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At least 937 records · Page 52

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NASA NTRS1989

Analytic theory for the selection of a two-dimensional needle crystal at arbitrary Peclet number

An accurate analytic theory is presented for the velocity selection of a two-dimensional needle crystal for arbitrary Peclet number for small values of the surface tension parameter. The velocity selection is caused by the effect of transcendentally small terms which are determined by analytic continuation to the complex plane and analysis of nonlinear equations. The work supports the general conclusion of previous small Peclet number analytical results of other investigators, though there are some discrepancies in details. It also addresses questions raised on the validity of selection theory owing to assumptions made on shape corrections at large distances from the tip.

Tanveer, S.↗

NASA NTRS1990

The Mach number of the cosmic flow - A critical test for current theories

A new cosmological, self-contained test using the ratio of mean velocity and the velocity dispersion in the mean flow frame of a group of test objects is presented. To allow comparison with linear theory, the velocity field must first be smoothed on a suitable scale. In the context of linear perturbation theory, the Mach number M(R) which measures the ratio of power on scales larger than to scales smaller than the patch size R, is independent of the perturbation amplitude and also of bias. An apparent inconsistency is found for standard values of power-law index n = 1 and cosmological density parameter Omega = 1, when comparing values of M(R) predicted by popular models with tentative available observations. Nonstandard models based on adiabatic perturbations with either negative n or small Omega value also fail, due to creation of unacceptably large microwave background fluctuations.

Ostriker, Jeremiah P.↗

NASA NTRS1990

Formula for the rms blur circle radius of Wolter telescope based on aberration theory

A formula for the rms blur circle for Wolter telescopes has been derived using the transverse ray aberration expressions of Saha (1985), Saha (1984), and Saha (1986). The resulting formula for the rms blur circle radius over an image plane and a formula for the surface of best focus based on third-, fifth-, and seventh-order aberration theory predict results in good agreement with exact ray tracing. It has also been shown that one of the two terms in the empirical formula of VanSpeybroeck and Chase (1972), for the rms blur circle radius of a Wolter I telescope can be justified by the aberration theory results. Numerical results are given comparing the rms blur radius and the surface of best focus vs the half-field angle computed by skew ray tracing and from analytical formulas for grazing incidence Wolter I-II telescopes and a normal incidence Cassegrain telescope.

Shealy, David L.↗

NASA NTRS1990

An introduction to chaos theory in CFD

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Pulliam, Thomas H.↗

NASA NTRS1990

Comparison of high-angle-of-attack slender-body theory and exact solutions for potential flow over an ellipsoid

The accuracy of high-alpha slender-body theory (HASBT) for bodies with elliptical cross-sections is presently demonstrated by means of a comparison with exact solutions for incompressible potential flow over a wide range of ellipsoid geometries and angles of attack and sideslip. The addition of the appropriate trigonometric coefficients to the classical slender-body theory decomposition yields the formally correct HASBT, and results in accuracies previously considered unattainable.

Hemsch, Michael J.↗

NASA NTRS1990

Barotropic instability with divergence - Theory and applications to Venus

IR images of Venus reveal a curious double-lobed hot spot in the polar region. Elson (1982) has suggested that this dipole represents a barotropic instability associated with a high-latitude jet. Unfortunately, the classical theory of barotropic instability cannot predict temperature variations. This paper generalizes the theory to include horizontal divergence, vertical motions, and temperature variations, and applies it to the stratosphere of Venus. The fastest-growing barotropic instability in the nominal model matches the observed dipole in period and horizontal temperature pattern. The accompanying wind variations are comparable to the speed of the mean jet, indicating strong nonlinear effects. It is concluded that the Venus dipole may represent the self-limited stage of a barotropic instability with divergence.

Dobrovolskis, Anthony R.↗

NASA NTRS1989

Correlation of theory to wind-tunnel data at Reynolds numbers below 500,000

This paper presents results obtained from two airfoil analysis methods compared with previously published wind tunnel test data at chord Reynolds numbers below 500,000. The analysis methods are from the Eppler-Somers airfoil design/analysis code and from ISES, the Drela-Giles Airfoil design/analysis code. The experimental data are from recent tests of the Eppler 387 airfoil in the NASA Langley Low Turbulence Pressure Tunnel. For R not less than 200,000, lift and pitching moment predictions from both theories compare well with experiment. Drag predictions from both theories also agree with experiment, although to different degrees. However, most of the drag predictions from the Eppler-Somers code are accompanied with separation bubble warnings which indicate that the drag predictions are too low. With the Drela-Giles code, there is a large discrepancy between the computed and experimental pressure distributions in cases with laminar separation bubbles, although the drag polar predictions are similar in trend to experiment.

Evangelista, Raquel↗

NASA NTRS1990

A new beam theory using first-order warping functions

Due to a certain type of loading and geometrical boundary conditions, each beam will respond differently depending on its geometrical form of the cross section and its material definition. As an example, consider an isotropic rectangular beam under pure bending. Plane sections perpendicular to the longitudinal axis of the beam will remain plane and perpendicular to the deformed axis after deformation. However, due to the Poisson effect, particles in the planes will move relative to each other resulting in a form of anticlastic deformation. In other words, even in pure bending of an isotropic beam, each cross section will deform in the plane. If the material of the beam above is replaced by a generally anisotropic material, then the cross sections will not only deform in the plane, but also out of plane. Hence, in general, both in-plane deformation and out-of-plane warping will exist and depend on the geometrical form and material definition of the cross sections and also on the loadings. For the purpose of explanation, an analogy is made. The geometrical forms of the bodies of each individual are unique. Hence, different sizes of clothes are needed. Finding the sizes of clothes for individuals is like determining the warping functions in beams. A new beam theory using first-order warping functions is introduced. Numerical examples will be presented for an isotropic beam with rectangular cross section. The theory can be extended for composite beams.

Ie, C. A.↗

NASA NTRS1989

Superaromatics: The key to a unified cosmic dust theory

The theory of Superaromatics, the key to a unified cosmic dust theory, was constructed by analyzing several thousand astronomical features covering every major aspect of astrophysics and astrochemistry relating to dust. To insure consistency between disciplines, the logical structure of the conclusions in each field was checked rather than accepting the current consensus. No substantial contradictory features are known to the author. The analysis falls into seven major parts: (1) kinetics of grain formation and destruction; (2) optical spectra of the interstellar medium (ISM); (3) meteorite interplanetary dust particle (IPD) chemistry; (4) structure and chemistry of the interstellar medium arising from surface catalysis; (6) dynamics of circumstellar and interstellar dust clouds, including galactic morphology; and (7) the chemistry and physics of previously unidentified compounds. Only tentative conclusions are presented here. The principle conclusion is that quantum mechanics as it is normally formulated is incomplete. The probable cause is that it is formulated with complex numbers rather than the more fundamental quaternion system. The manifestation in astrochemistry is that the most stable compounds are superaromatic and exotic enough to confound most classical analysis.

Manuel, Lawrence R.↗

NASA NTRS1991

Cockpit task management: A preliminary, normative theory

Cockpit task management (CTM) involves the initiation, monitoring, prioritizing, and allocation of resources to concurrent tasks as well as termination of multiple concurrent tasks. As aircrews have more tasks to attend to due to reduced crew sizes and the increased complexity of aircraft and the air transportation system, CTM will become a more critical factor in aviation safety. It is clear that many aviation accidents and incidents can be satisfactorily explained in terms of CTM errors, and it is likely that more accidents induced by poor CTM practice will occur in the future unless the issue is properly addressed. The first step in understanding and facilitating CTM behavior was the development of a preliminary, normative theory of CTM which identifies several important CTM functions. From this theory, some requirements for pilot-vehicle interfaces were developed which are believed to facilitate CTM. A prototype PVI was developed which improves CTM performance and currently, a research program is under way that is aimed at developing a better understanding of CTM and facilitating CTM performance through better equipment and procedures.

Funk, Ken↗

NASA NTRS1990

Receiving efficiency of monostatic pulsed coherent lidars. I - Theory. II - Applications

Pulsed coherent radars' receiving efficiency, eta, is presently investigated as a function of range z on the basis of a theory which relates eta(z) to both the transmitted laser intensity and the point-source receiving efficiency; this efficiency is calculated by a backward method employing the back-propagated local oscillator (BPLO) approach. The theory is applied to the ideal case, in order to study system optimization when both the transmitted and the BPLO fields at the antenna are Gaussian. In the second part of this work, eta(z) is calculated for various conditions of the NOAA/ERL Wave Propagation Laboratory CO2 Doppler lidar; the sensitivity of eta(z) to transmitted laser beam quality, telescope focal setting, telescope power, scanner astigmatism, and system misalignment.

Zhao, Yanzeng↗

NASA NTRS1991

A shock-layer theory based on thirteen-moment equations and DSMC calculations of rarefied hypersonic flows

Grad's thirteen-moment equations are applied to the flow behind a bow shock under the formalism of a thin shock layer. Comparison of this version of the theory with Direct Simulation Monte Carlo calculations of flows about a flat plate at finite attack angle has lent support to the approach as a useful extension of the continuum model for studying translational nonequilibrium in the shock layer. This paper reassesses the physical basis and limitations of the development with additional calculations and comparisons. The streamline correlation principle, which allows transformation of the 13-moment based system to one based on the Navier-Stokes equations, is extended to a three-dimensional formulation. The development yields a strip theory for planar lifting surfaces at finite incidences. Examples reveal that the lift-to-drag ratio is little influenced by planform geometry and varies with altitudes according to a 'bridging function' determined by correlated two-dimensional calculations.

Cheng, H. K.↗

NASA NTRS1989

Composite fracture using the normal stress ratio theory

Experiments were performed on center-notched specimens of unidirectional AS4/3501-6 graphite-epoxy subjected to varied far-field loading conditions. Specimens tested include on-axis and off-axis tensile coupons and Iosipescu shear specimens, allowing the study of normal, shear, and combined far-field loading conditions. From the tests, the direction of initial crack extension and the far-field stresses at crack initiation and fracture are obtained. The normal stress ratio theory is subsequently applied within a macroscopic-level homogeneous anisotropic stress solution to predict the direction of crack extension, critical stresses, and other crack growth behavior for the experiments. Comparison between experimental results and theoretical predictions indicates that application of the normal stress ratio theory within a macroscopic-level stress analysis has significant potential as an approach to modeling composite crack growth.

Beuth, J. L., Jr.↗

NASA NTRS1990

Analysis of cone-derived waveriders by hypersonic small-disturbance theory

Hypersonic small-disturbance theory is used to analyze slender waveriders derived from axisymmetric flows past circular cones. Viscous effects are accounted for by means of laminar boundary-layer theory. The shape of the waverider is determined by specifying the upper freestream surface, from which the lower compression surface can then be obtained. When this is done, the lift, drag, and pitching moment are determined in terms of quadratures over the shock layer in the base plane. They are functions of freestream Mach number, freestream Reynolds number based on the length of the waverider, some measure of slenderness, and other parameters relating to the shape of the waverider. The functional relationships can be cast in terms of similarity laws. The lift-to-drag ratio is determined for a wide range of shapes and parameters.

Rasmussen, Maurice L.↗

NASA NTRS1990

Theory on instability and transition

The fundamental fluid dynamics governing instability and transition to turbulence in boundary layers are considered, and attention is focused on the key aspects of nonlinear dynamics central to the transition process and to turbulent boundary-layer phenomena. Emphasis is placed on truly nonlinear theories, in which the boundary layer mean-flow profile is completely altered from its original form. Nonlinear TS transitions, Euler-stage interactions, and vortex/wave interactions are discussed, and compressible boundary layers are analyzed. Connections with experiments and computations are outlined, along with overall trends including the extension of the nonlinear theory and the advancement in the compressible and other flow regimes.

Smith, Frank T.↗

NASA NTRS1991

Polarimetric signatures of a layer of random nonspherical discrete scatterers overlying a homogeneous half-space based on first- and second-order vector radiative transfer theory

Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. Some of the salient features of the numerical results are as follows: (1) the inclusion of the nondiagonal extinction matrix in the vector radiative transfer theory accounts for an appreciable phase difference between vv and hh polarizations, particularly for aligned scatterers; (2) the ensemble-averaged scattered Stokes vector is generally partially polarized, with the degree of polarization less than unity; (3) there generally exists a pedestal in the copolarization return when plotted as a function of ellipticity and orientation angles, which may be due to heterogeneity of scattering objects and/or multiple scattering effects; and (4) multiple scattering effects generally enhance the pedestal in copolarization return, decrease the degree of polarization, affect phase difference, and also enhance the depolarization return.

Tsang, Leung↗

NASA NTRS1990

Learning control system design based on 2-D theory - An application to parallel link manipulator

An approach to iterative learning control system design based on two-dimensional system theory is presented. A two-dimensional model for the iterative learning control system which reveals the connections between learning control systems and two-dimensional system theory is established. A learning control algorithm is proposed, and the convergence of learning using this algorithm is guaranteed by two-dimensional stability. The learning algorithm is applied successfully to the trajectory tracking control problem for a parallel link robot manipulator. The excellent performance of this learning algorithm is demonstrated by the computer simulation results.

Geng, Z.↗

NASA NTRS1991

Secular perturbation theory and computation of asteroid proper elements

A new theory for the calculation of proper elements is presented. This theory defines an explicit algorithm applicable to any chosen set of orbits and accounts for the effect of shallow resonances on secular frequencies. The proper elements are computed with an iterative algorithm and the behavior of the iteration can be used to define a quality code.

Milani, Andrea↗