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NASA NTRS1996

The Kirchhoff Formulas for Moving Surfaces in Aeroacoustics - The Subsonic and Supersonic Cases

One of the active areas of computational aeroacoustics is the application of the Kirchhoff formulas to the problems of the rotating machinery noise predictions. The original Kirchhoff formula was derived for a stationary surface. In 1988, Farassat and Myers derived a Kirchhoff Formula obtained originally by Morgans using modem mathematics. These authors gave a formula particularly useful for applications in aeroacoustics. This formula is for a surface moving at subsonic speed. Later in 1995 these authors derived the Kirchhoff formula for a super-sonically moving surface. This technical memorandum presents the viewgraphs of a day long workshop by the author on the derivation of the Kirchhoff formulas. All necessary background mathematics such as differential geometry and multidimensional generalized function theory are discussed in these viewgraphs. Abstraction is kept at minimum level here. These viewgraphs are also suitable for understanding the derivation and obtaining the solutions of the Ffowcs Williams-Hawkings equation. In the first part of this memorandum, some introductory remarks are made on generalized functions, the derivation of the Kirchhoff formulas and the development and validation of Kirchhoff codes. Separate lists of references by Lyrintzis, Long, Strawn and their co-workers are given in this memorandum. This publication is aimed at graduate students, physicists and engineers who are in need of the understanding and applications of the Kirchhoff formulas in acoustics and electromagnetics.

Farassat, F.↗
NASA NTRS1994

Postinstability Models in Dynamics

This paper is devoted to the concept of instability in dynamical systems with the main emphasis on orbital, Hadamard, and Reynolds instabilities. It demonstrates that the requirement about differentiability in dynamics in some cases is not consistent with the physical nature of motions, and may lead to unrealistic solutions. Special attention is paid to the fact that instability is not an invariant of motion: it depends upon frames of reference, the metric of configuration space, and classes of functions selected for mathematical models of physical phenomena. This leads to the possibility of elimination of certain types of instabilities (in particular, those which lead to chaos and turbulence) by enlarging the class of functions using the Reynolds-type transformation in combination with the stabilization principle: the additional terms (the so-called Reynolds stresses) are found from the conditions that they suppress the original instability. Based upon these ideas, a new approach to chaos and turbulence as well as a new mathematical formalism for nonlinear dynamics are discussed.

Zak, Michail↗
NASA NTRS1994

Computational Control of Flexible Aerospace Systems

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Sharpe, Lonnie, Jr.↗
NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗
NASA NTRS1997

Modified Fully Utilized Design (MFUD) Method for Stress and Displacement Constraints

The traditional fully stressed method performs satisfactorily for stress-limited structural design. When this method is extended to include displacement limitations in addition to stress constraints, it is known as the fully utilized design (FUD). Typically, the FUD produces an overdesign, which is the primary limitation of this otherwise elegant method. We have modified FUD in an attempt to alleviate the limitation. This new method, called the modified fully utilized design (MFUD) method, has been tested successfully on a number of designs that were subjected to multiple loads and had both stress and displacement constraints. The solutions obtained with MFUD compare favorably with the optimum results that can be generated by using nonlinear mathematical programming techniques. The MFUD method appears to have alleviated the overdesign condition and offers the simplicity of a direct, fully stressed type of design method that is distinctly different from optimization and optimality criteria formulations. The MFUD method is being developed for practicing engineers who favor traditional design methods rather than methods based on advanced calculus and nonlinear mathematical programming techniques. The Integrated Force Method (IFM) was found to be the appropriate analysis tool in the development of the MFUD method. In this paper, the MFUD method and its optimality are presented along with a number of illustrative examples.

Patnaik, Surya↗
NASA NTRS1997

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft.

Lewis, Kemper↗
NASA NTRS1997

Numerical Modeling of HgCdTe Solidification: Effects of Phase Diagram, Double-Diffusion Convection and Microgravity Level

Melt convection, along with species diffusion and segregation on the solidification interface are the primary factors responsible for species redistribution during HgCdTe crystal growth from the melt. As no direct information about convection velocity is available, numerical modeling is a logical approach to estimate convection. Furthermore influence of microgravity level, double-diffusion and material properties should be taken into account. In the present study, HgCdTe is considered as a binary alloy with melting temperature available from a phase diagram. The numerical model of convection and solidification of binary alloy is based on the general equations of heat and mass transfer in two-dimensional region. Mathematical modeling of binary alloy solidification is still a challenging numericial problem. A Rigorous mathematical approach to this problem is available only when convection is not considered at all. The proposed numerical model was developed using the finite element code FIDAP. In the present study, the numerical model is used to consider thermal, solutal convection and a double diffusion source of mass transport.

Bune, Andris V.↗
NASA NTRS1997

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Silva, Walter A.↗
NASA NTRS1997

A Model for Space Shuttle Orbiter Tire Side Forces Based on NASA Landing Systems Research Aircraft Test Results

Forces generated by the Space Shuttle orbiter tire under varying vertical load, slip angle, speed, and surface conditions were measured using the Landing System Research Aircraft (LSRA). Resulting data were used to calculate a mathematical model for predicting tire forces in orbiter simulations. Tire side and drag forces experienced by an orbiter tire are cataloged as a function of vertical load and slip angle. The mathematical model is compared to existing tire force models for the Space Shuttle orbiter. This report describes the LSRA and a typical test sequence. Testing methods, data reduction, and error analysis are presented. The LSRA testing was conducted on concrete and lakebed runways at the Edwards Air Force Flight Test Center and on concrete runways at the Kennedy Space Center (KSC). Wet runway tire force tests were performed on test strips made at the KSC using different surfacing techniques. Data were corrected for ply steer forces and conicity.

Carter, John F.↗
NASA NTRS1998

Manuel Stein's Five Decades of Structural Mechanics Contributions (1944-1988)

Manuel Stein went to work for NACA (National Advisory Committee for Aeronautics) in 1944 and left in 1988. His research contributions spanned five decades of extremely defining times for the aerospace industry. Problems arising from the analysis and design of efficient thin plate and shell aerospace structures have stimulated research over the past half century. The primary structural technology drivers during Dr. Stein's career included 1940's aluminum aircraft, 1950's jet aircraft, 1960's launch vehicles and advanced spacecraft, 1970's reusable launch vehicles and commercial aircraft, and 1980's composite aircraft. Dr. Stein's research was driven by these areas and he made lasting contributions for each. Dr. Stein's research can be characterized by a judicious mixture of physical insight into the problem, understanding of the basic mechanisms, mathematical modeling of the observed phenomena, and extraordinary analytical and numerical solution methodologies of the resulting mathematical models. This paper summarizes Dr. Stein's life and his contributions to the technical community.

Mikulas, Martin M.↗
NASA NTRS1997

Trenholm State (AL) Technical College High School Science Enrichment Program 1996-1997 Evaluation Report

This document presents findings based on a third-year evaluation of Trenholm State (AL) Technical College's National Aeronautics and Space Administration (NASA) - supported High School Science Enrichment Program (HSSEP). HSSEP is an external (to school) program for area students from groups that are underrepresented in the mathematics, science, engineering and technology (MSET) professions. In addition to gaining insight into scientific careers, HSSEP participants learn about and deliver presentations that focus on mathematics applications, scientific problem-solving and computer programming during a seven-week summer or 10-week Academic-Year Saturday session.

Ross, Elizabeth G.↗
NASA NTRS1998

Space Suit Survivability Enhancement NASA Research Announcement 96-OLMSA-01B: Advanced Life Support and Environmental Technologies for Human Exploration and Development of Space

Conducted two meetings to review the project scope and develop concepts for self-sealing material compositions, Focus has been on developing concepts that would seal a penetration enough to allow the astronauts to re-enter the spacecraft within the window provided by the emergency air supply. Concepts discussed include: quilted fabrics containing a viscous flow material in the quilted cells which would seal the bladder breach when forced to flow by the internal suit pressure; a sealant impregnated felt liner which acts similar to above; and a "blousy" fibrous layer which would mechanically plug a rupture under pressure. Illustrations of the above concepts are included in the attached viewgraphs, which were used in a presentation. The most promising of these concepts will be made into prototypes for testing. ILC has developed a test fixture to test the scaling characteristics of various material layups by measuring real-time changes in pressure and make-up flow in a pressurized cylinder. Candidate viscous sealing compounds such as silicones and urethanes have been identified. These compounds will be coated on existing bladder cloth for initial tests. The most promising compounds will be integrated into the above material structures for final testing. Design and analysis of fabric weaves to improve cut and puncture resistance of the suit TMG layers is underway. Philadelphia Textile is developing a mathematical model to correlate yarn type and weave structure to cut and tear resistance. The computer mathematical modeling of the fabric failure mechanisms by Cornell University, as originally proposed, will be replaced with the above model and empirical testing methods, due to the loss of key Cornell personnel.

Source record↗
NASA NTRS1993

On the Shape of Liquid Metal Droplets in Electromagnetic Levitation Experiments

We present calculations and measurements on the shape of liquid metal droplets in electromagnetic levitation experiments. A normal stress balance model was developed to predict the shapes of liquid metal droplets that will be obtained in a microgravity experiment to measure the viscosity and surface tension of undercooled metals. This model was tested by calculating the droplet shapes in containerless experiments conducted to determine the surface tension of liquid metals. Inconsistencies associated with the results of a previous paper are elucidated. The computational results of the mathematical model are compared with the results of ground-based experiments for two different metals. The importance of the ratio of electromagnetic skin depth-to-droplet radius to the accuracy of the mathematical model is discussed. A planned alternate approach to modeling the shape by consideration of the entire droplet rather than only the surface is presented. As an example of an application. the influence of the shape on the splitting of the surface oscillation modes of levitated liquid metal droplets is discussed.

Schwartz, E.↗
NASA NTRS1998

A Formal Model of Partitioning for Integrated Modular Avionics

The aviation industry is gradually moving toward the use of integrated modular avionics (IMA) for civilian transport aircraft. An important concern for IMA is ensuring that applications are safely partitioned so they cannot interfere with one another. We have investigated the problem of ensuring safe partitioning and logical non-interference among separate applications running on a shared Avionics Computer Resource (ACR). This research was performed in the context of ongoing standardization efforts, in particular, the work of RTCA committee SC-182, and the recently completed ARINC 653 application executive (APEX) interface standard. We have developed a formal model of partitioning suitable for evaluating the design of an ACR. The model draws from the mathematical modeling techniques developed by the computer security community. This report presents a formulation of partitioning requirements expressed first using conventional mathematical notation, then formalized using the language of SRI'S Prototype Verification System (PVS). The approach is demonstrated on three candidate designs, each an abstraction of features found in real systems.

DiVito, Ben L.↗
NASA NTRS1997

Effects of Humidity Swings on Adsorption Columns for Air Revitalization: Modeling and Experiments

The goal of this research was to develop a dynamic model which can predict the effect of humidity swings on activated carbon adsorption beds used to remove trace contaminants from the atmosphere in spacecraft. Specifically, the model was to be incorporated into a computer simulation to predict contaminant concentrations exiting the bed as a function of time after a humidity swing occurs. Predicted breakthrough curves were to be compared to experimentally measured results. In all respects the research was successful. The two major aspects of this research were the mathematical model and the experiments. Experiments were conducted by Mr. Appel using a fixed-bed apparatus at NASA-Ames Research Center during the summers of 1994 and 1995 and during the first 8 months of 1996. Mr. Appel conducted most of his mathematical modeling work at the University of Virginia. The simulation code was used to predict breakthrough curves using adsorption equilibrium correlations developed previously by M. D. LeVan's research group at the University of Virginia. These predictions were compared with the experimental measurements, and this led to improvements in both the simulation code and the apparatus.

LeVan, M. Douglas↗
NASA NTRS1998

Generic Equations for Constructing Smooth Paths Along Circles and Tangent Lines With Application to Airport Ground Paths

The primary purpose of this publication is to develop a mathematical model to describe smooth paths along any combination of circles and tangent lines. Two consecutive circles in a path are either tangent (externally or internally) or they appear on the same (lateral) or opposite (transverse) sides of a connecting tangent line. A path may start or end on either a segment or circle. The approach is to use mathematics common to robotics to design the path as a multilink manipulator. This approach allows a hierarchical view of the problem and keeps the notation manageable. A user simply specifies a few parameters to configure a path. Necessary and sufficient conditions automatically ensure the consistency of the inputs for a smooth path. Two example runway exit paths are given, and an angle to go assists in knowing when to switch from one path element to the next.

Barker, L. Keith↗
NASA NTRS1999

Towards a Rational Model for the Triple Velocity Correlations of Turbulence

This paper presents a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of Group Representation Theory to determine the most general tensorial form of these correlations in terms of all the second- and third-order tensor quantities that appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and therefore had to be developed specifically for this purpose by Professor G. F. Smith. The outcome of this work is a mathematical framework for the construction of algebraic, explicit, and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be an incomplete subset of this new representation, even to lowest order.

Younis, B. A.↗
NASA NTRS1998

MAPS of Cancer

Our goal was to produce an interactive visualization from a mathematical model that successfully predicts metastases from head and neck cancer. We met this goal early in the project. The visualization is available for the public to view. Our work appears to fill a need for more information about this deadly disease. The idea of this project was to make an easily interpretable visualization based on what we call "functional maps" of disease. A functional map is a graphic summary of medical data, where distances between parts of the body are determined by the probability of disease, not by anatomical distances. Functional maps often beat little resemblance to anatomical maps, but they can be used to predict the spread of disease. The idea of modeling the spread of disease in an abstract multidimensional space is difficult for many people. Our goal was to make the important predictions easy to see. NASA must face this problem frequently: how to help laypersons and professionals see important trends in abstract, complex data. We took advantage of concepts perfected in NASA's graphics libraries. As an analogy, consider a functional map of early America. Suppose we choose travel times, rather than miles, as our measures of inter-city distances. For Abraham Lincoln, travel times would have been the more meaningful measure of separation between cities. In such a map New Orleans would be close to Memphis because of the Mississippi River. St. Louis would be close to Portland because of the Oregon Trail. Oklahoma City would be far from Little Rock because of the Cheyenne. Such a map would look puzzling to those of us who have always seen physical maps, but the functional map would be more useful in predicting the probabilities of inter-site transit. Continuing the analogy, we could predict the spread of social diseases such as gambling along the rivers and cattle rustling along the trails. We could simply print the functional map of America, but it would be more interesting to show meaningful patterns of dispersal. We had previously published the functional map of the head and neck, but it was difficult to explain to either patients or surgeons because that view of our body did not resemble anatomy. This discrepancy between functional and physical maps is just a mathematical restatement of the well-known fact that some diseases, such as head and neck cancer, spread in complex patterns, not always to the next nearest site. We had discovered that a computer could re-arrange anatomy so that this particular disease spreads to the next nearest site. The functional map explains over 95% of the metastases in 1400 patients. In a sense, we had graphed what our body "looks like" to a tumor. The tumor readily travels between adjacent areas in the functional map. The functional map is a succinct visual display of trends that are not easily appreciated in tables of probabilities.

Gray, Lincoln↗