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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.

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At least 703 records · Page 39

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NASA NTRS1985

Generation of Surface Coordinates by Elliptic Partial Differential Equations

The problem of generating spatial coordinates by numerical methods through carefully selected mathematical models is of current interest both in mechanics and physics. The problem of generation of a desired system of coordinates in a given surface was considered, which essentially is an effort directed to the problem of grid generation in a two-dimensional non-Euclidean space. The mathematical model selected for this purpose is based on the formulae of Gauss for a surface. The proposed equations can be used to generate a new coordinate system from the data of an already given coordinate system in a surface. If the coefficients of the first and second fundamental forms have been given, then the proposed equations can be used to generate a surface satisfying the given data (surface fitting). The proposed equations can also be used to generate surfaces in the space between two arbitrary given surfaces, thus providing 3D grids in an Euclidean space.

Warsi, Z. U. A.↗

NASA NTRS1988

Predicting debris

The probable amount, sizes, and relative velocities of debris are discussed, giving examples of the damage caused by debris, and focusing on the use of mathematical models to forecast the debris environment and solar activity now and in the future. Most debris are within 2,000 km of the earth's surface. The average velocity of spacecraft-debris collisions varies from 9 km/sec at 30 degrees of inclination to 13 km/sec near polar orbits. Mathematical models predict a 5 percent per year increase in the large-fragment population, producing a small-fragment population increase of 10 percent per year until the year 2060, the time of critical density. A 10 percent increase in the large population would cause the critical density to be reached around 2025.

Kessler, Donald J.↗

NASA NTRS2003

Extension of Liouville Formalism to Postinstability Dynamics

A mathematical formalism has been developed for predicting the postinstability motions of a dynamic system governed by a system of nonlinear equations and subject to initial conditions. Previously, there was no general method for prediction and mathematical modeling of postinstability behaviors (e.g., chaos and turbulence) in such a system. The formalism of nonlinear dynamics does not afford means to discriminate between stable and unstable motions: an additional stability analysis is necessary for such discrimination. However, an additional stability analysis does not suggest any modifications of a mathematical model that would enable the model to describe postinstability motions efficiently. The most important type of instability that necessitates a postinstability description is associated with positive Lyapunov exponents. Such an instability leads to exponential growth of small errors in initial conditions or, equivalently, exponential divergence of neighboring trajectories. The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Zak, Michail↗

NASA NTRS2011

A Deployable 4 Meter 180 to 680 GHz Antenna for the Scanning Microwave Limb Sounder

The Scanning Microwave Limb Sounder (SMLS) is a space-borne heterodyne radiometer which will measure pressure, temperature and atmospheric constituents from thermal emission between 180 and 680 GHz. SMLS, planned for the Global Atmospheric Composition Mission of the NRC Decadal Survey, uses a novel toric Cassegrain antenna to perform both elevation and azimuth scanning. These provide better horizontal and temporal resolution and coverage than were possible with elevation-only scanning at typical Low-Earth orbit spacing in the two previous MLS satellite instruments. Development of the SMLS antenna was the focus of a 2006 Small Business Innovative Research (SBIR) program whose phase II culminated in the fabrication and thermal stability testing of a composite demonstration model of the SMLS primary reflector. This reflector has the full 4m height and 1/3 the width planned for flight. An Instrument Incubator Program (IIP) titled "A deployable 4 Meter 180 to 680 GHz antenna for the Scanning Microwave Limb Sounder" continues development of the SMLS antenna with the study of 5 topics: 1) detailed mathematical modeling of the antenna patterns from which we simulate geophysical parameter retrievals in order to establish FOV performance requirements; 2) thorough correlation of finite element model predictions with measurements made on the SBIR reflector. We will again measure deformations of this reflector, under more flight-like thermal gradients, using higher precision metrology techniques available in a new large-aperture facility at JPL; 3) fabrication of a full-width primary reflector whose asbuilt surface figure will better meet the figure requirements of SMLS than did the SBIR reflector; 4) integration of the primary with other reflectors, and with residual front ends built in a 2007 IIP, in a breadboard antenna; and finally 5) RF testing of the breadboard on a Near Field Range at JPL. We report on significant progress in 3 areas of the current IIP: development of the mathematical model to predict SMLS antenna patterns and their application in a preliminary set of geophysical retrievals; the correlation between surface deformation predicted by finite element models and measurement in the 2009 isothermal stability tests of the SBIR, with implications for the thermal gradient testing to be performed at JPL; and aspects of the conceptual design of the full-width primary reflector to be fabricated and tested in the 2nd and 3rd years of the IIP.

heterodyne radiometer↗

NASA NTRS1978

Fluid mechanics of continuous flow electrophoresis

The following aspects of continuous flow electrophoresis were studied: (1) flow and temperature fields; (2) hydrodynamic stability; (3) separation efficiency, and (4) characteristics of wide gap chambers (the SPAR apparatus). Simplified mathematical models were developed so as to furnish a basis for understanding the phenomena and comparison of different chambers and operating conditions. Studies of the hydrodynamic stability disclosed that a wide gap chamber may be particularly sensitive to axial temperature variations which could be due to uneven heating or cooling. The mathematical model of the separation process includes effects due to the axial velocity, electro-osmotic cross flow and electrophoretic migration, all including the effects of temperature dependent properties.

Saville, D. A.↗

NASA NTRS1985

Transient Heat Transfer in Zero Gravity Environment

The objective is to provide computer codes and/or correlations for application in the design of transient heat transfer systems. The mathematical models in the computer codes are being tested by experimental data obtained in the laboratory using optical techniques. The elimination of natural convection (buoyancy) in the experimental data obtained in zero-g (KC-135) facilitates the study of thermal expansion effects which is of interest in the development and testing of the mathematical models of the transient heat transfer. Initial flight in the KC 135 (June 1983) suggested some modifications to the experimental apparatus and the data acquisition technique (high speed video will replace high speed movies for recording optical records generated during the experiments). A series of KC-135 flights with this experiment on board are scheduled for summer/fall 1984. The acquisition of the aforementioned data using interferometry and beam deflection optical techniques is anticipated. The measurements provide time dependent temperature fields above a horizontal heater surface submerged in a static fluid (Freon 13). The heater surface is electrically heated for a time interval approximately 0.100 sec. during which the data are optically recorded.

Giarratano, P. G.↗

NASA NTRS2024

Finite Element Simulation of the Direct Energy Deposition using Comsol Multiphysics

Direct Energy Deposition (DED) is an emerging technology extensively employed in metal Additive Manufacturing (AM). Despite its widespread industrial application, mathematical modeling in this domain remains challenging. This complexity arises from the intricate nature of the modeling approach and the nonlinear behavior of material parameters across a broad temperature range. Consequently, experimentalists often resort to a trial-and-error method to achieve structures with desired properties. However, this approach can be time-consuming and may not always yield parts with the requisite characteristics, highlighting the necessity for mathematical modeling to enhance manufacturing success. This study focuses on thin-walled manufacturing with a single bead thickness, adjusting laser parameters to produce such structures. The laser cladding speed, typical for DED manufacturing, is considered to be on the order of centimeters per second. The various wall thicknesses and heights are explored to discern the general characteristics of walls manufactured via this DED approach. Our modeling approach diverges from the conventional DED modeling based on activation-deactivation of predefined mesh domains, commonly implemented in many finite element codes. Instead, a method is proposed that effectively models layer cladding and melt pool dynamics, enabling predictions of the microstructure in the resulting structures. The formation mechanisms of cellular, dendritic columnar, and stray (equiaxed) grains, which arise from the interplay between nucleation and growth from the surface is analyzed. The study also examines the feasibility of microstructure formation to demonstrate the various thermal characteristics inherent in wall manufacturing. Our results illustrate how different process parameters influence the temperature gradient and cooling rate of the molten pool, subsequently affecting the primary dendrite arm spacing (PDAS). This modeling technique allows for the investigation of diverse thermal conditions, facilitating the prediction of microstructure and residual stresses in the manufactured parts.

modeling↗

NASA NTRS1966

Models of gas flows with chemical and radiative effects

Physical and mathematical models of gas flows with chemical and radiative effects

MATHEMATICAL MODEL↗

NASA NTRS2006

Thermal Imaging Applied to Cryocrystallography: Cryocooling and Beam Heating (Part I)

Thermal imaging provides a non-invasive method to study both the cryocooling process and the heating due to the X-ray beam interaction with a sample. The method has been used successfully to image cryocooling in a number of experimental situations, i.e. cooling as a function of sample volume and as a function of cryostream orientation. Although there are experimental limitations to the method, it has proved a powerful technique to aid cryocrystallography development. Due to the rapid spatial temperature information provided about the sample it is also a powerful tool in the testing of mathematical models. Recently thermal imaging has been used to measure the temperature distribution on both a model and typical crystal samples illuminated with an X-ray beam produced by an undulator. A brief overview of thermal imaging and previous results will be presented. In addition, a detailed description of the calibration and experimental aspects of the beam heating measurements will be described. This will complement the following talk on the mathematical modeling and analysis of the results.

Snell, Edward↗

NASA NTRS1984

Application of optimization techniques to the design of a flutter suppression control law for the DAST ARW-2

The design of a candidate flutter suppression (FS) control law for the symmetric degrees of freedom for the DAST ARW-2 aircraft is discussed. The results illustrate the application of several currently employed control law design techniques. Subsequent designs, obtained as the mathematical model of the ARW-2 is updated, are expected to employ similar methods and to provide a control law whose performance will be flight tested. This study represents one of the steps necessary to provide an assessment of the validity of applying current control law synthesis and analysis techniques in the design of actively controlled aircraft. Mathematical models employed in the control law design and evaluation phases are described. The control problem is specified by presenting the flutter boundary predicted for the uncontrolled aircraft and by defining objectives and constraints that the controller should satisfy. A full-order controller is obtained by using Linear Quadratic Gaussian (LQG) techniques. The process of obtaining an implementable reduced-order controller is described. One example is also shown in which constrained optimization techniques are utilized to explicitly include robustness criteria within the design algorithm.

Adams, W. M., Jr.↗

NASA NTRS1985

Dynamic Creep Buckling: Analysis of Shell Structures Subjected to Time-dependent Mechanical and Thermal Loading

The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.

Simitses, G. J.↗

NASA NTRS1991

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Simitses, George J.↗

NASA NTRS2007

Designing Rolling-Element Bearings

Bearing Analysis Tool (BAT) is a computer program for designing rolling-element bearings for cryogenic turbomachines. BAT provides a graphical user interface (GUI) that guides the entry of data to develop mathematical models of bearings. The GUI breaks model data into logical subsets that are entered through logic-driven input screens. The software generates a threedimensional graphical model of a bearing as the data are entered. Most dataentry errors become immediately obvious in the graphical model. BAT provides for storage of all the data on a shaft/bearing system, enabling the creation of a library of proven designs. Data from the library can be transferred to subsequent projects by use of simple cut-and-paste routines. BAT includes a library of temperature- dependent cryogenic bearing-material properties for use in the mathematical models. BAT implements algorithms that (1) enable the user to select combinations of design and/or operating-condition parameters, and then (2) automatically optimize the design by performing trade studies over all of the parameter combinations. This feature enables optimization over a large trade space in a fraction of the time taken when using prior bearingmodel software.

Moore, James D., Jr.↗

NASA NTRS2016

Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

module↗

NASA NTRS2016

Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics

Lightweight and high resolution optics↗

NASA NTRS1985

Tone excited jets. V - A theoretical model and comparison with experiment

A mathematical model of tone-excited jets is developed which consists of two major components: a mathematical description of the process by which the intrinsic instability waves of the jet are excited by the upstream tones; and the modeling of the nonlinear interaction between the mean flow of the jet, the excited large-scale instability waves or turbulence structure, and the fine scale turbulence. It is assumed that each of these jet flow components can be characterized by a few parameters, which are then related by conservation equations that are supplemented by closure models. This quasi-linear model's results are compared with experimental measurements, and good agreement is obtained over a wide range of excitation frequencies and excitation levels.

Tam, C. K. W.↗

NASA NTRS1988

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

This research is performed to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling, and ratcheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Simitses, G. J.↗

NASA NTRS1988

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

The objective of this research is to develop a general mathematical model and solution methodologies for analyzing structural response of thin, metallic shell-type structures under large transient, cyclic or static thermomechanical loads. Among the system responses, which are associated with these load conditions, are thermal buckling, creep buckling and racheting. Thus, geometric as well as material-type nonlinearities (of high order) can be anticipated and must be considered in the development of the mathematical model. Furthermore, this must also be accommodated in the solution procedures.

Simitses, G. J.↗