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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Alternative mathematical programming formulations for FSS synthesis

A variety of mathematical programming models and two solution strategies are suggested for the problem of allocating orbital positions to (synthesizing) satellites in the Fixed Satellite Service. Mixed integer programming and almost linear programming formulations are presented in detail for each of two objectives: (1) positioning satellites as closely as possible to specified desired locations, and (2) minimizing the total length of the geostationary arc allocated to the satellites whose positions are to be determined. Computational results for mixed integer and almost linear programming models, with the objective of positioning satellites as closely as possible to their desired locations, are reported for three six-administration test problems and a thirteen-administration test problem.

Reilly, C. H.↗
NASA NTRS1988

Minimum-Time Control For Robotic Manipulators

Existence theorem proved for nonlinear systems. Report discusses mathematical requirements for existence of solution to minimum-time control problem for robotic manipulator that obeys nonlinear equations of motion.

Wen, John T.↗
NASA NTRS1990

Coupled effects of conduction in the crystal and thermo-solutal convection in a rectangular inclined enclosure

To date modeling of crystal growth of optoelectronic materials using Physical Vapor Transport has been limited to the study of the fluid phase. To achieve it, the equations of coupled heat, mass and momentum transfer in the gas have to be solved. The first objective of this study is to examine the effect of heat conduction in the crystal on the fluid flow in the neighborhood of the interface. Heat transfer boundary conditions on both interfaces were modified to take into account the additional heat flux between gas and solid. It is proved that heat conduction does not affect the fluid flow. In the presence of gravity, density gradients in the fluid phase generate convection responsible for the problem of a nonplanar growth of the interface. The second objective is to study systematically under one-g the different possible flows in order to solve this problem. Depending on the parameters, a diffusive mode and three convective modes (thermal, solutal and thermo-solutal) are observed. The competition between thermal and solutal convections leads to a mathematical condition which can be used to achieve a planar growth. It is proven that, under the physical conditions chosen, this mathematical condition cannot be thermodynamically satisfied.

Mennetrier, Christophe↗
NASA NTRS1990

A circular median filter approach for resolving directional ambiguities in wind fields retrieved from spaceborne scatterometer data

The retrieval algorithm for spaceborne scatterometry proposed by Schultz (1985) is extended. A circular median filter (CMF) method is presented, which operates on wind directions independently of wind speed, removing any implicit wind speed dependence. A cell weighting scheme is included in the algorithm, permitting greater weights to be assigned to more reliable data. The mathematical properties of the ambiguous solutions to the wind retrieval problem are reviewed. The CMF algorithm is tested on twelve simulated data sets. The effects of spatially correlated likelihood assignment errors on the performance of the CMF algorithm are examined. Also, consideration is given to a wind field smoothing technique that uses a CMF.

Schultz, Howard↗
NASA NTRS1991

Computer Language For Optimization Of Design

SOL is computer language geared to solution of design problems. Includes mathematical modeling and logical capabilities of computer language like FORTRAN; also includes additional power of nonlinear mathematical programming methods at language level. SOL compiler takes SOL-language statements and generates equivalent FORTRAN code and system calls. Provides syntactic and semantic checking for recovery from errors and provides detailed reports containing cross-references to show where each variable used. Implemented on VAX/VMS computer systems. Requires VAX FORTRAN compiler to produce executable program.

Scotti, Stephen J.↗
NASA NTRS1990

Accumulated approximation: A new method for structural optimization by iterative improvement

A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.

Rasmussen, John↗
NASA NTRS1993

Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition).

Izmailov, Alexander F.↗
NASA NTRS2001

Geomagnetic Cutoff Rigidity Computer Program: Theory, Software Description and Example

The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.

Smart, D. F.↗
NASA NTRS1944

An Experimental Investigation of the Flow of Air in a Flat Broadening Channel

The wide use of diffusers, in various fields of technology, has resulted in several experimental projects to study the action and design of diffusers. Most of the projects dealt with steam (steam turbine nozzles). But diffusers have other applications - that is, ventilators, smoke ducts, air coolers, refrigeration, drying, and so forth. At present there is another application for diffusers in wind-tunnel design. Because of higher requirements and increased power of such installations more attention must be paid to the correctness of work and the decrease in losses due to every section of the tunnel. A diffuser, being one of the component parts of a tunnel , can in the event of faulty construction introduce considerable losses. Therefore, in the design of the new CAHI wind tunnel, it was suggested that an experimental study of diffusers be made, with a view to applying the results to wind tunnels. The experiments conducted by K. K. Baulin in the laboratories of CAHI upon models of diffusers of different cross sections, lengths, and angles of divergence, were a valuable source of experimental data. They were of no help, however, in reaching any conclusion regarding the optimum shape because of the complexity and diversity of the factors which all appeared simultaneously, thereby precluding the.study of the effects of any one factor separately. On the suggestion of the director of the CAHI,Prof. B. N. Ureff, it was decided to experiment on a two-dimensional diffuser model and determine the effect, of the angle of divergence. The author is acquainted with two experimental projects of like nature: the first was conducted with water, the other with air. The first of these works, although containing a wealth of experimental data, does not indicate the nature of flow or its relation to the angle of divergence. The second work is limited to four angles - that is, 12 deg, 24 deg, 45 deg, 90 deg. The study of this diffuser did not supply any information about the effect of smaller angles which, because of their advantages, are more commonly used, The author was able to acquaint himself with the second work only after the experiments were started. For these reasons, as well as because on the basis of those works no conclusion can be reached regarding the nature of flow distribution, of eddies, and so forth, experimental work was continued. The need for determining flow patterns follows from the fact that from them are determined methods of measurement - that is, the determination of velocities by means of the pitot tube, which, as is well known, gives correct indications only when placed with its axis parallel to the axis of flow. The data contained in this report were obtained from experiments conducted by the Aerodynamical Laboratories of the CAHI. The solutions to some. of the mathematical problems connected with the experiments are due to Prof. S. A, Chapligin.

Vedernikoff, A. N.↗
NASA NTRS2013

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Dichmann, Donald J.↗
NASA NTRS1978

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

D M Le Vine↗
NASA NTRS1988

Heat pipe dynamic behavior

The vapor flow in a heat pipe was mathematically modeled and the equations governing the transient behavior of the core were solved numerically. The modeled vapor flow is transient, axisymmetric (or two-dimensional) compressible viscous flow in a closed chamber. The two methods of solution are described. The more promising method failed (a mixed Galerkin finite difference method) whereas a more common finite difference method was successful. Preliminary results are presented showing that multi-dimensional flows need to be treated. A model of the liquid phase of a high temperature heat pipe was developed. The model is intended to be coupled to a vapor phase model for the complete solution of the heat pipe problem. The mathematical equations are formulated consistent with physical processes while allowing a computationally efficient solution. The model simulates time dependent characteristics of concern to the liquid phase including input phase change, output heat fluxes, liquid temperatures, container temperatures, liquid velocities, and liquid pressure. Preliminary results were obtained for two heat pipe startup cases. The heat pipe studied used lithium as the working fluid and an annular wick configuration. Recommendations for implementation based on the results obtained are presented. Experimental studies were initiated using a rectangular heat pipe. Both twin beam laser holography and laser Doppler anemometry were investigated. Preliminary experiments were completed and results are reported.

Issacci, F.↗
NASA NTRS2014

Comptonization in Ultra-Strong Magnetic Fields: Numerical Solution to the Radiative Transfer Problem

We consider the radiative transfer problem in a plane-parallel slab of thermal electrons in the presence of an ultra-strong magnetic field (B approximately greater than B(sub c) approx. = 4.4 x 10(exp 13) G). Under these conditions, the magnetic field behaves like a birefringent medium for the propagating photons, and the electromagnetic radiation is split into two polarization modes, ordinary and extraordinary, that have different cross-sections. When the optical depth of the slab is large, the ordinary-mode photons are strongly Comptonized and the photon field is dominated by an isotropic component. Aims. The radiative transfer problem in strong magnetic fields presents many mathematical issues and analytical or numerical solutions can be obtained only under some given approximations. We investigate this problem both from the analytical and numerical point of view, provide a test of the previous analytical estimates, and extend these results with numerical techniques. Methods. We consider here the case of low temperature black-body photons propagating in a sub-relativistic temperature plasma, which allows us to deal with a semi-Fokker-Planck approximation of the radiative transfer equation. The problem can then be treated with the variable separation method, and we use a numerical technique to find solutions to the eigenvalue problem in the case of a singular kernel of the space operator. The singularity of the space kernel is the result of the strong angular dependence of the electron cross-section in the presence of a strong magnetic field. Results. We provide the numerical solution obtained for eigenvalues and eigenfunctions of the space operator, and the emerging Comptonization spectrum of the ordinary-mode photons for any eigenvalue of the space equation and for energies significantly lesser than the cyclotron energy, which is on the order of MeV for the intensity of the magnetic field here considered. Conclusions. We derived the specific intensity of the ordinary photons, under the approximation of large angle and large optical depth. These assumptions allow the equation to be treated using a diffusion-like approximation.

acceleration of particles↗
NASA NTRS1950

Subsonic Gas Flow Past A Wing Profile

The use of the linearized equations of Chaplygin to calculate the subsonic flow of a gas permits solving the problem of the flow about a wing profile for absence and presence of circulation. The solution is obtained in a practical convenient form that permits finding all the required magnitudes for the gas flow (lift, lift moment velocity distribution over the profile, and critical Mach number). This solution is not expressed in simple closed form; for a certain simplifying assumption, however, the equations of Chaplygin can be reduced to equations with constant coefficients, and solutions are obtained by using only the mathematical apparatus of the theory of functions of a complex variable. The method for simplifying the equations was pointed out by Chaplygin himself. These applied similar equations to the solution of the flow problem and obtained a solution for the case of the absence of circulation.

Christianovich, S. A.↗
NASA NTRS1990

Convection-driven tectonics on Venus

An analysis is presented of convective stress coupling to an elastic lithosphere as applied to Venus. Theoretical solutions are introduced for the response of a mathematically thick elastic plate overlying a Newtonian viscous medium with an exponential depth dependence of viscosity, and a Green's function solution is obtained for the viscous flow driven by a harmonic density distribution at a specified depth. An elastic-plastic analysis is carried out for the deformation of a model Venus lithosphere. The results predict that dynamic uplift of Venusian topography must be accompanied by extensive brittle failure and viscous flow in the lithosphere.

Phillips, Roger J.↗
NASA NTRS1966

Computer program determines chemical composition of physical system at equilibrium

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Kwong, S. S.↗