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At least 1,243 records · Page 69
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

A clamped rectangular plate containing a crack

The general problem of a rectangular plate clamped along two parallel sides and containing a crack parallel to the clamps is considered. The problem is formulated in terms of a system of singular integral equations and the asymptotic behavior of the stress state near the corners is investigated. Numerical examples are considered for a clamped plate without a crack and with a centrally located crack, and the stress intensity factors and the stresses along the clamps are calculated.

Tang, R.↗
NASA NTRS1986

Shaping of airplane fuselages for minimum drag

The VSAERO surface panel method is employed to investigate fuselage shapes which can enhance the natural laminar flow (NLF) characteristics. The study is performed at cruise Re which are relevant to commuter, transport, and business aircraft. The technique is based on piecewise constant doublet and source singularities and takes into account the effects of compressibility. Inviscid pressure distributions were generated for five configurations to aid in the search for an optimized NLF body shape as a function of the transition locations and the drag coefficients. Granville's transition criteria are incorporated into the calculations to yield shapes with longer runs of laminar flow and reduced drag. In comparison with other transition prediction methods, the method described is shown to have significantly higher valicity for making three-dimensional transition predictions.

Dodbele, S. S.↗
NASA NTRS1986

Existence of needle crystals in local models of solidification

The way in which surface tension acts as a singular perturbation to destroy the continuous family of needle-crystal solutions of the steady-state growth equations is analyzed in detail for two local models of solidification. All calculations are performed in the limit of small surface tension or, equivalently, small velocity. The basic mathematical ideas are introduced in connection with a quasilinear, isotropic version of the geometrical model of Brower et al., in which case the continuous family of solutions dissappears completely. The formalism is then applied to a simplified boundary-layer model with an anisotropic kinetic attachment coefficient. In the latter case, the solvability condition for the existence of needle crystals can be satisfied whenever the coefficient of anisotropy is arbitrarily small but nonzero.

Langer, J. S.↗
NASA NTRS1985

Backward boundary layers in downward flame spread

The gas-phase combustion of a vertical fuel slab pyrolyzing at a finite rate under downward flame spread conditions is investigated theoretically. The backward boundary layer character of the flow is exploited, and a transformation that shifts the singularity associated with boundary-layer equations to a location, upstream of flame lift-off, where the surface temperature is nearly ambient, is employed. The boundary-layer flow is matched asymptotically for large Grashof number to a potential flow that allows the flow induced by the flame and along the upstream surface of the fuel bed to be calculated. Gas-phase temperature and velocity predictions are compared to experiment, and although analysis of the gas phase is emphasized, an approximate spread rate, based on a solid-phase energy balance, is calculated.

Vedha-Nayagam, M.↗
NASA NTRS1986

Ideal condensations due to perpendicular thermal conduction in a sheared magnetic field

Cool condensations generated by a radiative thermal instability in a sheared magnetic field have previously been the bases of solar filament formation models. Through the assumption of fully anisotropic heat flow, a new set of condensation modes are here obtained which become singular in the limit of vanishing perpendicular thermal conductivity. The growth rates are noted to typically be greater than those reported previously for sheared field condensations. The fastest growth is exhibited by modes possessing the fewest oscillations.

Van Hoven, G.↗
NASA NTRS1986

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

A variety of methods can be used in constructing solutions to the problem of mesh scattering. However, each of these methods has certain drawbacks. The present paper is concerned with a new technique which is valid for all spacings. The new method involved, called the fast Fourier transform-conjugate gradient method (FFT-CGM), represents an iterative technique which employs the conjugate gradient method to improve upon each iterate, utilizing the fast Fourier transform. The FFT-CGM method provides a new accurate model which can be extended and applied to the more difficult problems of woven mesh surfaces. The formulation of the FFT-conjugate gradient method for aperture fields and current densities for a planar periodic structure is considered along with singular operators, the formulation of the FFT-CG method for thin wires with finite conductivity, and reflection coefficients.

Christodoulou, C. G.↗
NASA NTRS1986

Multi-dimensional initial-boundary value problems with strong nonlinearities

Initial boundary value problems for the general scalar singularly perturbed parabolic equation in a cylindrical domain are studied. The one-dimensional reaction-diffusion equation is considered in the absence of convection. Then, the general one-dimensional and N-dimensional reaction-convection-diffusion equations are analyzed.

Howes, F. A.↗
NASA NTRS1986

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Liu, X.-H.↗
NASA NTRS1985

Multivariable control systems with saturating actuators antireset windup strategies

This paper contains preliminary, yet promising, results for introducing antirest windup (ARW) properties in multivariable feedback control systems with multiple saturating actuator nonlinearities and integrating action. The ARW method introduces simple nonlinear feedback around the integrators. The multiloop circle criterion is used to derive sufficient conditions for closed-loop stability that employ frequency-domain singular value tests. The improvement in transient response due to the ARW feedback is demonstrated using a 2-input 2-output control system based upon the F-404 jet engine dynamcis.

Kapasouris, P.↗
NASA NTRS1986

Confinement of thermocapillary floating zone flow by uniform rotation

Smith and Greenspan (1984) examined theoretically the idea of using a uniform rotation of the floating zone system to confine the thermocapillary flow in crystal growth experiments to the melt sidewall, leaving the interior of the melt passive. Here, that model is extended to a full zone with a more realistic temperature distribution imposed on the sidewall, and both linear and nonlinear thermocapillary flows are theoretically studied. Linearized, analytical solutions are found using singular perturbation theory and the various sidewall boundary layers described by Greenspan (1969) for rotating fluids. The analytical and linearized numerical results are compared, and the linear and nonlinear flows are discussed. The results demonstrate that the thermocapillary flow is strong and that rotation cannot confine the flow. Temperature advection by strongly nonlinear flow is significant even for the small Prandtl number of silicon.

Fowlis, W. W.↗
NASA NTRS1986

Steady flow past sudden expansions at large Reynolds number. I - Boundary layer solutions

A global Newton method is used to obtain accurate finite difference solutions for uniform inflows to several sudden expansion geometries, avoiding the instabilities encountered at large Reynolds numbers. Steady solutions for lambda values greater than those attained previously are obtained only if lambda is below a critical value. The presence of a singularity at this critical value renders invalid the assumptions of the boundary layer model. The results indicate that for uniform inflows and smaller values of the expansion ratio, the eddy length will no longer increase linearly with R when R becomes sufficiently large.

Milos, F. S.↗
NASA NTRS1986

Effects of noise on modal parameters identified by the Eigensystem Realization Algorithm

The basic concept of the Eigensystem Realization Algorithm for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators, such as the singular values of the data matrix and modal amplitude coherence, is provided, based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo Simulations are included to support the analytical studies.

Juang, J.-N.↗
NASA NTRS1986

Wave-packet evolution and quantization

A general relationship is established between wave-packet evolution and quantization in classically integrable systems. Because of wave-packet spreading, one cannot simply take the Fourier transform of the time evolution of a wave-packet. Instead, one must propagate the wave-packet using the actions as Hamiltonians. The energy eigenvalues which result are the Einstein-Brillouin-Keller values, and new forms for the eigenfunctions appear. These are free of caustic singularities, and represent averages of wave packets over the invariant torus.

Littlejohn, R. G.↗
NASA NTRS1986

Integrated analysis tools for trade studies of spacecraft controller and sensor locations

The present investigation was conducted with the aim to evaluate the practicality and difficulties of modern control design methods for large space structure controls. The evaluation is used as a basis for the identification of useful computer-based analysis tools which would provide insight into control characteristics of a spacecraft concept. A description is presented of the wrap-rib antenna and its packaging concept. Attention is given to active control requirements, a mathematical model of structural dynamics, aspects of sensor and actuator location, the analysis approach, controllability, observability, the concept of balanced realization, transmission zeros, singular value plots, analysis results, model reduction, and an interactive computer program. It is pointed out that the application of selected control analysis tools to the wrap-rib antenna demonstrates several capabilities which can be useful during conceptual design.

Rowell, L. F.↗
NASA NTRS1986

New models for fast steady state magnetic reconnection

A new unified family of models for incompressible, steady-state magnetic reconnection in a finite region is presented. The models are obtained by expanding in powers of the Alfven Mach number and may be used to elucidate some of the puzzling properties of numerical experiments on reconnection which are not present in the classical models. The conditions imposed on the inflow boundary of the finite region determine which member of the family occurs. Petscheklien and Sonnerup like solutions are particular members. The Sonneruplike regime is a special case of a weak slow mode expansion in the inflow region, and it separates two classes of members with reversed currents. The Petscheklike regime is a singular case of a weak fast mode expansion, and it separates the hybrid regime from a regime of slow mode compressions. Care should be taken in deciding which type of reconnection is operating in a numerical experiment. Indeed, no experiment to date has used boundary conditions appropriate for demonstrating steady state Petschek reconnection.

Priest, E. R.↗
NASA NTRS1986

Effects of noise on ERA-identified modal parameters

The basic concept of the Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators such as the singular values of the data matrix and modal amplitude coherence is provided based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo simulations are included to support the analytical studies.

Juang, J.-N.↗
NASA NTRS1986

Stress-intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads

The purpose of this paper is to present stress-intensity factors for a wide range of nearly semi-elliptical surface cracks in pipes and rods. The configurations were subjected to either remote tension or bending loads. For pipes, the ratio of crack depth to crack length (a/c) ranged from 0.6 to 1; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the ratio of internal radius to wall thickness (R/t) ranged from 1 to 10. For rods, the ratio of crack depth to crack length also ranged from 0.6 to 1; and the ratio of crack depth to rod diameter (a/D) ranged from 0.05 to 0.35. These particular crack configurations were chosen to cover the range of crack shapes (a/c) that have been observed in experiments conducted on pipes and rods under tension and bending fatigue loads. The stress-intensity factors were calculated by a three-dimensional finite-element method. The finite-element models employed singularity elements along the crack front and linear-strain elements elsewhere. The models had about 6500 degrees of freedom. The stress-intensity factors were evaluated using a nodal-force method.

Raju, I. S.↗
NASA NTRS1986

Influence of airfoil camber on convected gust interaction noise

This paper investigates the effect of airfoil steady loading on the sound generated by the interaction of an airfoil with a convected disturbance. A previous theory, which included only the incidence angle contribution to the mean loading, is extended to include camber. The theory is based on a linearization of the Euler equations about a nonuniform, 0(1) Mach number subsonic mean flow. The discussion concentrates on the case of a slightly cambered airfoil at small incidence angle, interacting with a gust whose wavelength is short compared to the airfoil chord. The small parameter representing the amount of camber and incidence, and the large parameter representing the ratio of airfoil chord to disturbance wavelength, are utilized in a singular perturbation solution to the governing equations. Acoustic power calculations reveal that the amount of sound generated increases significantly with increased loading. More importantly, it is shown that the radiated acoustic power correlates very well with the strength of the mean flow around the leading edge.

Myers, M. R.↗