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NASA NTRS1975

Theoretical investigations of plasma processes in the ion bombardment thruster

A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.

Wilhelm, H. E.↗

NASA NTRS1982

Docking of a spacecraft with an unrestrained orbiting structure

A methodology is presented for simulating a docking process involving a rigid body and an unrestrained nonuniform beam in orbit, and the issues that must be faced in the course of producing any such simulation are discussed. An algorithm is produced for the simulation of motions of the unrestrained structure, which necessitates the use of a structural analysis program for the purpose of constructing modal functions. An impulse problem then is solved in order to discover the changes that take place in certain variables in the course of the docking. This information is utilized to determine the initial values of variables used to characterize postdocking motions of the system under consideration, and an algorithm for simulating these motions is created, in which a structural analysis program is again used to produce modal functions. Finally, an extension of the methodology to the simulation of the docking of a rigid body with more complex orbiting structures is discussed.

Levinson, D. A.↗

NASA NTRS2004

The Mars Exploration Rover Project

The twin rovers of the Mars Exploration Rover Project successfully landed on the surface of Mars in January 2004, and initiated a highly successful science and exploration campaign. This marked the culmination of an unprecedented four-year effort to design, build, launch, and operate two of the most complex planetary spacecraft ever built. The project was started in the aftermath of the 1999 Mars mission failures, and was commissioned to take advantage of the highly advantageous 2003 opportunity. The development schedule from project start to launch was only 35 months, so schedule management was the most significant challenge facing the project. This problem was compounded when early assumptions about the extent of design heritage from Mars Pathfinder proved to be flawed. The project derived a number of useful lessons learned in solving these challenges that can be applied to future missions.

Mars↗

NASA NTRS1990

Unsteady transonic Navier-Stokes computations for an oscillating wing using single and multiple zones

Modern jet transports and maneuvering tactical fighters operating in the transonic regime often give rise to time-dependent fluid physics that interact with flexible structural components, e.g., vortical flow, shocks, and separation. Efficient computational fluid dynamic (CFD) methods are required to study such computationally intensive problems. In this work a numerical method is presented to address this problem. Time-dependent, compressible, Navier-Stokes equations are used to simulate unsteady transonic flow about a three-dimensional rigid wing undergoing a forced periodic motion in angle of attack. An efficient, implicit, diagonal algorithm is utilized because of its low operation count per time step compared to other methods that solve systems of block matrix equations. The formal time accuracy is addressed theoretically and demonstrated numerically by comparison of computational results with experimental data. A zonal grid approach, capable of treating complex geometries, is presented and its time accuracy is demonstrated by comparing a zonal computation with a single grid computation and experimental data.

Chaderjian, Neal M.↗

NASA NTRS1992

Lidar Investigation of Aerosol Pollution Distribution near a Coal Power Plant

Using aerosol lidars with high spatial and temporal resolution with the possibility of real-time data interpretation can solve a large number of ecological problems related to the aerosol-field distribution and variation and the structure of convective flows. Significantly less expensive specialized lidars are used in studying anthropogenic aerosols in the planetary boundary layer. Here, we present results of lidar measurements of the mass-concentration field around a coal-fired power plant with intensive local aerosol sources. We studied the pollution evolution as a function of the emission dynamics and the presence of retaining layers. The technique used incorporates complex analysis of three types of lidar mapping: horizontal map of the aerosol field, vertical cross-section map, and a series of profiles along a selected path. The lidar-sounding cycle was performed for the time of atmosphere's quasi-stationarity.

Mitsev, TS.↗

NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗

NASA NTRS2003

A Graph Based Backtracking Algorithm for Solving General CSPs

Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.

Pang, Wanlin↗

NASA NTRS1990

Operator function modeling: Cognitive task analysis, modeling and intelligent aiding in supervisory control systems

The design, implementation, and empirical evaluation of task-analytic models and intelligent aids for operators in the control of complex dynamic systems, specifically aerospace systems, are studied. Three related activities are included: (1) the models of operator decision making in complex and predominantly automated space systems were used and developed; (2) the Operator Function Model (OFM) was used to represent operator activities; and (3) Operator Function Model Expert System (OFMspert), a stand-alone knowledge-based system was developed, that interacts with a human operator in a manner similar to a human assistant in the control of aerospace systems. OFMspert is an architecture for an operator's assistant that uses the OFM as its system and operator knowledge base and a blackboard paradigm of problem solving to dynamically generate expectations about upcoming operator activities and interpreting actual operator actions. An experiment validated the OFMspert's intent inferencing capability and showed that it inferred the intentions of operators in ways comparable to both a human expert and operators themselves. OFMspert was also augmented with control capabilities. An interface allowed the operator to interact with OFMspert, delegating as much or as little control responsibility as the operator chose. With its design based on the OFM, OFMspert's control capabilities were available at multiple levels of abstraction and allowed the operator a great deal of discretion over the amount and level of delegated control. An experiment showed that overall system performance was comparable for teams consisting of two human operators versus a human operator and OFMspert team.

Mitchell, Christine M.↗

NASA NTRS2011

Multi-Axis Identifiability Using Single-Surface Parameter Estimation Maneuvers on the X-48B Blended Wing Body

The problem of parameter estimation on hybrid-wing-body type aircraft is complicated by the fact that many design candidates for such aircraft involve a large number of aero- dynamic control effectors that act in coplanar motion. This fact adds to the complexity already present in the parameter estimation problem for any aircraft with a closed-loop control system. Decorrelation of system inputs must be performed in order to ascertain individual surface derivatives with any sort of mathematical confidence. Non-standard control surface configurations, such as clamshell surfaces and drag-rudder modes, further complicate the modeling task. In this paper, asymmetric, single-surface maneuvers are used to excite multiple axes of aircraft motion simultaneously. Time history reconstructions of the moment coefficients computed by the solved regression models are then compared to each other in order to assess relative model accuracy. The reduced flight-test time required for inner surface parameter estimation using multi-axis methods was found to come at the cost of slightly reduced accuracy and statistical confidence for linear regression methods. Since the multi-axis maneuvers captured parameter estimates similar to both longitudinal and lateral-directional maneuvers combined, the number of test points required for the inner, aileron-like surfaces could in theory have been reduced by 50%. While trends were similar, however, individual parameters as estimated by a multi-axis model were typically different by an average absolute difference of roughly 15-20%, with decreased statistical significance, than those estimated by a single-axis model. The multi-axis model exhibited an increase in overall fit error of roughly 1-5% for the linear regression estimates with respect to the single-axis model, when applied to flight data designed for each, respectively.

Ratnayake, Nalin A.↗

NASA NTRS1991

Parallel algorithms for boundary value problems

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are twofold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Lin, Avi↗

NASA NTRS1991

Unified formulation of dynamics for serial rigid multibody systems

There has been a growing interest in the development of new and efficient algorithms for multibody dynamics in recent years. Serial rigid multibody systems form the basic subcomponents of general multibody systems, and a variety of algorithms to solve the serial chain forward dynamics problem have been proposed. In this paper, the economy of representation and analysis tools provided by the spatial operator algebra are used to clarify the inherent structure of these algorithms, to identify those that are similar, and to study the relationships among the ones that are distinct. For the purposes of this study, the algorithms are categorized into three classes: algorithms that require the explicit computation of the mass matrix, algorithms that are completely recursive in nature, and algorithms of intermediate complexity. In addition, alternative factorizations for the mass matrix and closed form expressions for its inverse are derived. These results provide a unifying perspective, within which these diverse dynamics algorithms arise naturally as a consequence of a progressive exploitation of the structure of the mass matrix.

Jain, Abhinandan↗

NASA NTRS1990

Parallel algorithms for boundary value problems

A general approach to solve boundary value problems numerically in a parallel environment is discussed. The basic algorithm consists of two steps: the local step where all the P available processors work in parallel, and the global step where one processor solves a tridiagonal linear system of the order P. The main advantages of this approach are two fold. First, this suggested approach is very flexible, especially in the local step and thus the algorithm can be used with any number of processors and with any of the SIMD or MIMD machines. Secondly, the communication complexity is very small and thus can be used as easily with shared memory machines. Several examples for using this strategy are discussed.

Lin, Avi↗

NASA NTRS1997

The Effects of Sooting and Radiation on Droplet Combustion

The burning of liquid hydrocarbon fuels accounts for a significant portion of global energy production. With predicted future increases in demand and limited reserves of hydrocarbon fuel, it is important to maximize the efficiency of all processes that involve conversion of fuel. With the exception of unwanted fires, most applications involve introduction of liquid fuels into an oxidizing environment in the form of sprays which are comprised of groups of individual droplets. Therefore, tremendous benefits can result from a better understanding of spray combustion processes. Yet, theoretical developments and experimental measurements of spray combustion remains a daunting task due to the complex coupling of a turbulent, two-phase flow with phase change and chemical reactions. However, it is recognized that individual droplet behavior (including ignition, evaporation and combustion) is a necessary component for laying the foundation for a better understanding of spray processes. Droplet combustion is also an ideal problem for gaining a better understanding of non-premixed flames. Under the idealized situation producing spherically-symmetric flames (produced under conditions of reduced natural and forced convection), it represents the simplest geometry in which to formulate and solve the governing equations of mass, species and heat transfer for a chemically reacting two phase flow with phase change. The importance of this topic has promoted extensive theoretical investigations for more than 40 years.

Lee, Kyeong-Ook↗

NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson s Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗

NASA NTRS2003

Transport Equation Based Wall Distance Computations Aimed at Flows With Time-Dependent Geometry

Eikonal, Hamilton-Jacobi and Poisson equations can be used for economical nearest wall distance computation and modification. Economical computations may be especially useful for aeroelastic and adaptive grid problems for which the grid deforms, and the nearest wall distance needs to be repeatedly computed. Modifications are directed at remedying turbulence model defects. For complex grid structures, implementation of the Eikonal and Hamilton-Jacobi approaches is not straightforward. This prohibits their use in industrial CFD solvers. However, both the Eikonal and Hamilton-Jacobi equations can be written in advection and advection-diffusion forms, respectively. These, like the Poisson's Laplacian, are commonly occurring industrial CFD solver elements. Use of the NASA CFL3D code to solve the Eikonal and Hamilton-Jacobi equations in advective-based forms is explored. The advection-based distance equations are found to have robust convergence. Geometries studied include single and two element airfoils, wing body and double delta configurations along with a complex electronics system. It is shown that for Eikonal accuracy, upwind metric differences are required. The Poisson approach is found effective and, since it does not require offset metric evaluations, easiest to implement. The sensitivity of flow solutions to wall distance assumptions is explored. Generally, results are not greatly affected by wall distance traits.

Tucker, Paul G.↗

NASA NTRS2007

Decision-Tree Formulation With Order-1 Lateral Execution

A compact symbolic formulation enables mapping of an arbitrarily complex decision tree of a certain type into a highly computationally efficient multidimensional software object. The type of decision trees to which this formulation applies is that known in the art as the Boolean class of balanced decision trees. Parallel lateral slices of an object created by means of this formulation can be executed in constant time considerably less time than would otherwise be required. Decision trees of various forms are incorporated into almost all large software systems. A decision tree is a way of hierarchically solving a problem, proceeding through a set of true/false responses to a conclusion. By definition, a decision tree has a tree-like structure, wherein each internal node denotes a test on an attribute, each branch from an internal node represents an outcome of a test, and leaf nodes represent classes or class distributions that, in turn represent possible conclusions. The drawback of decision trees is that execution of them can be computationally expensive (and, hence, time-consuming) because each non-leaf node must be examined to determine whether to progress deeper into a tree structure or to examine an alternative. The present formulation was conceived as an efficient means of representing a decision tree and executing it in as little time as possible. The formulation involves the use of a set of symbolic algorithms to transform a decision tree into a multi-dimensional object, the rank of which equals the number of lateral non-leaf nodes. The tree can then be executed in constant time by means of an order-one table lookup. The sequence of operations performed by the algorithms is summarized as follows: 1. Determination of whether the tree under consideration can be encoded by means of this formulation. 2. Extraction of decision variables. 3. Symbolic optimization of the decision tree to minimize its form. 4. Expansion and transformation of all nested conjunctive-disjunctive paths to a flattened conjunctive form composed only of equality checks when possible. If each reduced conjunctive form contains only equality checks and all of these forms use the same variables, then the decision tree can be reduced to an order-one operation through a table lookup. The speedup to order one is accomplished by distributing each decision variable over a surface of a multidimensional object by mapping the equality constant to an index

James, Mark↗

NASA NTRS2013

Numerical Modeling of Ablation Heat Transfer

A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured solutions. These verifications are used to demonstrate solution accuracy and proper error convergence rates. A simple demonstration of a mechanical erosion (spallation) model is also provided to illustrate the unique capabilities of the method.

Ewing, Mark E.↗

NASA NTRS1990

CFD spinoff - Computational electromagnetics for radar cross section (RCS) studies

A finite-volume discretization procedure derived from proven CFD methods is used to solve the conservation form of the time-domain Maxwell's equations, in order to compute EM scattering from layered objects. This time-domain approach handles both single-frequency/continuous wave and broadband-frequency/pulse incident excitation. Arbitrarily shaped objects are modeled by means of a body-fitted coordinate transformation; complex internal/external structures with many material layers are treated through the implementation of a multizone framework capable of handling any type of zonal boundary condition. Results are presented for various two- and three-dimensional problems.

Shankar, Vijaya↗