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At least 343 records · Page 19

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NASA NTRS1981

The influence of the interplanetary magnetic field and thermal pressure on the position and shape of the magnetopause

An ellipsoidal model, in which the size of an ellipsoid of revolution with a constant eccentricity is inversely proportional to the sixth root of the stream pressure of the solar wind, is used to represent the location of the dayside magnetopause and to study the influences of the interplanetary magnetic field and thermal pressure on its location. The effects of the IMF and thermal pressure on the location of the magnetopause are calculated analytically by using the Chapman-Ferraro theory. The changes in magnetopause size, shape and orientation caused by including the thermal pressure are inversely proportional to the square of the sonic Mach number of the solar wind and are sufficient to explain the observed slight departure of the magnetotail from the expected aberration due to the earth's orbital motion. The results suggest that little angular momentum is being carried away from the sun by the solar wind.

Zhuang, H. C.↗

NASA NTRS1980

A semi-analytic approach to the self induced motion of vortex sheets

The rolling up of the trailing vortex sheet produced by a wing of finite span was calculated as a series expansion in time. For a vorticity distribution corresponding to a wing with cusped tips, the shape of the sheet was found by summing the series using Pade approximants. The sheet remains analytic for some time but ultimately develops an exponential spiral at the tips. The centroid of vorticity was conserved to high accuracy.

Schwartz, L. W.↗

NASA NTRS2000

Determination of Interfacial Rheological Properties through Microgravity Oscillations of Bubbles and Drops

This report summarizes our derivations of analytical expressions for the frequencies and damping constants for small-amplitude axisymmetric shape oscillations of a liquid drop suspended in an immiscible fluid host in microgravity. In particular, this work addresses large Reynolds number shape oscillations and focuses on the surface rheological effects that arise from the presence of insoluble surfactants at the interface. Parameters characterizing viscous effects from the bulk phases, surface viscous effects, Marangoni effects from the surface advection and diffusion of surfactants, and the Gibbs elasticity are all considered and analyzed to determine the relative importance of each contribution. Supplementing the analytical treatment for small-amplitude oscillations, a numerical boundary integral equation formulation is developed for the study of large-amplittide axisymmetric oscillations of a drop in vacuum. The boundary integral formulation is an extension of classical potential flow theory and approximately accounts for viscous effects in the bulk fluid as well as the surface viscous and Marangoni effects resulting from an insoluble surfactant contaminating the interface. Theoretical and numerical results are presented for four distinct cases. These, range from the case when the effects of the surfactants are 'negligible' to 'large' when compared to the viscous effects in the bulk phases. The feasibility of the non-contact measurement of the surface parameters, using experimental observations for the oscillation frequencies and damping constants of drops and bubbles, is discussed.

Nadim, Ali↗

NASA NTRS1993

Experimental and analytical investigation of dynamic characteristics of extension-twist-coupled composite tubular spars

The results from a study aimed at improving the dynamic and aerodynamic characteristics of composite rotor blades through the use of extension-twist coupling are presented. A set of extension-twist-coupled composite spars was manufactured with four plies of graphite-epoxy cloth prepreg. These spars were noncircular in cross-section design and were therefore subject to warping deformations. Three different cross-sectional geometries were developed: D-shape, square, and flattened ellipse. Three spars of each type were fabricated to assess the degree of repeatability in the manufacturing process of extension-twist-coupled structures. Results from free-free vibration tests of the spars were compared with results from normal modes and frequency analyses of companion shell-finite-element models. Five global modes were identified within the frequency range from 0 to 2000 Hz for each spar. The experimental results for only one D-shape spar could be determined, however, and agreed within 13.8 percent of the analytical results. Frequencies corresponding to the five global modes for the three square spars agreed within 9.5, 11.6, and 8.5 percent of the respective analytical results and for the three elliptical spars agreed within 4.9, 7.7, and 9.6 percent of the respective analytical results.

Lake, Renee C.↗

DOE OSTI2021

Alpha Shape Analysis (ASA) Framework for Post- Clustering Property Determination in Atom Probe Tomographic Data

While application of clustering algorithms to atom probe tomography data have enabled quantification of solute clusters in terms of number density, size, and subcomposition there exist other properties (e.g., volume, surface area, and composition) that are better determined by defining an interface between the cluster and the surrounding matrix. The limitation in composition results from an ion selection step where the expected matrix ion types are omitted from the cluster search algorithm to enhance the contrast between the matrix and cluster and to reduce the complexity of the search. Previously, composition determination within solute clusters has utilized a secondary envelopment and erosion step on top of conventional methods such as maximum separation. In this work, we present a novel stochastic method that combines the particle identification fidelity of a conventional clustering algorithm with the analytical flexibility of mesh-based approaches through the generation of alpha shapes for each identified cluster. Furthermore, the corresponding mesh accounts for concave components of the clusters and determines the volume and surface area of the clusters; additionally, the mesh boundary is utilized to update the total composition according to the internal ions.

42 ENGINEERING↗

NASA NTRS1981

A semi-analytic approach to the self-induced motion of vortex sheets

The rolling-up of the trailing vortex sheet produced by a wing of finite span is calculated as a series expansion in time. For a vorticity distribution corresponding to a wing with cusped tips, the shape of the sheet is found by summing the series using Pade approximants. The sheet remains analytic for some time but ultimately develops an exponential spiral at the tips. The centroid of vorticity is conserved to high accuracy.

Schwartz, L. W.↗

NASA NTRS2000

Efficient Simulation of Wing Modal Response: Application of 2nd Order Shape Sensitivities and Neural Networks

At the preliminary design stage of a wing structure, an efficient simulation, one needing little computation but yielding adequately accurate results for various response quantities, is essential in the search of optimal design in a vast design space. In the present paper, methods of using sensitivities up to 2nd order, and direct application of neural networks are explored. The example problem is how to decide the natural frequencies of a wing given the shape variables of the structure. It is shown that when sensitivities cannot be obtained analytically, the finite difference approach is usually more reliable than a semi-analytical approach provided an appropriate step size is used. The use of second order sensitivities is proved of being able to yield much better results than the case where only the first order sensitivities are used. When neural networks are trained to relate the wing natural frequencies to the shape variables, a negligible computation effort is needed to accurately determine the natural frequencies of a new design.

Kapania, Rakesh K.↗

DOE OSTI2020

Large-d phase transitions in holographic mutual information

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in G N in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large- d , we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large- d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large- d expansion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight into the character of high-aspect-ratio stellarator shapes, such as the dependence of the rotational transform and the plasma beta limit on geometrical properties of the resulting flux surfaces. The approach developed here is based on an asymptotic expansion on the inverse aspect ratio of the ideal magnetohydrodynamics equation. The analysis is simplified by using an orthogonal coordinate system relative to the Frenet–Serret frame at the magnetic axis. The magnetic field vector, the toroidal magnetic flux, the current density, the field line label and the rotational transform are derived at arbitrary order in the expansion parameter. Moreover, a comparison with a near-axis expansion formalism employing an inverse coordinate method based on Boozer coordinates (the so-called Garren–Boozer construction) is made, where both methods are shown to agree at lowest order. Finally, as a practical example, a numerical solution using a W7-X equilibrium is presented, and a comparison between the lowest-order solution and the W7-X magnetic field is performed.

Physics↗

NASA NTRS1971

Nonlinear, nonlaminar-3D computation of electron motion through the output cavity of a klystron

The equations of motion used in the computation are discussed along with the space charge fields and the integration process. The following assumptions were used as a basis for the computation: (1) The beam is divided into N axisymmetric discs of equal charge and each disc into R rings of equal charge. (2) The velocity of each disc, its phase with respect to the gap voltage, and its radius at a specified position in the drift tunnel prior to the interaction gap is known from available large signal one dimensional programs. (3) The fringing rf fields are computed from exact analytical expressions derived from the wave equation assuming a known field shape between the tunnel tips at a radius a. (4) The beam is focused by an axisymmetric magnetic field. Both components of B, that is B sub z and B sub r, are taken into account. (5) Since this integration does not start at the cathode but rather further down the stream prior to entering the output cavity it is assumed that each electron moved along a laminar path from the cathode to the start of integration.

Albers, L. U.↗

NASA NTRS1978

Analytical design of a contoured wind-tunnel liner for supercritical testing

The present analytical design procedure is being developed in order to determine the shape of a contoured nonporous wind tunnel liner for use in the Ames 12-foot pressure wind tunnel test of a large chord, laminar flow control, swept wing panel which has a supercritical airfoil section. This procedure is applicable to the two-dimensional streamlined tunnel problem wall shape with that found experimentally.

Newman, P. A.↗

NASA NTRS1986

SR-7A aeroelastic model design report

A scale model was designed to simulate the aeroelastic characteristics and performance of the 2.74 meter (9 ft.) diameter SR-7L blade. The procedures used in this model blade design are discussed. Included in this synopsis is background information concerning scaling parameters and an explanation of manufacturing limitations. A description of the final composite model blade, made of titanium, fiberglass, and graphite, is provided. Analytical methods for determining the blade stresses, natural frequencies and mode shapes, and stability are discussed at length.

Nagle, D.↗

NASA NTRS1989

Problems in determining the surface density of the Galactic disk

A new method is presented for determining the local surface density of the Galactic disk from distance and velocity measurements of stars toward the Galactic poles. The procedure is fully three-dimensional, approximating the Galactic potential by a potential of Staeckel form and using the analytic third integral to treat the tilt and the change of shape of the velocity ellipsoid consistently. Applying the procedure to artificial data superficially resembling the K dwarf sample of Kuijken and Gilmore (1988, 1989), it is shown that the current best estimates of local disk surface density are uncertain by at least 30 percent. Of this, about 25 percent is due to the size of the velocity sample, about 15 percent comes from uncertainties in the rotation curve and the solar galactocentric distance, and about 10 percent from ignorance of the shape of the velocity distribution above z = 1 kpc, the errors adding in quadrature. Increasing the sample size by a factor of 3 will reduce the error to 20 percent. To achieve 10 percent accuracy, observations will be needed along other lines of sight to constrain the shape of the velocity ellipsoid.

Statler, Thomas S.↗

NASA NTRS1991

On the solution of a lubrication problem with particulate solids

The lubrication characteristic of a fluid with solid particles is studied using the continuum theory of mixtures. The governing equations are formulated and appropriate boundary conditions are introduced for an arbitrary-shaped lubricant film thickness. As a special case, closed-form analytical perturbation solutions for pressure and shear stress are obtained for a mixture of a conventional oil and solid particles with small values of solid-volume fraction sheared in the clearance space of an infinitely long slider bearing. It is found that when compared with a pure fluid, the mixture of the fluid and solid generates a higher pressure and therefore a higher load-carrying capacity with the added advantage of a reduction in the coefficient of friction.

Dai, F.↗

NASA NTRS1990

Steady-state thermal-solutal convection and diffusion in a simulated float zone

Models describing the steady-state thermal diffusion in a pure system, the thermal-solutal diffusion in a binary system, and heat and momentum transverse in a pure system are presented. The geometry of the model is described by a 2D Cartesian coordinate system that is applicable for crystal sheets. The melting, solidifying, and melt/gas interfacial shapes as well as the thermal, flow, and solutal profiles are analytically evaluated as functions of the heat and ambient temperature profiles and material properties. The solution procedure involves a coupled asymptotic/numerical approach which reduces the coupled set of partial differential equations to ordinary type. The results should be applicable in situations where melt flows are not intense enough to change the thermal field in pure systems, or where the physical properties of the melt are such that the convective field is decoupled from the thermal field, the latter being established primarily by diffusion.

Young, G. W.↗

NASA NTRS1992

Parallel-vector design sensitivity analysis in structural dynamics

This paper presents a parallel-vector algorithm for sensitivity calculations in linear structural dynamics. The proposed alternative formulation works efficiently with the reduced system of dynamic equations, since it eliminates the need for expensive and complicated based-vector derivatives, which are required in the conventional reduced system formulation. The relationship between the alternative formulation and the conventional reduced system formulation has been established, and it has been proven analytically that the two approaches are identical when all the mode shapes are included. This paper validates the proposed alternative algorithm through numerical experiments, where only a small number of mode shapes are used. In addition, a modified mode acceleration method is presented, thus not only the displacements but also the velocities and accelerations are shown to be improved.

Zhang, Y.↗

NASA NTRS1994

Prediction of particulate contamination on aperture window

This paper presents an analysis to predict the effects of light scattering by surface particles on the sensor window of a missile during ascent flight. The particulate contaminant distribution on the window is calculated by tallying the number of particles in a set of size ranges. The particulate contamination at the end of the mission is predicted by adding the contributions from the events of ground and flight operations. The surface particle redistributions caused by vibroacoustically induced surface acceleration was found to contribute the most of the particulate surface contamination. The analytical surface obscuration calculation with a set of particle counts was compared to the results of image analyzer measurement. The analytical results, which were calculated with a given function of particle shape depending on the size, were more conservative than the measurement. A scattering calculation using a verified BSDF model showed that the scattering was less than 0.001 at 20 off the direction of the incident light in the mid IR wavelength when the surfaces were at Level 300 initially.

Lee, Aleck L.↗

NASA NTRS1995

Aerodynamic shape optimization of wing and wing-body configurations using control theory

This paper describes the implementation of optimization techniques based on control theory for wing and wing-body design. In previous studies it was shown that control theory could be used to devise an effective optimization procedure for airfoils and wings in which the shape and the surrounding body-fitted mesh are both generated analytically, and the control is the mapping function. Recently, the method has been implemented for both potential flows and flows governed by the Euler equations using an alternative formulation which employs numerically generated grids, so that it can more easily be extended to treat general configurations. Here results are presented both for the optimization of a swept wing using an analytic mapping, and for the optimization of wing and wing-body configurations using a general mesh.

Reuther, James↗