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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Alignment of velocity and field changes across tangential discontinuities in the solar wind

Three-dimensional IMP 8 and Voyager 2 plasma and field data are used to investigate the relative changes in direction of the velocity and magnetic field vectors across tangential discontinuities in the solar wind. It is found that Delta-v and Delta-B/rho exp 1/2 are closely aligned either parallel or antiparallel to each other in the sense associated with the propagation of Alfven waves or rotational discontinuities outward from the sun. This alignment is observed at all solar distances betwen 1 and 2.2 AU and is independent of the solar wind stream structure. Several possible causes of the effect are briefly discussed, including interplanetary turbulence, the propagation of large-amplitude Alfvenic fluctuations traveling independently through the solar wind on both sides of the discontinuities, and the propagation of surface waves on tangential discontinuities.

Neugebauer, M.↗
NASA NTRS1986

The construction and use of divergence free vector expansions for incompressible fluid flow calculations

For incompressible fluids the law of mass conservation reduces to a constraint on the velocity vector, namely that it be divergence free. This constraint has long been a source of great difficulty to the numericist seeking to discretize the Navier-Stokes and Euler equations. A spectral method is discussed which overcomes this difficulty. Its efficacy is demonstrated on some simple problems. The velocity is approximated by a finite sum of divergence free vectors, each of which satisfies the same boundary conditions as the velocity. Projecting the governing equation onto the space of inviscid vector fields eliminates the pressure term and produces a set of ordinary differential equations that must be solved for the coefficents in the velocity. The pressure can then be recovered if it is needed.

Mhuiris, N. M. G.↗
NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗
NASA NTRS1985

Preparation for microgravity science investigation of compound semiconductor crystal growth

Preparatory work on Bridgman directional solidification (BDS) of PbSnTe crystals prior to microgravity crystal growth experiments on Shuttle flights are reported. Gravitational effects become important in crystal growth when density gradients are present. The situation is critical in BDS of PbSnTe because of the necessity of obtaining homogeneous compositional distributions, which can be disturbed when convective processes occur. Numerical models have been defined which quantify the effects of convection in the crystal growth solution. The models were verified by earth-based crystal-growth tests in a two-zone furnace using equal concentrations of each of the elements. Data are provided to demonstrate the differences in composition among crystals grown at different orientations to the gravitational field vector.

Fripp, A. L.↗
NASA NTRS1986

Electromagnetic scattering theory

Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.

Bird, J. F.↗
NASA NTRS1986

A canonical expansion for nonlinear systems

The importance of differential geometry, particularly Lie brackets of vector fields, in the study of nonlinear systems is well established. Under very mild assumptions, it is shown that a real-analytic nonlinear system has an expansion in which the coefficients are computed in terms of Lie brackets. This expansion occurs in a special coordinate system. The concept of a pure feedback system is also explained. For control design involving a nonlinear system, one approach is to put the system in its canonical expansion and approximate by that part having only feedback paths.

Su, R.↗
NASA NTRS1987

Algebra and topology for applications to physics

The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.

Rozhkov, S. S.↗
NASA NTRS1986

Tangential discontinuities in the solar wind - Correlated field and velocity changes and the Kelvin-Helmholtz instability

Three-dimensional Helios plasma and field data are used to investigate the relative changes in direction of the velocity and magnetic field vectors across tangential discontinuities (TDs) in the solar wind at solar distances of 0.29-0.50 AU. It is found for TDs with large Delta-v and (Delta-B)/B that Delta-v and Delta-B are closely aligned with each other, in agreement with the unexpected results of previous studies of TDs observed at 1 AU and beyond. It is shown that this effect probably results from the destruction by the Kelvin-Helmholtz instability of TDs for which Delta-v and Delta-B are not aligned. The observed decrease in the number of interplanetary discontinuities with increasing solar distance may be associated with the growth of the Kelvin-Helmholtz instability with decreasing Alfven speed.

Neugebauer, M.↗
NASA NTRS1988

Numerical methods for incompressible viscous flows with engineering applications

A numerical scheme has been developed to solve the incompressible, 3-D Navier-Stokes equations using velocity-vorticity variables. This report summarizes the development of the numerical approximation schemes for the divergence and curl of the velocity vector fields and the development of compact schemes for handling boundary and initial boundary value problems.

Rose, M. E.↗
NASA NTRS1987

Rectangular subsonic jet flowfield study

The flowfield of a rectangular jet with 2:1 aspect ratio was studied at an axial Reynolds number of 127,000, using a three-dimensional laser anemometer. The flowfield surveys resulted in mean velocity vector field plots and contour plots of the Reynolds stress tensor components for the major and minor axes. These data contribute substantially to currently available data of jet flowfields.

Morrison, Gerald L.↗
NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x/t/) + the sum to m terms (i = 1) u sub i (t)g sub i (x/t/) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗
NASA NTRS1988

Two-dimensional interaction of vortices with a blade

The problem of blade-vortex interaction is studied experimentally and numerically. Vortices are generated in the laboratory by pitching an airfoil upstream of the model. LDV measurements are obtained in the neighborhood of the leading edge of the airfoil. Ensemble-averaged velocity vector fields and vorticity contours are thus constructed. A vortex is modeled numerically by a cloud of discrete ideal point vortices. The problem is solved via a Joukowski transformation. The interaction of distributed vorticity with the leading edge of the airfoil is examined.

Poling, David R.↗
NASA NTRS1988

Lightning initiation on aircraft in thunderstorms

The physical model of the initiation of lightning flashes by aircraft in thunderstorms is presented. The model is based on the 'bi-directional uncharged leader' concept by Kasemir, and is verified with airborne data from lightning strikes to an instrumented airplane (NASA F-106B and FAA CV-580). The characteristics of electromagnetic processes during lightning attachment are identified by comparison with those studied in natural flashes, those triggered by wire trailing rockets, and laboratory discharges. A triggered flash starts with either a negative corona or a positive leader that depends on the ambient electric field vector and the airplane form factor. The positive leader with continuous current that increases with time is followed in a few milliseconds by the negative stepped leader with current pulses of a few kA. The two leaders develop in space simultaneously and bi-directionally from the oppositely charged extremities of the airplane.

Mazur, Vladislav↗
NASA NTRS1987

Stochastic estimation of organized structures in turbulent channel flow

Linear stochastic estimation is used to approximate the conditional vector fields associated with high Reynolds stress producing events in numerically simulated turbulent channel flow. Joint probability density distributions of u-v are presented for y(+) between 1.35 and 180, and at each position the u-v values that make the greatest contributions to the average uv3 are used to define conditional ejection- and sweep-type events. In the y-z plane the conditional fields appear to be pairs of counter-rotating vortices. When the conditional event defined by the weighted probability density function is specified at a point close to the wall, the spacing and size of these eddies are consistent with the accepted wall streak spacing. As this point moves outwards, the eddy size increases significantly. An abrupt change in the flow angle occurs in the buffer layer and may indicate transition from streamwise oriented wall layer structures to hairpin vortices characterizing the outer layer.

Moin, P.↗
NASA NTRS1988

Lightning initiation on aircraft in thunderstorms

A physical model of the initiation of lightning flashes in thunderstorms is presented. The model is based on the bi-directional charged leader concept of Kasemir, and is verified with airborne data from lightning strikes to instrumented airplanes (NASA F-106B and FAA CV-580). The characteristics of electromagnetic processes during lightning attachment are identified by comparison with those studied in natural flashes, those triggered by wire trailing rockets, and laboratory discharges. A triggered flash starts with either a negative corona or a positive leader that depends on the ambient electric field vector and the airplane form factor. The positive leader with continuous current that increases with time is followed in a few milliseconds by the negative stepped leader with current pulses of a few kA. The two leaders develop in space simultaneously and bi-directionally from the oppositely charged extremities of the airplane.

Mazur, Vladislav↗
NASA NTRS1988

The magnetic field investigation on Cluster

The magnetic field investigation of the Cluster four-spacecraft mission is designed to provide intercalibrated measurements of the B magnetic field vector. The instrumentation and data processing of the mission are discussed. The instrumentation is identical on the four spacecraft. It consists of two triaxial fluxgate sensors and of a failure tolerant data processing unit. The combined analysis of the four spacecraft data will yield such parameters as the current density vector, wave vectors, and the geometry and structure of discontinuities.

Balogh, A.↗
NASA NTRS1988

Three-dimensional singular points in aerodynamics

When three-dimensional separation occurs on a body immersed in a flow governed by the incompressible Navier-Stokes equations, the geometrical surfaces formed by the three vector fields (velocity, vorticity and the skin-friction) and a scalar field (pressure) become interrelated through topological maps containing their respective singular points and extremal points. A mathematically consistent description of these singular points becomes inevitable when we want to study the geometry of the separation. A separated stream surface requires, for example, the existence of a saddle-type singular point on the skin-friction surface. This singular point is actually, in the proper language of mathematics, a saddle of index two. The index is a measure of the dimension of the outset (set leaving the singular point). Hence, when a saddle of index two is specified, a two dimensional surface that becomes separated from the osculating plane of the saddle is implied. The three-dimensional singular point is interpreted mathematically and the most common aerodynamical singular points are discussed through this perspective.

Unal, Aynur↗
NASA NTRS1987

Geometric foundations of the theory of feedback equivalence

A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.

Hermann, R.↗