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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗
NASA NTRS1993

Analytical evaluation of a surface integral expressing the coupling between interior and exterior volumes in a FE-IE approach

Recently an approach which combines the finite element technique and an integral equation to determine the fields scattered by inhomogeneous bodies of complicated shape has been proposed. Basically, a mathematical surface which encloses the scatterers is introduced, thus dividing the space into an interior and an exterior volume, in which the finite element technique and an integral equation for EM scattering, respectively, are applied. The integral equation is set up for the tangential components of the fields at the surface, while the interior volume the unknowns are the total fields. Continuity of the tangential fields at the boundary, as required by Maxwell's equations, is imposed, thus coupling the two methods to obtain a consistent solution. The coupling term is expressed by a surface integral formed by the dot product of a FE basis function and an IE testing function, or viceversa. By choosing the boundary to be a surface of revolution and by making a convenient selection of IE basis (testing) functions, it is possible to evaluate the integrals analytically on surfaces such as curved triangles, curved quadrilaterals and curved pentagons. We will illustrate the salient steps involved in setting up and carrying out these integrals and discuss what class of basis (testing) functions and analytic surfaces of revolution they are applicable to. Analytic calculations offer the advantage of better accuracy than purely numerical ones, and, when combined with them, often shed light on issues of numerical convergence and limiting values. Furthermore, they may reduce computation time and storage requirements.

Zuffada, C.↗
NASA NTRS1998

Optimization of Supersonic Transport Trajectories

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗
NASA NTRS1998

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗
NASA NTRS1999

Development of a Multiobjective Optimization Procedure for Sonic Boom Minimization

A design optimization procedure for improved sonic boom and aerodynamic performance of high speed aircraft is presented. The multiobjective optimization procedure simultaneously minimizes the sonic boom at a given distance from the aircraft and the drag-to-lift ratio (C(sub D)/C(sub L)) Of the aircraft. Upper and lower bounds are also imposed on the lift coefficient. The Kreisselmeier - Steinhauser function is used for the multiobjective optimization formulation. A discrete semi-analytical aerodynamic sensitivity analysis procedure coupled with an analytical grid sensitivity analysis technique is used for evaluating design sensitivities. The use of the semi-analytical sensitivity analysis techniques results in significant computational savings. The flow equations are solved using a three-dimensional parabolized Navier-Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. A nonlinear programming technique and an approximate analysis procedure are used for the optimization. The optimization procedure developed is applied to the design of two high speed configurations, namely, a doubly swept wing-body configuration and a delta wing-body configuration. For the two sweep case only, minimization of the first peak in the pressure signature is performed first by optimizing only the nose radius and length of the aircraft. Minimization of the second peak in the pressure signature is performed next by optimizing only the wing geometric parameters. Significant improvements are obtained in the sonic boom characteristics and the aerodynamic performance of the wing-body configurations.

Narayan, J. R.↗
NASA NTRS2002

A Systems Approach to the Solid Lubrication of Foil Air Bearings for Oil-Free Turbomachinery

Foil air bearings are self-acting hydrodynamic bearings which rely upon solid lubricants to reduce friction and minimize wear during sliding which occurs at start-up and shut-down when surface speeds are too low to allow the formation of a hydrodynamic air film. This solid lubrication is typically accomplished by coating the non-moving foil surface with a thin, soft polymeric film. The following paper introduces a systems approach in which the solid lubrication is provided by a combination of self lubricating shaft coatings coupled with various wear resistant and lubricating foil coatings. The use of multiple materials, each providing different functions is modeled after oil-lubricated hydrodynamic sleeve bearing technology which utilizes various coatings and surface treatments in conjunction with oil lubricants to achieve optimum performance. In this study, room temperature load capacity tests are performed on journal foil air bearings operating at 14,000 rpm. Different shaft and foil coating technologies such as plasma sprayed composites, ceramic, polymer and inorganic lubricant coatings are evaluated as foil bearing lubricants. The results indicate that bearing performance is improved through the individual use of the lubricants and treatments tested. Further, combining several solid lubricants together yielded synergistically better results than any material alone.

DellaCorte, Christopher↗
NASA NTRS1998

Six axis force feedback input device

The present invention is a low friction, low inertia, six-axis force feedback input device comprising an arm with double-jointed, tendon-driven revolute joints, a decoupled tendon-driven wrist, and a base with encoders and motors. The input device functions as a master robot manipulator of a microsurgical teleoperated robot system including a slave robot manipulator coupled to an amplifier chassis, which is coupled to a control chassis, which is coupled to a workstation with a graphical user interface. The amplifier chassis is coupled to the motors of the master robot manipulator and the control chassis is coupled to the encoders of the master robot manipulator. A force feedback can be applied to the input device and can be generated from the slave robot to enable a user to operate the slave robot via the input device without physically viewing the slave robot. Also, the force feedback can be generated from the workstation to represent fictitious forces to constrain the input device's control of the slave robot to be within imaginary predetermined boundaries.

Ohm, Timothy↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Diskin, Boris↗
NASA NTRS2005

Stroboscopic Interferometer for Measuring Mirror Vibrations

Stroboscopic interferometry is a technique for measuring the modes of vibration of mirrors that are lightweight and, therefore, unavoidably flexible. The technique was conceived especially for modal characterization of lightweight focusing mirror segments to be deployed in outer space; however, the technique can be applied to lightweight mirrors designed for use on Earth as well as the modal investigation of other optical and mechanical structures. To determine the modal structure of vibration of a mirror, it is necessary to excite the mirror by applying a force that varies periodically with time at a controllable frequency. The excitation can utilize sinusoidal, square, triangular, or even asynchronous waveforms. Because vibrational modes occur at specific resonant frequencies, it is necessary to perform synchronous measurements and sweep the frequency to locate the significant resonant modes. For a given mode it is possible to step the phase of data acquisition in order to capture the modal behavior over a single cycle of the resonant frequency. In order to measure interferometrically the vibrational response of the mirror at a given frequency, an interferometer must be suitably aligned with the mirror and adjustably phase-locked with the excitation signal. As in conventional stroboscopic photography, the basic idea in stroboscopic interferometry is to capture an image of the shape of a moving object (in this case, the vibrating mirror) at a specified instant of time in the vibration cycle. Adjusting the phase difference over a full cycle causes the interference fringes to vary over the full range of motion for the mode at the excitation frequency. The interference-fringe pattern is recorded as a function of the phase difference, and, from the resulting data, the surface shape of the mirror for the given mode is extracted. In addition to the interferometer and the mirror to be tested, the equipment needed for stroboscopic interferometry includes an arbitrary-function generator (that is, a signal generator), an oscilloscope, a trigger filter, and an advanced charge-coupled-device (CCD) camera. The optical components are positioned to form a pupil image of the mirror under test on the CCD chip, so that the interference pattern representative of the instantaneous mirror shape is imaged on the CCD chip.

Stahl, H. Philip↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS1961

A Study of the Free Oscillations of the Earth

Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

MacDonald, Gordon J. F.↗
NASA NTRS2013

Radiation Belt Electron Dynamics Driven by Large-Amplitude Whistlers

Acceleration of radiation belt electrons driven by oblique large-amplitude whistler waves is studied. We show analytically and numerically that this is a stochastic process; the intensity of which depends on the wave power modified by Bessel functions. The type of this dependence is determined by the character of the nonlinear interaction due to coupling between action and phase. The results show that physically significant quantities have a relatively weak dependence on the wave power.

whistlers↗
NASA NTRS2014

Magnetosphere-Ionosphere Energy Interchange in the Electron Diffuse Aurora

The diffuse aurora has recently been shown to be a major contributor of energy flux into the Earth's ionosphere. Therefore, a comprehensive theoretical analysis is required to understand its role in energy redistribution in the coupled ionosphere-magnetosphere system. In previous theoretical descriptions of precipitated magnetospheric electrons (E is approximately 1 keV), the major focus has been the ionization and excitation rates of the neutral atmosphere and the energy deposition rate to thermal ionospheric electrons. However, these precipitating electrons will also produce secondary electrons via impact ionization of the neutral atmosphere. This paper presents the solution of the Boltzman-Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E greater than 600 eV) and their ionosphere-magnetosphere coupling processes. In this article, we discuss for the first time how diffuse electron precipitation into the atmosphere and the associated secondary electron production participate in ionosphere-magnetosphere energy redistribution.

Diffuse aurora↗
NASA NTRS1997

[Photodissociation of Acetylene and Acetone using Step-Scan Time-Resolved FTIR Emission Spectroscopy]

The photodissociation of acetylene and acetone was investigated as a function of added quenching gas pressures using step-scan time-resolved FTIR emission spectroscopy. Its main components consist of Bruker IFS88, step-scan Fourier Transform Infrared (FTIR) spectrometer coupled to a flow cell equipped with Welsh collection optics. Vibrationally excited C2H radicals were produced from the photodissociation of acetylene in the unfocused experiments. The infrared (IR) emission from these excited C2H radicals was investigated as a function of added argon pressure. Argon quenching rate constants for all C2H emission bands are of the order of 10(exp -13)cc/molecule.sec. Quenching of these radicals by acetylene is efficient, with a rate constant in the range of 10(exp -11) cc/molecule.sec. The relative intensity of the different C2H emission bands did not change with the increasing argon or acetylene pressure. However, the overall IR emission intensity decreased, for example, by more than 50% when the argon partial pressure was raised from 0.2 to 2 Torr at fixed precursor pressure of 160mTorr. These observations provide evidence for the formation of a metastable C2H2 species, which are collisionally quenched by argon or acetylene. Problems encountered in the course of the experimental work are also described.

McLaren, Ian A.↗
NASA NTRS1978

Engineering description of the OMS/RCS/DAP modes used in the HP-9825A High Fidelity Relative Motion Program (HFRMP)

Simplified mathematical models are reported for the space shuttle's Orbital Maneuvering System (OMS), Reaction Control System (RCS), and on-orbit Digital Autopilot (DAP) that have been incorporated in the High-Fidelity Relative Motion Program (HFRMP) for the HP-9825A desk-top calculator. Comparisons were made between data generated by the HFRMP and by the Space Shuttle Functional Simulator (SSFS), which models the cited shuttle systems in much greater detail. These data include propellant requirements for representative translational maneuvers, rotational maneuvers, and attitude maintenance options. Also included are data relating to on-orbit trajectory deviations induced by RCS translational cross coupling. Potential close-range stationkeeping problems that are suggested by HFRMP simulations of 80 millisecond (as opposed to 40 millisecond) DAP cycle effects are described. The principal function of the HFRMP is to serve as a flight design tool in the area of proximity operations.

Wilson, S. W.↗
NASA NTRSDate not supplied

Analysis of Transonic Unsteady Aerodynamic Environments using Unsteady Pressure Sensitive Paint for the Space Launch System Block 1 Cargo Launch Vehicle

Predicting launch vehicle unsteady aerodynamic loads due to buffet remains a significant challenge. Current practices for modeling buffet environments involve the development of buffet forcing functions using discrete unsteady pressure measurements acquired during wind-tunnel tests. These practices often result in significant uncertainty in buffet environments for coupled loads analyses due to the complex spatio-temporal nature of the unsteady pressure field and the challenge of its estimation using discrete sensors. Unsteady pressure sensitive paint, on the other hand, can provide unsteady pressure data at a comparatively high spatial density and may overcome the challenge of unsteady pressure field estimation with discrete sensors and lead to improvements in the development of buffet forcing functions. In this paper, comparisons of the fluctuating pressure field are made for the Space Launch System Block 1 cargo launch vehicle measured using unsteady pressure sensitive paint and pressure transducers.

buffet↗
NASA NTRSDate not supplied

Analysis of Transonic Unsteady Aerodynamic Environments using Unsteady Pressure Sensitive Paint for the Space Launch System Block 1 Cargo Launch Vehicle

Predicting launch vehicle unsteady aerodynamic loads due to buffet remains a significant challenge. Current practices for modeling buffet environments involve the development of buffet forcing functions using discrete unsteady pressure measurements acquired during wind-tunnel tests. These practices often result in significant uncertainty in buffet environments for coupled loads analyses due to the complex spatio-temporal nature of the unsteady pressure field and the challenge of its estimation using discrete sensors. Unsteady pressure sensitive paint, on the other hand, can provide unsteady pressure data at a comparatively high spatial density and may overcome the challenge of unsteady pressure field estimation with discrete sensors and lead to improvements in the development of buffet forcing functions. In this paper, comparisons of the fluctuating pressure field are made for the Space Launch System Block 1 cargo launch vehicle measured using unsteady pressure sensitive paint and pressure transducers.

buffet↗
NASA NTRS1989

Extension-torsion coupling behavior of advanced composite tilt-rotor blades

An analytic model was developed to study the extension-bend-twist coupling behavior of an advanced composite helicopter or tilt-rotor blade. The outer surface of the blade is defined by rotating an arbitrary cross section about an initial twist axis. The cross section can be nonhomogeneous and composed of generally anisotropic materials. The model is developed based upon a three dimensional elasticity approach that is recast as a coupled two-dimensional boundary value problem defined in a curvilinear coordinate system. Displacement solutions are written in terms of known functions that represent extension, bending, and twisting and unknown functions for local cross section deformations. The unknown local deformation functions are determined by applying the principle of minimum potential energy to the discretized two-dimensional cross section. This is an application of the Ritz method, where the trial function family is the displacement field associated with a finite element (8-node isoparametric quadrilaterals) representation of the section. A computer program was written where the cross section is discretized into 8-node quadrilateral subregions. Initially the program was verified using previously published results (both three-dimensional elasticity and technical beam theory) for pretwisted isotropic bars with an elliptical cross section. In addition, solid and thin-wall multi-cell NACA-0012 airfoil sections were analyzed to illustrate the pronounced effects that pretwist, initial twist axis location, and spar location has on coupled behavior. Currently, a series of advanced composite airfoils are being modeled in order to assess how the use of laminated composite materials interacts with pretwist to alter the coupling behavior of the blade. These studies will investigate the use of different ply angle orientations and the use of symmetric versus unsymmetric laminates.

Kosmatka, J. B.↗