Geometric theory of functional-differential equations.
Functional differential equations geometric theory, with rate of change of physical system mathematical model dependent on past history
Hale, J. K.↗
SEARCH · Engineering Papers
Results for “Physical systems”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Evaluation of thermal network correction program using test temperature data
An evaluation process to determine the accuracy of a computer program for thermal network correction is discussed. The evaluation is required since factors such as inaccuracies of temperatures, insufficient number of temperature points over a specified time period, lack of one-to-one correlation between temperature sensor and nodal locations, and incomplete temperature measurements are not present in the computer-generated information. The mathematical models used in the evaluation are those that describe a physical system composed of both a conventional and a heat pipe platform. A description of the models used, the results of the evaluation of the thermal network correction, and input instructions for the thermal network correction program are presented.
Ishimoto, T.↗
Heat transfer characteristics of an emergent strand
A mathematical model was developed to describe the heat transfer characteristics of a hot strand emerging into a surrounding coolant. A stable strand of constant efflux velocity is analyzed, with a constant (average) heat transfer coefficient on the sides and leading surface of the strand. After developing a suitable governing equation to provide an adequate description of the physical system, the dimensionless governing equation is solved with Laplace transform methods. The solution yields the temperature within the strand as a function of axial distance and time. Generalized results for a wide range of parameters are presented, and the relationship of the results and experimental observations is discussed.
Simon, W. E.↗
Parachute-deployment-parameter identification based on an analytical simulation of Viking BLDT AV-4
A six-degree-of-freedom analytical simulation of parachute deployment dynamics developed at the Langley Research Center is presented. A comparison study was made using flight results from the Viking Balloon Launched Decelerator Test (BLDT) AV-4. Since there are significant voids in the knowledge of vehicle and decelerator aerodynamics and suspension system physical properties, a set of deployment-parameter input has been defined which may be used as a basis for future studies of parachute deployment dynamics. The study indicates the analytical model is sufficiently sophisticated to investigate parachute deployment dynamics with reasonable accuracy.
Talay, T. A.↗
A Computing Method for Sound Propagation Through a Nonuniform Jet Stream
Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.
Padula, S. L.↗
Investigation B: Laminar confined coaxial entrance flow with heat generation
The results of a parametric study on the entrance flow region in a gas core nuclear reactor are presented. The physical system is modeled as laminar confined, coaxial flow with heat generation in the inner fluid. The governing equations include the boundary layer approximations and the assumptions of only radial radiative transport of energy represented as an energy diffusion term. The Von Mises transformation and a zeta transformation are used to transform the equations into nonlinear nonhomogeneous convective-diffusion equations. A unique combination of forward and backward difference equations which yields accurate results at moderate computational times, is used in the numerical method. Results show that the rapidly accelerating, heat generating inner stream actually shrinks in radius as it expands axially.
Bobba, G. K. M.↗
Application of the CINGEN program a thermal network data generator
The application of the CINGEN computer program and two of its supporting programs for the evaluation of structural and thermal performance of physical systems was described. The CINGEN program was written and implemented to avoid the duplication effort of performing a finite element approach for structural analysis and a finite differencing technique for thermal analysis, as well as the desire for a geometrical representation of the thermal model to reduce modeling errors. The program simplifies the thermal modeling process by performing all of the capacitance and conductance calculations normally done by the analyst. Each solid element is divided into five tetrahedrons, allowing the total volume to be calculated precisely. A sample problem was illustrated.
Shultz, W. E.↗
Index to NASA Tech Briefs, 1974
The following information was given for 1974: (1) abstracts of reports dealing with new technology derived from the research and development activities of NASA or the U.S. Atomic Energy Commission, arranged by subjects: electronics/electrical, electronics/electrical systems, physical sciences, materials/chemistry, life sciences, mechanics, machines, equipment and tools, fabrication technology, and computer programs, (2) indexes for the above documents: subject, personal author, originating center.
Source record↗
Mixed boundary value problems in mechanics
Certain boundary value problems were studied over a domain D which may contain the point at infinity and may be multiply connected. Contours forming the boundary are assumed to consist of piecewise smooth arcs. Mixed boundary value problems are those with points of flux singularity on the boundary; these are points on the surface, either side of which at least one of the differential operator has different behavior. The physical system was considered to be described by two quantities, the potential and the flux type quantities. Some of the examples that were illustrated included problems in potential theory and elasticity.
Erdogan, F.↗
Thermal hydraulic analyzer
Program solves thermal, hydraulic, or combined thermal and hydraulic problems. It can handle transient and steady-state hydraulic problems and combined thermal/hydraulic transient of steady-state problems. Physical system of interest is approximated to any degree of accuracy with lumped-parameter representation, using elements provided by program.
Core, T. C.↗
NASA Tech Briefs Index, 1976
Abstracts of new technology derived from the research and development activities of the National Aeronautics and Space Administration are presented. Emphasis is placed on information considered likely to be transferrable across industrial, regional, or disciplinary lines. Subject matter covered includes: electronic components and circuits; electronic systems; physical sciences; materials; life sciences; mechanics; machinery; fabrication technology; and mathematics and information sciences.
Source record↗
Creation of lumped parameter thermal model by the use of finite elements
In the finite difference technique, the thermal network is represented by an analogous electrical network. The development of this network model, which is used to describe a physical system, often requires tedious and mental data preparation and checkout by the analyst which can be greatly reduced through the use of the computer programs to develop automatically the mathematical model and associated input data and graphically display the analytical model to facilitate model verification. Three separate programs are involved which are linked through common mass storage files and data card formats. These programs are SPAR, CINGEN and GEOMPLT, and are used to (1) develop thermal models for the MITAS II thermal analyzer program; (2) produce geometry plots of the thermal network; and (3) produce temperature distribution and time history plots.
Source record↗
The natural and perturbed troposphere
A quantitative assessment of the chemical and climatic effects of industrial emissions into the atmosphere requires an understanding of the complex interactions of species within the atmosphere and of the atmosphere with other physical systems such as the oceans, lithosphere, and biosphere. The concentration of a particular species is determined by competition between various production and loss processes. The abundances of tropospheric gases are examined. The reactions of the members of the oxygen group are considered along with the models which have been developed to describe the involved relationships. Attention is also given to the natural carbon cycle, perturbations to the carbon cycle, the natural nitrogen cycle, perturbations to the nitrogen cycle, the hydrogen group, the sulfur group, and the halogen group.
Stewart, R. W.↗
Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine
Lumped volume dynamic equations are derived using an energy state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.
Daniele, C. J.↗
Concerning an application of the method of least squares with a variable weight matrix
An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.
Sukhanov, A. A.↗
Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine
Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.
Daniele, C. J.↗
Polar motion from laser range measurements of GEOS-3
Using two-day arcs of GEOS-3 laser data, simultaneous solutions for pole position components, x sub p and y sub p, and orbit elements have been obtained for the period spanning 3 February to 6 March 1976 using three NASA Goddard Space Flight Center laser stations located near Washington, D.C. (STALAS) and on the islands of Bermuda and Grand Turk. The results are in general agreement with the BIH results. However, because of the locations of the laser sites, the x sub p solution is weaker than the y sub p solution. The x sub p and y sub p estimates were smoothed with a straight line by weighted least squares using the variance associated with the pole estimates as weights in order to reflect the effect of widely different data distributions. The smoothed y sub p differs by one meter with respect to the BIH smoothed values and the smoothed x sub p differs by about two meters. Spectral analysis of the results has identified frequencies associated with the orbital motion indicating the need for further improvements in the model of the physical system.
Schutz, B. E.↗
An approximation for inverse Laplace transforms
Programmable calculator runs simple finite-series approximation for Laplace transform inversions. Utilizing family of orthonormal functions, approximation is used for wide range of transforms, including those encountered in feedback control problems. Method works well as long as F(t) decays to zero as it approaches infinity and so is appliable to most physical systems.
Lear, W. M.↗