Relative Motion of Four Space Payloads Launched from a Sub-Orbital NASA Rocket

One problem, which is comparatively new in the field of GPS applications, is the determination of the relative trajectories of space vehicles. Applications include the docking of spacecraft, collision avoidance in the area of space stations, and trajectory reconstruction of multiple payloads. The required precision in any of these applications will vary, according to the requirements of the task and abilities of GPS to cope with the environment and the dynamics. This paper describes the post-mission reconstruction of the relative trajectories of four GPS receivers attached to four payloads jettisoned from a Black Brant XII rocket. This vehicle was launched by the National Aeronautics and Space Administration (NASA) in January 1999 from the Poker Flats Research Range near Fairbanks, Alaska. The Black Brant XII is a sub-orbital rocket designed to carry payloads of 100 to 500 kg into the upper atmosphere. Flight time is generally in the order of 10-20 minutes. In this experiment, a GPS receiver and antenna was attached to each of the four payloads. One of the GPS receivers was assigned as the "base station", while the other 3 receivers were designated as remotes. GPS time, code and phase measurements were telemetered to a ground station for real-time processing and storage. The object of the mission was to re-compute the position and velocity of the remote units with respect to the base station during the launch phase and after the payloads separated. During the launch segment the 3 baseling distances between the 4 antennas are known from plans and are constant values until each payload is released. On the fly ambiguity determination was used to establish local coordinates from the base antenna to each of the other 3 GPS units during flight. Distance computations were made from the GPS-derived coordinates and compared to plan distances. Using this methodology an error analysis of the relative GPS accuracies has been presented and in addition a description given of the respective payload behaviour following separation from the vehicle.

Martell, Hugh↗

NASA NTRS1999

Tracking the Relative Motion of Four Space Payloads Launched From a Sub-Orbital NASA Rocket

Martel, Hugh↗

NASA NTRS1996

Computations of Drop Collision and Coalescence

Computations of drops collisions, coalescence, and other problems involving drops are presented. The computations are made possible by a finite difference/front tracking technique that allows direct solutions of the Navier-Stokes equations for a multi-fluid system with complex, unsteady internal boundaries. This method has been used to examine the various collision modes for binary collisions of drops of equal size, mixing of two drops of unequal size, behavior of a suspension of drops in linear and parabolic shear flows, and the thermal migration of several drops. The key results from these simulations are reviewed. Extensions of the method to phase change problems and preliminary results for boiling are also shown.

Tryggvason, Gretar↗

NASA NTRS1974

A design method for minimizing sensitivity to plant parameter variations

A method is described for minimizing the sensitivity of multivariable systems to parameter variations. The variable parameters are considered as random variables and their effect is included in a quadratic performance index. The performance index is a weighted sum of the state and control covariances that stem from both the random system disturbances and the parameter uncertainties. The numerical solution of the problem is described and application of the method to several initially sensitive tracking systems is discussed. The sensitivity factor of reduction was typically 2 or 3 over a system based on random system noise only, and yet resulted in state RMS increases of only about a factor of two.

Hadass, Z.↗

NASA NTRS1980

Geometric representation methods for multi-type self-defining remote sensing data sets

Efficient and convenient representation of remote sensing data is highly important for an effective utilization. The task of merging different data types is currently dealt with by treating each case as an individual problem. A description is provided of work which is carried out to standardize the multidata merging process. The basic concept of the new approach is that of the self-defining data set (SDDS). The creation of a standard is proposed. This standard would be such that data which may be of interest in a large number of earth resources remote sensing applications would be in a format which allows convenient and automatic merging. Attention is given to details regarding the multidata merging problem, a geometric description of multitype data sets, image reconstruction from track-type data, a data set generation system, and an example multitype data set.

Anuta, P. E.↗

NASA NTRS1987

Solar object tracking for the Hubble Space Telescope

The Hubble Space Telescope (HST) is designed to carry five major scientific instruments to collect imagery, spectrographic, and photometric astronomical data. The Pointing Control System is to achieve pointing accuracies and line of sight jitter levels an order of magnitude less than can be achieved with ground mounted telescopes. In addition, the HST must be able to acquire and track solar system targets with apparent motion up to 0.21 arcsec/s. Such targets include planetary satellites, planetary surface features and comets. It is to perform this tracking with an accuracy under 0.03 arcsec at the maximum rate. Tracking of solar objects by the Space Telescope accounts for the effects of velocity aberration and parallax, as well as solar targeting a celestial object in a science instrument aperture. The design of the Pointing Control System solar object tracking features is discussed, with emphasis on the special timing and granulation problems inherent with a sampled-data, multirate digital control system.

Rodden, J. J.↗

NASA NTRS1990

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photovoltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic controls system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Bosela, Paul A.↗

NASA NTRS1991

Digital Accumulators In Phase- And Frequency-Tracking Loops

Report describes investigation of deleterious effects of digital accumulators upon performances of phase- and frequency-tracking electronic circuits used to compute averages and reduce processing rates. Emphasizes problems encountered with respect to digital accumulators in operation of receivers in Global Positioning System (GPS). Also applicable to more general receivers or other signal-processing systems that include digital accumulators.

Hinedi, Sami↗

NASA NTRS1990

Dynamic analysis of space-related linear and non-linear structures

In order to be cost effective, space structures must be extremely light weight, and subsequently, very flexible structures. The power system for Space Station Freedom is such a structure. Each array consists of a deployable truss mast and a split blanket of photo-voltaic solar collectors. The solar arrays are deployed in orbit, and the blanket is stretched into position as the mast is extended. Geometric stiffness due to the preload make this an interesting non-linear problem. The space station will be subjected to various dynamic loads, during shuttle docking, solar tracking, attitude adjustment, etc. Accurate prediction of the natural frequencies and mode shapes of the space station components, including the solar arrays, is critical for determining the structural adequacy of the components, and for designing a dynamic control system. The process used in developing and verifying the finite element dynamic model of the photo-voltaic arrays is documented. Various problems were identified, such as grounding effects due to geometric stiffness, large displacement effects, and pseudo-stiffness (grounding) due to lack of required rigid body modes. Analysis techniques, such as development of rigorous solutions using continuum mechanics, finite element solution sequence altering, equivalent systems using a curvature basis, Craig-Bampton superelement approach, and modal ordering schemes were utilized. The grounding problems associated with the geometric stiffness are emphasized.

Bosela, Paul A.↗

NASA NTRS1996

Inertial Head-Tracker Sensor Fusion by a Complementary Separate-Bias Kalman Filter

Current virtual environment and teleoperator applications are hampered by the need for an accurate, quick-responding head-tracking system with a large working volume. Gyroscopic orientation sensors can overcome problems with jitter, latency, interference, line-of-sight obscurations, and limited range, but suffer from slow drift. Gravimetric inclinometers can detect attitude without drifting, but are slow and sensitive to transverse accelerations. This paper describes the design of a Kalman filter to integrate the data from these two types of sensors in order to achieve the excellent dynamic response of an inertial system without drift, and without the acceleration sensitivity of inclinometers.

Foxlin, Eric↗

NASA NTRS1996

Inertial head-tracker sensor fusion by a complementary separate-bias Kalman filter

Current virtual environment and teleoperator applications are hampered by the need for an accurate, quick responding head-tracking system with a large working volume. Gyroscopic orientation sensors can overcome problems with jitter, latency, interference, line-of-sight obscurations, and limited range, but suffer from slow drift. Gravimetric inclinometers can detect attitude without drifting, but are slow and sensitive to transverse accelerations. This paper describes the design of a Kalman filter to integrate the data from these two types of sensors in order to achieve the excellent dynamic response of an inertial system without drift, and without the acceleration sensitivity of inclinometers.

Foxlin, Eric↗

NASA NTRS2011

Advection of Microphysical Scalars in Terminal Area Simulation System (TASS)

The Terminal Area Simulation System (TASS) is a large eddy scale atmospheric flow model with extensive turbulence and microphysics packages. It has been applied successfully in the past to a diverse set of problems ranging from prediction of severe convective events (Proctor et al. 2002), tracking storms and for simulating weapons effects such as the dispersion and fallout of fission debris (Bacon and Sarma 1991), etc. More recently, TASS has been used for predicting the transport and decay of wake vortices behind aircraft (Proctor 2009). An essential part of the TASS model is its comprehensive microphysics package, which relies on the accurate computation of microphysical scalar transport. This paper describes an evaluation of the Leonard scheme implemented in the TASS model for transporting microphysical scalars. The scheme is validated against benchmark cases with exact solutions and compared with two other schemes - a Monotone Upstream-centered Scheme for Conservation Laws (MUSCL)-type scheme after van Leer and LeVeque's high-resolution wave propagation method. Finally, a comparison between the schemes is made against an incident of severe tornadic super-cell convection near Del City, Oklahoma.

Ahmad, Nashat N.↗

NASA NTRS2020

Direct Exploration of the L2 Isolated Invariant Set Using Isolating Neighborhoods

Previous studies have used isolating blocks to explore the isolated invariant set around the L2 Lagrange point in the circular restricted three-body problem by computing trajectories on the asymptotic set and using them to track particular orbits. Once an initial map of the location of the orbits within the isolated invariant set projected into configuration space has been found, it is possible to further explore these orbits more directly by starting from appropriately chosen points within the mapped space. Here, we develop a method that uses these points to explore the periodic and quasiperiodic orbits within the isolated invariant set.

Lo, Martin W.↗

NASA NTRS2017

Orbital Space Solar Power Option for a Lunar Village

One of the most significant challenges to the implementation of a continuously manned lunar base is power. During the lunar day (14 Earth days), it is conceptually simple to deploy solar arrays to generate the estimated 35 kilowatts of continuous power required. However, generating this level of power during the lunar night (also 14 Earth days) has been an extremely difficult problem to solve. Conventional solutions range from the requirement that the base be located at the lunar south pole so as to take advantage of the continuous sunshine available there to developing a space-qualified nuclear reactor and power plant to generate the needed energy. There is a third option: Use the soon-to-be-available Space Launch System to place a space based solar power station in lunar orbit that would beam the needed energy to the lunar base. Several detailed studies have been performed by NASA, universities and others looking at the lunar south pole for locating the base. The results are encouraging: by taking advantage of the moon's orbital tilt, large solar arrays can be deployed there to track the sun continuously and generate the power needed to sustain the base. The problem with this approach is inherent to its design: it will only work at the lunar south pole. There is no other site on the Moon with geometry favorable to generating continuous solar power. NASA has also considered the development of a compact fission reactor and power plant to generate the needed power, allowing the base to be sited anywhere on the Moon. The problem with this approach is that there are no space fission reactors available, none are being planned and the cost of developing one is prohibitively expensive. Using an orbiting space based solar power station to generate electrical power and beam it to a base sited anywhere on the moon should therefore be considered. The technology to collect sunlight, generate greater than the estimated 35 kilowatts of power, and beam it to the surface using microwaves is available today. The problem with this concept in the past would have been the mass and packaging volume (for launch) required to put such a system in place in lunar orbit. This problem is potentially solved with the advent of the Space Launch System (SLS). The SLS, with its 70 mT launch capacity, it more than capable of placing such a system into lunar orbit in a single launch. This paper will examine the potential use of an SLS-launched, space solar power system in lunar orbit as the primary power source for a first-generation, continuously-occupied lunar base and compare it with the other power generation and storage options previously considered.

Johnson, Les↗