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NASA NTRS1983

The propagation of torsion along flux tubes subject to dynamical nonequilibrium

It is noted that the dynamical nonequilibrium of close-packed flux tubes is driven by the torsion in the individual tubes. Because of this, whenever tubes with the same sense of twisting come into contact, there is reconnection of their azimuthal field components. The reconnection consumes the local torsion, and this causes the propagation of torsional Alfven waves into the region from elsewhere along the tubes. The formal problem of the propagation of the torsion along twisted flux tubes is presented, along with some of the basic physical properties worked out in the limit of small torsion. It is noted that in tubes with finite twisting the propagation of torsional Alfven waves can be a more complicated phenomenon. Application to the sun suggests that the propagation of torsion from below the visible surface up into the corona is an important energy supply to the corona for a period of perhaps 10-20 hours after the emergence of the flux tubes through the surface of the sun, bringing up torsion from depths of 10,000 km or more. Torsion is of course continually furnished by the manipulation and shuffling of the field by the convection.

Parker, E. N.↗

NASA NTRS1983

Vibrations of blades with variable thickness and curvature by shell theory

A procedure for analyzing the vibrations of rotating turbomachinery blades has been previously developed. This procedure is based upon shallow shell theory, and utilizes the Ritz method to determine frequencies and mode shapes. However, it has been limited heretofore to blades of uniform thickness, uniform curvature, and/or twist and rectangular planform. The present work shows how the procedure may be generalized to eliminate the aforementioned restrictions. Nonrectangular planforms are dealt with by a suitable coordinate transformation. This, as well as variable thickness, curvature and twist, require using numerical integration. The procedure is demonstrated on four examples of cantilevered blades for which theoretical and experimental data have been previously published: (1) flat plate with spanwise taper, (2) flat plate with chordwise taper, (3) twisted plate with chordwise taper, and (4) cylindrical shell with chordwise taper.

Lee, J. K.↗

NASA NTRS1983

The influence of gyroscopic forces on the dynamic behavior and flutter of rotating blades

The structural dynamics of a cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever, to a tapered twisted cantilever of arbitrary cross-section. In every instance the formulation is from first principles using a finite element based on beam theory. Both ramp-type and periodic-type precessional angular displacements are considered. In concluding, forced vibrating and flutter are studied using the final and most sophisticated structural model. The analysis of stability is presented and a number of numerical examples are worked out.

Sisto, F.↗

NASA NTRS1984

Condensation modes in magnetized cylindrical plasmas

In order to understand the formation and stability of solar prominences, attention is given to the condensation modes of the thermal instability in a cylindriical plasma whose magnetic field has both potential (longitudinal) and nonpotential (poloidal) components forming helically twisted field lines. It is noted that the field line twist has a significant effect on the stability of condensation modes which are unstable if field lines are straight, but become stable as the twist increases. The problem is treated in a fully self-consistent way, to derive a second-order ordinary differential equation for radiative MHD stability. The approximation made by neglecting inertial terms is valid for coronal loop conditions if there is no singular surface in the plasma, and a simplified differential equation is derived. Attention is given to stability for the m = zero, 1, and 2 modes numerically, for various loop parameters.

An, C.-H.↗

NASA NTRS1985

Formation of prominences by condensation modes in magnetized cylindrical plasmas

Condensation modes in a magnetized cylindrical plasma are studied to shed light on the formation and stability of solar prominences. A rigorous mathematical derivation of the perturbation equation is developed, and the effect of field twist on the stability is studied for an equilibrium with uniform field twist, in which temperature increases, but density does not, as pressure increases. The results imply that prominences may form in globally magnetohydrodynamic-stable magnetic loops with very low field twist. Also, prominences are more likely to form in a region of weaker area-averaged magnetic field.

An, C.-H.↗

NASA NTRS1986

Magnetic nonequilibrium and current sheet formation

This paper investigates the equilibrium of a cluster of long, straight, twisted magnetic flux tubes extending in the z-direction in a highly conducting fluid, subject to the boundary condition that the cluster is surrounded by a uniform pressure P. It is shown that there is equilibrium only for axial symmetry, i.e., only for a single twisted flux tube. Any more complicated cluster of twisted tubes is subject to nonequilibrium reconnection of the transverse component of the field. The example provides another perspective on the general absence of equilibrium, and consequent rapid dissipation, of any magnetic field subject to random small-scale internal strains, such as the fields extending outward from the convective zones of stars.

Vainshtein, S. I.↗

NASA NTRS1987

Thermally induced stresses and deformations in angle-ply composite tubes

Cure-induced uniform temperature change effects on the stresses, axial expansion, and thermally-induced twist of four specific angle-ply tube designs are discussed with a view to the tubes' use as major space structure components. The stresses and deformations in the tubes are studied as a function of the four designs, the off-axis angle, and the single-material and hybrid reinforcing-material construction used. It is found that tube design has a minor influence on the stresses, axial stiffness, and axial thermal expansion characteristics, which are more directly a function of off-axis angle and material selection; tube design is, however, the primary influence in the definition of thermally-induced twist and torsional stiffness characteristics. None of the designs is free of thermally induced twist.

Hyer, M. W.↗

NASA NTRS1988

Parametric studies of advanced turboprops

The effects of geometric variables (sweep and twist) on the structural performance of advanced turboprops are investigated. The investigation is limited to aerodynamically efficient turboprops using an acceptable design configuration as a baseline. The baseline configuration is modified using a seven by seven array of independently varying sweep and twist parameters while maintaining acceptable aerodynamic efficiency. The turboprop structural performance is evaluated in terms of critical speeds, tip displacements, and vibration frequencies where geometric nonlinearities are included. The results obtained are presented in such a manner as to highlight the effects of sweep and twist on the structural performance of aerodynamically efficient turboprop configurations.

Fertis, D. G.↗

NASA NTRS1988

Development of an advanced high-speed rotor - Final results from the Advanced Flight Research Rotor program

The final results of the Advanced Flight Research Rotor (AFRR) study, a NASA sponsored research program, are summarized. First, the results of the initial phase of the AFRR program, consisting of the definition of a conventional rotor with planform and prescribed twist distributions, are briefly reviewed. The mechanism of the calculated performance benefit is then explained, and a detailed analysis of the prescribed twist distribution is presented. Recommendations are made on the practical means of approximating the prescribed twist on the actual rotor.

Jenks, Mark↗

NASA NTRS1988

Parametric studies of advanced turboprops

Maser, J. G.↗

NASA NTRS1988

Experimental study of thin-walled composite beams

Thin-walled rectangular section composite beams are built out of graphite-epoxy prepreg tape using an autoclave molding technique. Cantilevered beams are tested under static loads using a specially-built apparatus and bending slope and elastic twist at a station are measured using a laser system. Measured bending slope and bending-induced twist distributions are correlated with predicted results obtained using a simple beam analysis as well as a refined finite element analysis. Natural vibration characteristics at different rotational speeds are determined experimentally by testing beams in a specially built 10 ft diameter vacuum chamber. The rotor is excited by piezo-electric crystals and response is determined from strain gages mounted on the surface. For composite beams with bending-twisting couplings (symmetric layup), effects of section warping and transverse shear on structural response are found to be substantial. These results were substantiated by the analyses.

Chandra, Ramesh↗

NASA NTRS1992

Survey and analysis of research on supersonic drag-due-to-lift minimization with recommendations for wing design

A survey of research on drag-due-to-lift minimization at supersonic speeds, including a study of the effectiveness of current design and analysis methods was conducted. The results show that a linearized theory analysis with estimated attainable thrust and vortex force effects can predict with reasonable accuracy the lifting efficiency of flat wings. Significantly better wing performance can be achieved through the use of twist and camber. Although linearized theory methods tend to overestimate the amount of twist and camber required for a given application and provide an overly optimistic performance prediction, these deficiencies can be overcome by implementation of recently developed empirical corrections. Numerous examples of the correlation of experiment and theory are presented to demonstrate the applicability and limitations of linearized theory methods with and without empirical corrections. The use of an Euler code for the estimation of aerodynamic characteristics of a twisted and cambered wing and its application to design by iteration are discussed.

Carlson, Harry W.↗

NASA NTRS1992

Effects of constraint on crack growth under aircraft spectrum loading

The objective is to study the effects of constraint on fatigue crack growth under aircraft spectrum loading. A plasticity-induced crack-closure model that accounts for constraint variations during the transition from flat-to-slant crack growth was used to correlate crack-growth rate data under constant-amplitude loading and to calculate crack growth under simulated aircraft spectrum loading. The model was applied to several thin-sheet aluminum alloy materials. Under laboratory air conditions, the transition was shown to be related to the size of the cyclic plastic zone based on the effective stress-intensity factor range for several sheet materials and thicknesses. Results from three-dimensional, elastic-plastic, finite-element analyses of a flat, straight-through crack in a thin-sheet aluminum alloy specimen showed a constraint loss similar to that assumed in the model. Using test data and the closure model, the location of the constraint-loss regime in terms of growth rate and the value of the constraint factor at these rates were determined by trial and error. The model was then used to calculate crack growth under the TWIST spectrum. The calculated results agreed reasonably well with test data. In general, the model predicted shorter crack-growth lives than tests under the TWIST spectrum by about 40 percent. For the TWIST spectrum clipped at Level 3, the calculated lives were within about 20 percent. The results demonstrated that constraint variations, especially for thin-sheet alloys, should be accounted for to predict crack growth under typical aircraft spectra.

Newman, J. C., Jr.↗

NASA NTRS1992

Features of wavy vortices in a curved channel from experimental and numerical studies

Results are reported from an experimental study obtaining evidence of time-dependent, wavy vortex motions associated with undulating and twisting Dean vortices in a curved channel with 40-to-1 aspect ratio, and mild curvature (radius ratio = 0.979). The results are compared with direct numerical simulations of time-dependent 3D Navier-Stokes equations using boundary conditions in the spanwise and streamwise directions. When viewed in cross section, experimental visualizations of undulating and twisting vortex flows show rocking motion and changes in the direction of the flow between vortices that are like those observed in the simulations. Experimental spectra show that undulating vortices are replaced by the higher-frequency, shorter streamwise wavelength twisting vortices at higher Reynolds numbers. When undulating vortices are present, experimental power spectra and visualizations give frequencies that are somewhat lower than the most unstable frequencies predicted by linear stability analysis.

Ligrani, P. M.↗

NASA NTRS1990

Predicted and measured in-flight wing deformations of a forward-swept-wing aircraft

An electrooptical flight-deflection measurement system (FDMS) is described in terms of its use in structural testing of the composite forward-swept wing of the X-29 aircraft. The wing deflected shapes measured using the present system are compared to the shapes predicted by NASTRAN and other codes as well as data from ground-test load measurements. The electrooptical FDMS is based on a control unit, two receivers, a target driver, and 12-16 IR LED targets. The FDMS determines the in-flight deflected wing shapes at a variety of altitudes at Mach 0.9, and the results are compared to the analytically predicted wing-twist distributions. The FDMS data describe the predicted increasing streamwise twist with increasing dynamic pressure and suggest that the streamwise twist is more prevalent at the inboard measurement station than at the wing tip. This hook shape is not represented in the predicted data, and suggestions are given for improving the modeling of the X-29 wing.

Lokos, William A.↗

NASA NTRS1992

Topological variation in the magnetic field line at the dayside magnetopause

This paper uses normal mode analysis to examine topological changes in magnetic field lines at the magnetopause. For a modified Harris sheet, the normal modes include a symmetric solution (tearing mode) and an antisymmetric solution (twisting mode). Both modes form flux ropes. The tearing mode in the presence of shear flow is studied. By modeling the external region plasma with drift kinetic formalism, the growth rate of the tearing mode is found to be reduced by shear flow. On the other hand, the shear flow generates a Kelvin-Helmholtz instability which makes the magnetic field perturbation a twisting mode structure. When magnetopause parameters are used, it is difficult to induce a tearing mode in the presence of shear flow, though a shear flow twisting mode did grow under these conditions.

Wang, Zhi↗

NASA NTRS1956

The Interference Effects of a Body on the Spanwise Load Distributions of Two 45 Degree Sweptback Wings of Aspect Ratio 8.02 from Low-Speed Tests

Tests of two wing-body combinations have been conducted in the Langley 19-foot pressure tunnel at a Reynolds number of 4 x 10(exp 6) and a Mach number of 0.19 to determine the effects of the bodies on the wing span load distributions. The wings had 45 degrees sweepback of the quarter-chord line, aspect ratio 8.02, taper ratio 0.45, and incorporated 12-percent-thick airfoil sections streamwise. One wing was untwisted and uncambered whereas the second wing incorporated both twist and camber. Identical bodies of revolution, of 10:1 fineness ratio, having diameter-to-span ratios of 0.10, were mounted in mid-high-wing arrangements. The effects of wind incidence, wing fences, and flap deflection were determined for the plane uncambered wing. The addition of the body to the plane wing increased the exposed wing loading at a given lift coefficient as much as 10 percent with the body at 0 degrees incidence and 4 percent at 4 degrees incidence. The bending-moment coefficients at the wing-body juncture were increased about 2 percent with the body at 0 degrees incidence, whereas the increases were as much as 10 percent with the body at 4 degrees incidence. The spanwise load distributions due to the body on the plane wing as calculated by using a swept-wing method employing 19 spanwise lifting elements and control points generally showed satisfactory agreement with experiment. The spanwise load distributions due to body on the flapped plane wing and on the twisted and cambered wing were dissimilar to those obtained on the plane wing. Neither of the methods of calculation which were employed yielded distributions that agreed consistently with experiment for either the flapped plane wing or the twisted and cambered wing.

Martina, Albert P.↗

NASA NTRS1993

An improved CAMRAD model for aeroelastic stability analysis of the XV-15 with advanced technology blades

In pursuit of higher performance, the XV-15 Tiltrotor Research Aircraft was modified by the installation of new composite rotor blades. Initial flights with the Advanced Technology Blades (ATB's) revealed excessive rotor control loads that were traced to a dynamic mismatch between the blades and the aircraft control system. The analytical models of both the blades and the mechanical controls were extensively revised for use by the CAMRAD computer program to better predict aeroelastic stability and loads. This report documents the most important revisions and discusses their effects on aeroelastic stability predictions for airplane-mode flight. The ATB's may be flown in several different configurations for research, including changes in blade sweep and tip twist. The effects on stability of 1 deg and 0 deg sweep are illustrated, as are those of twisted and zero-twist tips. This report also discusses the effects of stiffening the rotor control system, which was done by locking out lateral cyclic swashplate motion with shims.

Acree, C. W., Jr.↗