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At least 829 records · Page 46

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NASA NTRS1990

Calculation of shocked one-dimensional flows on abruptly changing grids by mathematical programming

Cell-centered finite differences on cells of an arbitrarily spaced grid are presently used to discretize the steady-state inviscid and nearly inviscid Burgers' equations for steady-state shocked flow in a quasi-one-dimensional nozzle. The everdetermined system of nonlinear algebraic equations thus obtained is solved by a procedure which minimizes a weighted sum of the residuals' absolute values. Numerical solutions for both viscous and inviscid problems are accurate and nonoscillatory, on grids whose abrupt mesh lengths refinements are as great as a factor of 10,000.

Lavery, John E.↗

NASA NTRS1990

A mathematical model of the structure and evolution of small scale discrete auroral arcs

A three dimensional fluid model which includes the dispersive effect of electron inertia is used to study the nonlinear macroscopic plasma dynamics of small scale discrete auroral arcs within the auroral acceleration zone and ionosphere. The motion of the Alfven wave source relative to the magnetospheric and ionospheric plasma forms an oblique Alfven wave which is reflected from the topside ionosphere by the negative density gradient. The superposition of the incident and reflected wave can be described by a steady state analytical solution of the model equations with the appropriate boundary conditions. This two dimensional discrete auroral arc equilibrium provides a simple explanation of auroral acceleration associated with the parallel electric field. Three dimensional fully nonlinear numerical simulations indicate that the equilibrium arc configuration evolves three dimensionally through collisionless tearing and reconnection of the current layer. The interaction of the perturbed flow and the transverse magnetic field produces complex transverse structure that may be the origin of the folds and curls observed to be associated with small scale discrete arcs.

Seyler, C. E.↗

NASA NTRS1990

Mathematical modeling of the flow field and particle motion in a rotating bioreactor at unit gravity and microgravity

The biotechnology group at NASA Johnson Space Center is developing systems for culturing mammalian cells that stimulate some aspect of microgravity and provide a low shear environment for microgravity-based studies on suspension and anchorage dependent cells. The design of these vessels for culturing cells is based on the need to suspend cells and aggregates of cells and microcarrier beads continually in the culturing medium. The design must also provide sufficient circulation for adequate mass transfer of nutrients to the cells and minimize the total force on the cells. Forces, resulting from sources such as hydrodynamic fluid shear and collisions of cells and walls of the vessels, may damage delicate cells and degrade the formation of three dimensional structures. This study examines one particular design in both unit gravity and microgravity based on two concentric cylinders rotating in the same direction at different speeds to create a Couette flow between them. A numerical simulation for the flow field and the trajectories of particles in the vessel. The flow field for the circulation of the culturing medium is modeled by the Navier-Stokes equations. The forces on a particle are assumed to be drag from the fluid's circulation, buoyancy from the gravitational force and centrifugal force from the rotation of the vessel. The problem requires first solving the system of partial differential equations for the fluid flow by a finite difference method and then solving the system of ordinary differential equations for the trajectories by Gear's stiff method. Results of the study indicate that the trajectories in unit gravity and microgravity are very similar except for small spatial deviations on the fast time scale in unit gravity. The total force per unit cross sectional area on a particle in microgravity, however, is significantly smaller than the corresponding value in unit gravity, which is also smaller than anticipated. Hence, this study indicates that this design for a bioreactor with optimal rates of rotation can provide a good environment for culturing cells in microgravity with adequate circulation and minimal force on the cells.

Boyd, Ernest J.↗

NASA NTRS1989

Mathematical models for film sensitivity measurements

The quality of the pictorial record developed from photographic material depends on the composition of the material, the procedures used in its exposure and processing, as well as, the nature of the physical and temporal environment extant during the creation of the record. By holding many of the variables fixed, the effect of the two environmental parameters, namely temperature and aging are examined on the characteristic curve of a given film. Polynomial and exponential functions are evaluated as empirical formulas for the characteristic curve, and the sensitivity of derived coefficients to the selected parameters is assessed.

Hammond, Ernest C., Jr.↗

NASA NTRS1990

A mathematical model of the structure and evolution of small-scale discrete auroral arcs

A three-dimensional fluid model for the structure and evolution of small-scale discrete auroral arcs originating from Alfven waves is developed and used to study the nonlinear macroscopic plasma dynamics of these auroral arcs. The results of simulations show that stationary auroral arcs can be unstable to a collisionless tearing mode which may be responsible for the observed transverse structuring in the form of folds and curls. At late times, the plasma becomes turbulent having transverse electric field power spectra that tend toward a universal k exp -5/3 spectral form.

Seyler, Charles E.↗

NASA NTRS1991

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

Ozguven, H. Nevzat↗

NASA NTRS1991

A mathematical basis for the design optimization of adaptive trusses in precision control

Optimal actuator placement schemes are presently studied for cases of adaptive truss precision control and prestressing control, with a view to the maximization of actuator efficiencies. In statically indeterminate truss structures, the optimal placement criteria and techniques differ, depending on whether the primary determinate structure is known. A suboptimal actuator-placement solution to the global optimization problem which combines displacement control and prestressing control is suggested, by combining the separate displacement control and prestressing control optimization results. Attention is given to the results obtained for the illustrative case of a two-bay, three-dimensional precision truss structure.

Das, S. K.↗

NASA NTRS1991

Solution of steady-state, two-dimensional conservation laws by mathematical programming

A truly two-dimensional algorithm is created for solving the steady-state two-dimensional conservation-law problem. An overdetermined system of algebraic equations is obtained through discretization by finite-volume formulas. These equations are perturbed nonsingularly and are solved by an efficient geometrically oriented l(1) procedure. The basic algorithm and the theory for the linear case f(u) = u are presented, and computational results for the nonlinear case f(u) = sq u are also analyzed. It is noted that the l(1) procedure captures boundary shocks as well as oblige and zigzag interior shocks in bands that are one cell wide, and the solution values are accurate up to the edge of the shock.

Lavery, John E.↗

NASA NTRS1992

Mathematical Modeling Of The Terrain Around A Robot

In conceptual system for modeling of terrain around autonomous mobile robot, representation of terrain used for control separated from representation provided by sensors. Concept takes motion-planning system out from under constraints imposed by discrete spatial intervals of square terrain grid(s). Separation allows sensing and motion-controlling systems to operate asynchronously; facilitating integration of new map and sensor data into planning of motions.

Slack, Marc G.↗

NASA NTRS1992

Mathematical Model For Engineering Analysis And Optimization

Computational support for engineering design process reveals behavior of designed system in response to external stimuli; and finds out how behavior modified by changing physical attributes of system. System-sensitivity analysis combined with extrapolation forms model of design complementary to model of behavior, capable of direct simulation of effects of changes in design variables. Algorithms developed for this method applicable to design of large engineering systems, especially those consisting of several subsystems involving many disciplines.

Sobieski, Jaroslaw↗

NASA NTRS1991

Structural damage identification using mathematical optimization techniques

An identification procedure is proposed to identify damage characteristics (location and size of the damage) from dynamic measurements. This procedure was based on minimization of the mean-square measure of difference between measurement data (natural frequencies and mode shapes) and the corresponding predictions obtained from the computational model. The procedure is tested for simulated damage in the form of stiffness changes in a simple fixed free spring mass system and symmetric cracks in a simply supported Bernoulli Euler beam. It is shown that when all the mode information is used in the identification procedure it is possible to uniquely determine the damage properties. Without knowing the complete set of modal information, a restricted region in the initial data space has been found for realistic and convergent solution from the identification process.

Shen, Mo-How Herman↗

NASA NTRS1991

Adsorbent testing and mathematical modeling of a solid amine regenerative CO2 and H2O removal system

The paper examines the design and the construction details of the test bed built for testing a solid-amine-based Regenerable CO2 Removal System (RCRS) built at the NASA/Johnson Space Center for the extended Orbiter missions. The results of tests are presented, including those for the adsorption breakthrough and the adsorption and desorption of CO2 and H2O vapor. A model for predicting the performance of regenerative CO2 and H2O vapor adsorption of the solid amine system under various operating conditions was developed in parallel with the testing of the test stand, using the coefficient of mass transfer calculated from test results. The results of simulations are shown to predict the adsorption performance of the Extended Duration Orbiter test bed fairly well. For the application to the RCRS at various operating conditions the model has to be modified.

Jeng, F. F.↗

NASA NTRS1990

Formal mathematical solutions of the force-free equations, spontaneous discontinuities, and dissipation in large-scale magnetic fields

Direct integration of the force-free field equation del x B = alpha B, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active X-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the X-ray corona.

Parker, E. N.↗

NASA NTRS1991

Mathematical morphology for automated analysis of remotely sensed objects in radar images

A symbiosis of pyramidal segmentation and morphological transmission is described. The pyramidal segmentation portion of the symbiosis has resulted in low (2.6 percent) misclassification error rate for a one-look simulation. Other simulations indicate lower error rates (1.8 percent for a four-look image). The morphological transformation portion has resulted in meaningful partitions with a minimal loss of fractal boundary information. An unpublished version of Thicken, suitable for watersheds transformations of fractal objects, is also presented. It is demonstrated that the proposed symbiosis works with SAR (synthetic aperture radar) images: in this case, a four-look Seasat image of sea ice. It is concluded that the symbiotic forms of both segmentation and morphological transformation seem well suited for unsupervised geophysical analysis.

Daida, Jason M.↗

NASA NTRS1992

Mathematical model of the Space Shuttle Main Engine gaseous oxygen control valve

A computer program for modeling transient flow behavior of the GOX control valve (GCV) has been developed which makes it possible to model a variety of operating conditions and changes of physical hardware. The SSME GCV controls the flow of GOX that pressurizes the Pogo accumulator. The model simulates the transient flow behavior of the original, tight stacked, and redesigned valve configurations during start and shutdown. The model reads a user-prepared input file that defines the valve configurations and thus provides maximum flexibility.

Langer, Susan L.↗

NASA NTRS1991

What procedure to choose while designing a fuzzy control? Towards mathematical foundations of fuzzy control

Fuzzy control has been successfully applied in industrial systems. However, there is some caution in using it. The reason is that it is based on quite reasonable ideas, but each of these ideas can be implemented in several different ways, and depending on which of the implementations chosen different results are achieved. Some implementations lead to a high quality control, some of them not. And since there are no theoretical methods for choosing the implementation, the basic way to choose it now is experimental. But if one chooses a method that is good for several examples, there is no guarantee that it will work fine in all of them. Hence the caution. A theoretical basis for choosing the fuzzy control procedures is provided. In order to choose a procedure that transforms a fuzzy knowledge into a control, one needs, first, to choose a membership function for each of the fuzzy terms that the experts use, second, to choose operations of uncertainty values that corresponds to 'and' and 'or', and third, when a membership function for control is obtained, one must defuzzy it, that is, somehow generate a value of the control u that will be actually used. A general approach that will help to make all these choices is described: namely, it is proved that under reasonable assumptions membership functions should be linear or fractionally linear, defuzzification must be described by a centroid rule and describe all possible 'and' and 'or' operations. Thus, a theoretical explanation of the existing semi-heuristic choices is given and the basis for the further research on optimal fuzzy control is formulated.

Kreinovich, Vladik YA.↗

NASA NTRS1992

Thermal mathematical modeling of a multicell common pressure vessel nickel-hydrogen battery

A two-dimensional and time-dependent thermal model of a multicell common pressure vessel (CPV) nickel-hydrogen battery was developed. A finite element solver called PDE/Protran was used to solve this model. The model was used to investigate the effects of various design parameters on the temperature profile within the cell. The results were used to help find a design that will yield an acceptable temperature gradient inside a multicell CPV nickel-hydrogen battery. Steady-state and unsteady-state cases with a constant heat generation rate and a time-dependent heat generation rate were solved.

Kim, Junbom↗

NASA NTRS1992

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Madnia, C. K.↗