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At least 1,099 records · Page 61

Recent advances in methods for numerical solution of O.D.E. initial value problems

In the mathematical modeling of physical systems, it is often necessary to solve an initial value problem (IVP), consisting of a system of ordinary differential equations (ODE). A typical program produces approximate solutions at certain mesh points. Almost all existing codes try to control the local truncation error, while the user is really interested in controlling the true or global error. The present investigation provides a review of recent advances regarding the solution of the IVP, giving particular attention to stiff systems. Stiff phenomena are customarily defined in terms of the eigenvalues of the Jacobian. There are, however, some difficulties connected with this approach. It is pointed out that an estimate of the Lipschitz constant proves to be a very practical way to determine the stiffness of a problem.

Bui, T. D.↗

Variable-Conductance Heat Pipes

In response to need to accurately and efficiently predict performance of variable-conductance heat pipes (VCHP's) incorporated in spacecraft thermalcontrol systems, computer code VCHPDA developed to interact with thermal analyzer programs such as SINDA (Systems Improved Numerical Differencing Analyzer). Calculates length of gas-blocked region and vapor temperature in active portion. Advantages of VCHPDA over prior programs improved accuracy, unconditional stability, and increased efficiency of solution resulting from novel approach and use of state-of-the-art numerical techniques for solving VCHP mathematical model. Code valuable tool in design and evaluation of advanced thermal-control systems using variable-conductance heat pipes. Written in FORTRAN IV for use on CDC 600 computers.

Antoniuk, D.↗

Divergence thrust loss calculations for convergent-divergent nozzles: Extensions to the classical case

The analytical derivations of the non-axial thrust divergence losses for convergent-divergent nozzles are described as well as how these calculations are embodied in the Navy/NASA engine computer program. The convergent-divergent geometries considered are simple classic axisymmetric nozzles, two dimensional rectangular nozzles, and axisymmetric and two dimensional plug nozzles. A simple, traditional, inviscid mathematical approach is used to deduce the influence of the ineffectual non-axial thrust as a function of the nozzle exit divergence angle.

Berton, Jeffrey J.↗

Linearized aerodynamic and control law models of the X-29A airplane and comparison with flight data

Flight control system design and analysis for aircraft rely on mathematical models of the vehicle dynamics. In addition to a six degree of freedom nonlinear simulation, the X-29A flight controls group developed a set of programs that calculate linear perturbation models throughout the X-29A flight envelope. The models include the aerodynamics as well as flight control system dynamics and were used for stability, controllability, and handling qualities analysis. These linear models were compared to flight test results to help provide a safe flight envelope expansion. A description is given of the linear models at three flight conditions and two flight control system modes. The models are presented with a level of detail that would allow the reader to reproduce the linear results if desired. Comparison between the response of the linear model and flight measured responses are presented to demonstrate the strengths and weaknesses of the linear models' ability to predict flight dynamics.

Bosworth, John T.↗

ExMASS: A viable model for authentic student-scientist research partnerships

The Exploration of the Moon and Asteroids by Secondary Students (ExMASS) program provides students the opportunity to conduct authentic, student-led, open-inquiry research with assistance from their teacher and a scientist. One goal of the program is to enhance participants’ attitudes toward science. Most students enter the ExMASS program with positive attitudes toward science. However, the attitude survey developed for ExMASS measured small but statistically significant increases in attitudes. This paper discusses the ExMASS program, an attitude towards science survey designed for the program’s specific audience, and the results of statistical analyses of the survey. The validity of the attitudes survey was tested with an exploratory factor analysis (EFA). The results of the EFA revealed two salient factors measured by the survey: 1) Personal Importance of Science and 2) Importance of Science to Society. A reliability analysis revealed a Cronbach alpha value of 0.89. Paired t-tests revealed statistically significant differences in students’ attitudes before and after the program. For Factor 1, participants’ before scores were statistically significantly lower than their post scores, t(88) = 3.16, p<0.05. For Factor 2, participants’ before scores were statistically significantly lower than their post scores, t(88) = 4.47, p<0.05. ExMASS has been shown to be a practical model for programs designed to increase high school student attitudes toward science. More information on the ExMASS program is available at https://www.lpi.usra.edu/exploration/education/hsResearch/.

science↗

Simulation of Mariner Mars 1971 spacecraft

Preparation for the Mariner Mars 1971 mission is reported, including an extensive training program for operations personnel during which the primary source of spacecraft data was a computer program simulating the spacecraft. The objectives of a simulation model for training purposes differed from objectives appropriate to a design or analysis model. Model subsystems were designed to provide realistic telemetry data reflecting changes due both to commands and environmental parameters affecting the spacecraft at various times during the mission. The spacecraft is modeled along two separate functional lines. Boolean operations are concentrated in the spacecraft logic model, which determines the spacecraft state or mode, while mathematical operations or algorithms are executed in computational subsystem models. Although logic parameters are interrogated as a part of each computational pass, actual logic model processing occurs only when a change-of-state input is generated by the operations organization. The program design, some of the special characteristics of each of the modeled subsystems, and how the model was used in support of mission operations training are presented.

Ausman, N. E., Jr.↗

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.↗

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.↗

Kennedy Space Center Coronary Heart Disease Risk Screening Program

The number one cause of death in the U.S. is coronary heart disease (CHD). It is probably a major cause of death and disability in the lives of employees at Kennedy Space Center (KSC) as well. The KSC Biomedical Office used a multifactorial mathematical formula from the Framingham Heart Study to calculate CHD risk probabilities for individuals in a segment of the KSC population that required medical evaluation for job certification. Those assessed to be high-risk probabilities will be targeted for intervention. Every year, several thousand KSC employees require medical evaluations for job related certifications. Most medical information for these evaluations is gathered on-site at one of the KSC or Cape Canaveral Air Station (CCAS) medical clinics. The formula used in the Framingham Heart Study allows calculation of a person's probability of acquiring CHD within 10 years. The formula contains the following variables: Age, Diabetes, Smoking, Left Ventricular Hypertrophy, Blood Pressure (Systolic or Diastolic), Cholesterol, and HDL cholesterol. The formula is also gender specific. It was used to calculate the 10-year probabilities of CHD in KSC employees who required medical evaluations for job certifications during a one-year time frame. This KSC population was profiled and CHD risk reduction interventions could be targeted to those at high risk. Population risk could also be periodically reevaluated to determine the effectiveness of intervention. A 10-year CHD risk probability can be calculated for an individual quite easily while gathering routine medical information. An employee population's CHD risk probability can be profiled graphically revealing high risk segments of the population which can be targeted for risk reduction intervention. The small audience of NASA/contractor physicians, nurses and exercise/fitness professionals at the breakout session received the lecture very well. Approximately one third indicated by a show of hands that they would be interested in implementing a similar program at their NASA Center. Questions were asked pertaining to standardization for age, the validity of using the idealized male values also for the female population, and indications of the screening test's sensitivity and specificity.

Tipton, David A.↗

Teaching Soil Science in Primary and Secondary Schools

Earth's thin layer of soil is a fragile resource, made up of minerals, organic materials, air, water, and billions of living organisms. Soils plays a variety of critical roles that sustain life on Earth. If we think about soil, we tend to see it first as the source of most of the food we eat and the fibers we use, such as wood and cotton. Few students realize that soils also provide the key ingredients to many of the medicines (including antibiotics), cosmetics, and dyes that we use. Fewer still understand the importance of soils in integrating, controlling, and regulating the movement of air, water, materials, and energy between the hydrosphere, lithosphere, atmosphere, and biosphere. Because soil sustains life, it offers both a context and a natural laboratory for investigating these interactions. The enclosed poster, which integrates soil profiles with typical landscapes in which soils form, can also help students explore the interrelationships of Earth systems and gain an understanding of our soil resources. The poster, produced jointly by the American Geological Institute and the Soil Science Society of America, aims to increase awareness of the importance of soil, as does the GLOBE (Global Learning and Observations To Benefit the Environment) Program. Vice President Al Gore instituted the GLOBE Program on Earth Day of 1993 to increase environmental awareness of individuals throughout the world, contribute to a better scientific understanding of the Earth, and help all students reach higher levels of achievement in science and mathematics. GLOBE functions as a partnership between scientists, students, and teachers in which scientists design protocols for specific measurements they need for their research that can be performed by K-12 students. Teachers are trained in the GLOBE protocols and teach them to their students. Students make the measurements, enter data via the Internet to a central data archive, and the data becomes available to scientists and the general community. Students benefit by having a "hands-on"experience in science, math, and technology, using their local environment as a learning laboratory, as well as contact with scientists and other students around the world. Soil investigations have become an essential component of GLOBE. The protocols that have been developed so far within the GLOBE program include GPS Location, Atmosphere/Climate, Soil Characterization, Soil Moisture and Temperature, Land Cover/Biometry, Hydrology, and Satellite Image Classification. For the GLOBE Soil Characterization Protocol, students explore the physical. chemical, and morphological properties of the soil at their study site. They are asked to dig a pit or use an auger to about 1 meter at at least 2 sites.

Levine, Elissa R.↗

Mathematical analysis of a Vuilleumier refrigerator.

A comprehensive analysis of the Vuilleumier refrigerator was conducted. This analysis includes the effects of nonisothermal gas heat addition and rejection, hot and cold regenerator inefficiencies, conduction losses, and gas leakage losses. A computer program was written which solves the equations resulting from the analysis. The program calculates internal pressures, temperatures, and gas flow rates as functions of refrigerator crank angle, as well as overall refrigerator cooling load and power input. Comparisons between the program results and available data show good agreement, with a marked improvement over the predictions of the ideal model.

Sherman, A.↗

Simulation test results for lift/cruise fan research and technology aircraft

A flight simulation program was conducted on the flight simulator for advanced aircraft (FSAA). The flight simulation was a part of a contracted effort to provide a lift/cruise fan V/STOL aircraft mathematical model for flight simulation. The simulated aircraft is a configuration of the Lift/Cruise Fan V/STOL research technology aircraft (RTA). The aircraft was powered by three gas generators driving three fans. One lift fan was installed in the nose of the aircraft, and two lift/cruise fans at the wing root. The thrust of these fans was modulated to provide pitch and roll control, and vectored to provide yaw, side force control, and longitudinal translation. Two versions of the RTA were defined. One was powered by the GE J97/LF460 propulsion system which was gas-coupled for power transfer between fans for control. The other version was powered by DDA XT701 gas generators driving 62 inch variable pitch fans. The flight control system in both versions of the RTA was the same.

Bland, M. P.↗

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗

A study of the longevity and operational reliability of Goddard Spacecraft, 1960-1980

Compiled data regarding the design lives and lifetimes actually achieved by 104 orbiting satellites launched by the Goddard Spaceflight Center between the years 1960 and 1980 is analyzed. Historical trends over the entire 21 year period are reviewed, and the more recent data is subjected to an examination of several key parameters. An empirical reliability function is derived, and compared with various mathematical models. Data from related studies is also discussed. The results provide insight into the reliability history of Goddard spacecraft an guidance for estimating the reliability of future programs.

Shockey, E. F.↗

Computer Program for Flow in a Combustor

New version of TEACH computer program developed specifically for use in analysis of subsonic, swirling, reacting, turbulent flow in cylindrical bluff-body research combustor. Combustor design widely used as research tool for mathematical modeling of gas turbines and for development of diagnostic instrumentation.

Chiappetta, Louis M.↗

Stability of mixing layers

The research program for the first year of this project (see the original research proposal) consists of developing an explicit marching scheme for solving the parabolized stability equations (PSE). Performing mathematical analysis of the computational algorithm including numerical stability analysis and the determination of the proper boundary conditions needed at the boundary of the computation domain are implicit in the task. Before one can solve the parabolized stability equations for high-speed mixing layers, the mean flow must first be found. In the past, instability analysis of high-speed mixing layer has mostly been performed on mean flow profiles calculated by the boundary layer equations. In carrying out this project, it is believed that the boundary layer equations might not give an accurate enough nonparallel, nonlinear mean flow needed for parabolized stability analysis. A more accurate mean flow can, however, be found by solving the parabolized Navier-Stokes equations. The advantage of the parabolized Navier-Stokes equations is that its accuracy is consistent with the PSE method. Furthermore, the method of solution is similar. Hence, the major part of the effort of the work of this year has been devoted to the development of an explicit numerical marching scheme for the solution of the Parabolized Navier-Stokes equation as applied to the high-seed mixing layer problem.

Tam, Christopher↗

Statistical computation of tolerance limits

Based on a new theory, two computer codes were developed specifically to calculate the exact statistical tolerance limits for normal distributions within unknown means and variances for the one-sided and two-sided cases for the tolerance factor, k. The quantity k is defined equivalently in terms of the noncentral t-distribution by the probability equation. Two of the four mathematical methods employ the theory developed for the numerical simulation. Several algorithms for numerically integrating and iteratively root-solving the working equations are written to augment the program simulation. The program codes generate some tables of k's associated with the varying values of the proportion and sample size for each given probability to show accuracy obtained for small sample sizes.

Wheeler, J. T.↗

FNAS/summer faculty fellowship research continuation program. Task 6: Integrated model development for liquid fueled rocket propulsion systems. Task 9: Aspects of model-based rocket engine condition monitoring and control

The objective of Phase I of this research effort was to develop an advanced mathematical-empirical model of SSME steady-state performance. Task 6 of Phase I is to develop component specific modification strategy for baseline case influence coefficient matrices. This report describes the background of SSME performance characteristics and provides a description of the control variable basis of three different gains models. The procedure used to establish influence coefficients for each of these three models is also described. Gains model analysis results are compared to Rocketdyne's power balance model (PBM).

Santi, L. Michael↗