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Results for “Analytic linearization”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Interchange instability of the earth's plasmapause

The factors that affect the interchange instability of the earth's plasmapause are investigated using an extension of Richmond's (1973) procedure based on computing individual particle motions. The effects of particle inertia, centrifugal force, and gravity are estimated. A general differential equation is derived for the time variation of the perturbation potential characterizing an electrostatic ripple with no field-aligned potential drop, which can be solved as an eigenvalue problem to find the linear growth rate. Approximate analytic solutions to this equation were obtained from which it was deduced that the interchange instability is caused by the sharp change in plasma pressure at the plasmapause; its growth rate is limited by ionospheric conductivity and, for very short wavelengths, by the inertia of the magnetospheric particles.

Huang, T. S.↗
NASA NTRS1991

Nonadiabatic and three-dimensional effects in compressible turbulent boundary layers

A defect stream function formulation for nonadiabatic flow with small crossflow is developed. The first-integral property of this formulation provides for two removal of the streamline curvature term in the governing equation so that the form of the reduced equation for small crossflow is the same as that for two dimensional flow. The combined law of the wall and wake is used in place of the no-slip boundary condition. The tangential velocity equation for law-of-the-wall flow is shown to be the same for three-dimensions as for two when the Boussinesq approximation applies, and a closed form solution for the crossflow angle in the inner region is obtained. Analytic solutions for nonadiabatic, compressible, equilibrium flow with a Clauser outer-region eddy-viscosity model are obtained, and excellent agreement with experimental skin friction and velocity profile data for nonadiabatic, compressible flat-plate flow is achieved. An analytic solution for a linear inner-region eddy-viscosity model is also obtained; the wake function part of this solution is found to be inconsistent with the empirically established law of the wake.

Barnwell, Richard W.↗
NASA NTRS1990

Polarization properties of non-symmetric retroreflectors

The on- and off-axis polarizing properties of asymmetric retroreflectors are studied in detail for various angles of incidence and for various incident linear polarization states. An analytic model is developed by applying Fresnel law to the incident and reflecting radiation on each facet of the retroreflector. It is shown that the polarization state of retroreflected radiation is a sensitive function of incident angle, incident polarization rate, and retroreflector material. These characteristics may be applicable to the determination of the relative angular position between the retroreflector and the analyzer.

An, C.-H.↗
NASA NTRS1991

Continuum modeling of catastrophic collisions

A two dimensional hydrocode based on 2-D SALE was modified to include strength effects and fragmentation equations for fracture resulting from tensile stress in one dimension. Output from this code includes a complete fragmentation summary for each cell of the modeled object: fragment size (mass) distribution, vector velocities of particles, peak values of pressure and tensile stress, and peak strain rates associated with fragmentation. Contour plots showing pressure and temperature at given times within the object are also produced. By invoking axial symmetry, three dimensional events can be modeled such as zero impact parameter collisions between asteroids. The code was tested against the one dimensional model and the analytical solution for a linearly increasing tensile stress under constant strain rate.

Ryan, Eileen V.↗
NASA NTRS1992

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

In the area of solar physics, new calculations of the acoustic wave energy fluxes generated in the solar convective zone was performed. The original theory developed was corrected by including a new frequency factor describing temporal variations of the turbulent energy spectrum. We have modified the original Stein code by including this new frequency factor, and tested the code extensively. Another possible source of the mechanical energy generated in the solar convective zone is the excitation of magnetic flux tube waves which can carry energy along the tubes far away from the region. The problem as to how efficiently those waves are generated in the Sun was recently solved. The propagation of nonlinear magnetic tube waves in the solar atmosphere was calculated, and mode coupling, shock formation, and heating of the local medium was studied. The wave trapping problems and evaluation of critical frequencies for wave reflection in the solar atmosphere was studied. It was shown that the role played by Alfven waves in the wind accelerations and the coronal hole heating is dominant. Presently, we are performing calculations of wave energy fluxes generated in late-type dwarf stars and studying physical processes responsible for the heating of stellar chromospheres and coronae. In the area of physics of waves, a new analytical approach for studying linear Alfven waves in smoothly nonuniform media was recently developed. This approach is presently being extended to study the propagation of linear and nonlinear magnetohydrodynamic (MHD) waves in stratified, nonisothermal and solar atmosphere. The Lighthill theory of sound generation to nonisothermal media (with a special temperature distribution) was extended. Energy cascade by nonlinear MHD waves and possible chaos driven by these waves are presently considered.

Musielak, Z. E.↗
NASA NTRS1992

Reconnection of stressed magnetic fields

It is shown that magnetized plasma configurations under magnetic stress relax irreversibly to the state of minimum stress at a rate that is essentially Alfvenic provided a magnetic null is present. The relaxation is effected by the reconnection at the field null and proceeds at a rate proportional to the absolute value of ln(eta) exp-1, where eta is the resistivity. An analytic calculation in the linear regime is presented.

Hassam, A. B.↗
NASA NTRS1992

A comparative analysis of two land surface heterogeneity representations

Two contrasting representations of land surface variability used in general circulation models (GCMs) are compared through an analysis of their corresponding surface energy balance equations. In one representation (the 'mixture' approach), different vegetation types are assumed to be homogeneously mixed over a grid square, so that the GCM atmosphere sees near-surface conditions pertaining to the mixture only. In the second representation (the 'mosaic' approach), different vegetation types are viewed as separate 'tiles' of a grid-square 'mosaic', and each tile interacts with the atmosphere independently. The mosaic approach is computationally simpler and in many ways more flexible than the mixture approach. Analytical solutions to the linearized energy balance equations and numerical solutions to the nonlinear equations both demonstrate that the mixture strategy, when applied to two coexisting vegetation types that differ only in canopy transpiration resistance, promotes both total turbulent flux and latent heat flux relative to the mosaic strategy. The effective differences between the strategies, however, are small over a wide range of conditions. In particular, the strategies are effectively equivalent when the transpiration resistances of the different vegetation types are of the same order of magnitude.

Koster, Randal D.↗
NASA NTRS1993

Magnetohydrodynamic wave propagation in one-dimensional nonhomogeneous, self-gravitating clouds

We study the propagation of magnetohydrodynamic (MHD) waves through nonhomogeneous, selfgravitating, magnetic media representative of molecular cloud environments and focus on the issues of cloud support and line profiles. Since the general treatment of this topic is burdened by a complex mathematical formalism, we consider simplifying geometries which yield analytical solutions in the linear wave limit. In particular, we study both magnetoacoustic and Alfven wave propagation along the density gradient in a one-imensional slab. Of specific relevance to molecular clouds, we find that the back reaction of the Alfven waves can provide a pressure along the direction of the magnetic field lines; this pressure can help support a density enhancement against gravitational collapse. Furthermore, we find that the velocity amplitudes of these waves increase as the density decreases, in rough agreement with observational estimates of line width versus density relations.

Fatuzzo, Marco↗
NASA NTRS1995

Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers

The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.

Gajjar, J. S. B.↗
NASA NTRS1994

An analytical and experimental investigation of the response of the curved, composite frame/skin specimens

Six-foot diameter, semicircular graphite/epoxy specimens representative of generic aircraft frames were loaded quasi-statistically to determine their load response and failure mechanisms for large deflections that occur in airplanes crashes. These frame/skin specimens consisted of a cylindrical skin section co-cured with a semicircular I-frame. The skin provided the necessary lateral stiffness to keep deformations in the plane of the frame in order to realistically represent deformations as they occur in actual fuselage structures. Various frame laminate stacking sequences and geometries were evaluated by statically loading the specimen until multiple failures occurred. Two analytical methods were compared for modeling the frame/skin specimens: a two-dimensional shell finite element analysis and a one-dimensional, closed-form, curved beam solution derived using an energy method. Flange effectivities were included in the beam analysis to account for the curling phenomenon that occurs in thin flanges of curved beams. Good correlation was obtained between experimental results and the analytical predictions of the linear response of the frames prior to the initial failure. The specimens were found to be useful for evaluating composite frame designs.

Moas, Eduardo↗
NASA NTRS1999

A "Kanes's Dynamics" Model for the Active Rack Isolation System

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an appropriate isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller. ARIS provides the ISS response to the first requirement. This paper presents one response to the second, in a state-space framework intended to facilitate an optimal-controls approach to the third. The authors use "Kane's Dynamics" to develop an state-space, analytical (algebraic) set of linearized equations of motion for ARIS.

Hampton, R. David↗
NASA NTRS2001

A "Kane's Dynamics" Model for the Active Rack Isolation System

Many microgravity space science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (International Standard Payload Rack (ISPR)) level. Effective model-based vibration isolation requires: (1) an appropriate isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller. ARIS provides the ISS response to the first requirement. This paper presents one response to the second, in a state space framework intended to facilitate an optimal-controls approach to the third. The authors use "Kane's Dynamics" to develop a state-space, analytical (algebraic) set of linearized equations of motion for ARIS.

Hampton, R. D.↗
NASA NTRS2000

Nonlinear Local Bending Response and Bulging Factors for Longitudinal and Circumferential Cracks in Pressurized Cylindrical Shells

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.

Young, Richard D.↗
NASA NTRS2003

An Improved Green's Function for Ion Beam Transport

Ion beam transport theory allows testing of material transmission properties in the laboratory environment generated by particle accelerators. This is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are the main emphasis of the present work. In consequence, an analytic solution of the linear Boltzmann equation is pursued in the form of a Green's function allowing flexibility in application to a broad range of boundary value problems. It has been established that simple solutions can be found for the high charge and energy (HZE) by ignoring nuclear energy downshifts and dispersion. Such solutions were found to be supported by experimental evidence with HZE ion beams when multiple scattering was added. Lacking from the prior solutions were range and energy straggling and energy downshift with dispersion associated with nuclear events. Recently, we have found global solutions including these effects providing a broader class of HZE ion solutions.

Tweed, J.↗
NASA NTRS2003

Modeling and Evaluation of Miles-in-Trail Restrictions in the National Air Space

Miles-in-trail restrictions impact flights in the national air space on a daily basis and these restrictions routinely propagate between adjacent Air Route Traffic Control Centers. Since overly restrictive or ineffective miles-in-trail restrictions can reduce the overall efficiency of the national air space, decision support capabilities that model miles-in-trail restrictions should prove to be very beneficial. This paper presents both an analytical formulation and a linear programming approach for modeling the effects of miles-in-trail restrictions. A methodology for monitoring the conformance of an existing miles-in-trail restriction is also presented. These capabilities have been implemented in the Future ATM Concepts Evaluation Tool for testing purposes. To allow alternative restrictions to be evaluated in post-operations, a new mode of operation, which is referred to as the hybrid-playback mode, has been implemented in the simulation environment. To demonstrate the capabilities of these new algorithms, the miles-in-trail restrictions, which were in effect on June 27, 2002 in the New York Terminal Radar Approach Control, are examined. Results from the miles-in-trail conformance monitoring functionality are presented for the ELIOT, PARKE and WHITE departure fixes. In addition, the miles-in-trail algorithms are used to assess the impact of alternative restrictions at the PARKE departure fix.

Grabbe, Shon↗
NASA NTRS2004

An improved Green's function for ion beam transport

Ion beam transport theory allows testing of material transmission properties in the laboratory environment generated by particle accelerators. This is a necessary step in materials development and evaluation for space use. The approximations used in solving the Boltzmann transport equation for the space setting are often not sufficient for laboratory work and those issues are the main emphasis of the present work. In consequence, an analytic solution of the linear Boltzmann equation is pursued in the form of a Green's function allowing flexibility in application to a broad range of boundary value problems. It has been established that simple solutions can be found for high charge and energy (HZE) ions by ignoring nuclear energy downshifts and dispersion. Such solutions were found to be supported by experimental evidence with HZE ion beams when multiple scattering was added. Lacking from the prior solutions were range and energy straggling and energy downshift with dispersion associated with nuclear events. Recently, we have found global solutions including these effects providing a broader class of HZE ion solutions. c2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

NASA Center LaRC↗
NASA NTRS2017

Digital Cellular Solid Pressure Vessels: A Novel Approach for Human Habitation in Space

It is widely assumed that human exploration beyond Earth's orbit will require vehicles capable of providing long duration habitats that simulate an Earth-like environment - consistent artificial gravity, breathable atmosphere, and sufficient living space- while requiring the minimum possible launch mass. This paper examines how the qualities of digital cellular solids - high-performance, repairability, reconfigurability, tunable mechanical response - allow the accomplishment of long-duration habitat objectives at a fraction of the mass required for traditional structural technologies. To illustrate the impact digital cellular solids could make as a replacement to conventional habitat subsystems, we compare recent proposed deep space habitat structural systems with a digital cellular solids pressure vessel design that consists of a carbon fiber reinforced polymer (CFRP) digital cellular solid cylindrical framework that is lined with an ultra-high molecular weight polyethylene (UHMWPE) skin. We use the analytical treatment of a linear specific modulus scaling cellular solid to find the minimum mass pressure vessel for a structure and find that, for equivalent habitable volume and appropriate safety factors, the use of digital cellular solids provides clear methods for producing structures that are not only repairable and reconfigurable, but also higher performance than their conventionally manufactured counterparts.

Robotics↗
NASA NTRS1983

Development of finite analytic method for unsteady three-dimensional Navier-Stokes equation

A finite analytic (FA) numerical method is described for the numerical study of three-dimensional fluid flow problems. The FA method incorporates a local linearization scheme and a classical analytic solution technique to formulate the algebraic representation of unsteady three-dimensional Navier Stokes Equations. The twenty-eight point FA formula thus obtained gives all positive coefficients and desired upwind shift. Cubic cavity flows are then solved by the FA method for Reynolds numbers of 100 and 400. A simple variant of SIMPLER algorithm is used to resolve the pressure-velocity coupling problem. The numerical solutions show that the presence of side walls reduce the strength of the primary vortex when compared with the two-dimensional square cavity flows.

Chen, H.-C.↗