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At least 109 records · Page 6

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NASA NTRS1971

Prediction of flow profiles in arteries from local measurements.

This paper develops an approximate numerical method for calculating flow profiles in arteries. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the large deformations of the arterial wall. The method, assuming axially symmetric flow, determines velocity distribution and wall shear at a given location from the locally measured values of the pressure, pressure gradient, and pressure-radius relation. The computed results agree well with the corresponding experimental data.

Ling, S. C.↗

NASA NTRS1973

Detection and Estimation of an Optical Image by Photon-Counting Techniques

Statistical description of a photoelectric detector is given. The photosensitive surface of the detector is divided into many small areas, and the moment generating function of the photo-counting statistic is derived for large time-bandwidth product. The detection of a specified optical image in the presence of the background light by using the hypothesis test is discussed. The ideal detector based on the likelihood ratio from a set of numbers of photoelectrons ejected from many small areas of the photosensitive surface is studied and compared with the threshold detector and a simple detector which is based on the likelihood ratio by counting the total number of photoelectrons from a finite area of the surface. The intensity of the image is assumed to be Gaussian distributed spatially against the uniformly distributed background light. The numerical approximation by the method of steepest descent is used, and the calculations of the reliabilities for the detectors are carried out by a digital computer.

Wang, Lily Lee↗

NASA NTRS1973

Evaluation of control laws and actuator locations for control systems applicable to deformable astronomical telescope mirrors

Some of the major difficulties associated with large orbiting astronomical telescopes are the cost of manufacturing the primary mirror to precise tolerances and the maintaining of diffraction-limited tolerances while in orbit. One successfully demonstrated approach for minimizing these problem areas is the technique of actively deforming the primary mirror by applying discrete forces to the rear of the mirror. A modal control technique, as applied to active optics, has previously been developed and analyzed. The modal control technique represents the plant to be controlled in terms of its eigenvalues and eigenfunctions which are estimated via numerical approximation techniques. The report includes an extension of previous work using the modal control technique and also describes an optimal feedback controller. The equations for both control laws are developed in state-space differential form and include such considerations as stability, controllability, and observability. These equations are general and allow the incorporation of various mode-analyzer designs; two design approaches are presented. The report also includes a technique for placing actuator and sensor locations at points on the mirror based upon the flexibility matrix of the uncontrolled or unobserved modes of the structure. The locations selected by this technique are used in the computer runs which are described. The results are based upon three different initial error distributions, two mode-analyzer designs, and both the modal and optimal control laws.

Ostroff, A. J.↗

NASA NTRS1972

A nonlinear analysis of pulsatile flow in arteries.

An approximate numerical method for calculating flow profiles in arteries is developed. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the nonlinear behaviour and large deformations of the arterial wall. Through the locally measured values of the pressure, pressure gradient, and pressure-radius function, the velocity distribution and wall shear at a given location along the artery can be determined. The computed results agree well with the corresponding experimental data.

Ling, S. C.↗

NASA NTRS1973

Viscous effects in rapidly rotating stars with application to white-dwarf models. I, II.

A general approximate numerical technique is proposed for constructing evolutionary sequences of rapidly rotating axisymmetric barytropic equilibrium configurations, with allowance for angular momentum transfer by a nonconstant isotropic viscosity. The principal physical assumption involved is the constancy of the angular momentum per unit mass on cylinders about the axis of rotation. Rapidly rotating nonmagnetic white-dwarf models with a zero-temperature degenerate-electron equation of state are considered as a particular application. The viscosity used in the analysis is that of the degenerate electrons.

Durisen, R. H.↗

NASA NTRS1973

The constraint method: A new finite element technique

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

Tsai, C.↗

NASA NTRS1974

Steady incompressible potential flow around lifting bodies immersed in a fluid

The refinement was investigated of a method for evaluating the pressure distribution on a body surface of arbitrary shape in incompressible flow. The solution was obtained in terms of the velocity potential, through numerical approximations which require the use of a high speed digital computer. The box method and the modal method are described in detail, and were applied to a very thin, rectangular wing in incompressible, steady flow. The box method is found to be more practical as it is applicable to more general geometries (the modal method requires a new set of functions for each geometry), and requires less computer time (fifty percent of that required by the modal method for the same problem).

Chiuchiolo, E. A.↗

NASA NTRS1975

Synthesis of the antenna pattern for a radiating slot in a metal cylinder

The synthesis of a prescribed far-field pattern by means of a radiating slot in a perfectly conducting infinite circular cylinder is considered. The narrow circumferential slot and the infinite axial slot are studied in detail. In either case, the problem is to find the distribution of the electromagnetic field in the aperture that yields a radiation pattern that is the best mean-square approximation to a given pattern, under certain constraints. Various quality factors for cylindrical models are discussed, and a detailed comparison with the synthesis problem for a planar aperture is performed. It turns out that Rhodes' synthesis method has no equivalent in the cylindrical case, and that the best admissible mean-square approximation to a given pattern may be a very poor approximation in amplitude. However, an iteration scheme is developed in which the phase approximation is sacrificed for the sake of substantially improving the amplitude approximation. Numerical results based on such a scheme are displayed, for prescribed omnidirectional and sectoral patterns.

Einarsson, O.↗

NASA NTRS1975

Amplitude effects on the dynamic performance of a hydrostatic gas thrust bearing

The Reynolds' equation is applied to a strip gas thrust bearing to analyze amplitude disturbance effects on its dynamic performance. The Reynolds' equation is numerically approximated using finite difference techniques. The time dependent load carrying capacity is represented by a Fourier series up to and including the third harmonics. Design curves for the load capacity and the linear stiffness and damping are presented as a function of inlet location, restrictor coefficient, supply pressure, amplitude of oscillation, and squeeze number. For the range of amplitudes investigated the dimensionless load capacity, stiffness and damping does not exhibit an appreciable change in magnitude; thus, only one design curve is needed to represent each relationship. A design methodology is presented.

Stiffler, A. K.↗

NASA NTRS1977

Investigations of primary and secondary impact structures on the moon and laboratory experiments to study the ejecta of secondary particles

Young lunar impact structures were investigated by using lunar orbiter, Apollo Metric and panorama photographs. Measurements on particularly homogeneous areas low in secondary craters made possible an expansion of primary crater distribution to small diameters. This is now sure for a range between 20m or = D or = 20km and this indicates that the size and velocity distribution of the impacting bodies in the last 3 billion years has been constant. A numerical approximation in the form of a 7th degree polynomial was obtained for the distribution.

Koenig, B.↗

NASA NTRS1977

The clouds of Venus. II - An investigation of the influence of coagulation on the observed droplet size distribution

An approximate numerical technique is used to investigate the influence of coagulation, sedimentation and turbulent motions on the observed droplet size distribution in the upper layers of the Venus clouds. If the cloud mass mixing ratio is less than 0.000001 at 250 K or the eddy diffusivity throughout the cloud is greater than 1,000,000 sq cm per sec, then coagulation is unimportant. In this case, the observed droplet size distribution is the initial size distribution produced by the condensation of the droplets. It is found that all cloud models with droplet formation near the cloud top (e.g., a photochemical model) must produce the observed droplet size distribution by condensation without subsequent modification by coagulation. However, neither meteoritic or surface dust can supply sufficient nucleating particles to account for the observed droplet number density. If the cloud droplets are formed near the cloud bottom, the observed droplet size distribution can be produced solely by the interaction of coagulation and dynamics; all information about the initial size distribution is lost. If droplet formation occurs near the cloud bottom, the lower atmosphere of Venus is oxidizing rather than reducing.

Rossow, W. B.↗

NASA NTRS1979

Singular perturbations and the sounding rocket problem

In this paper, Goddard's problem of maximizing the final altitude of a sounding rocket (a singular problem of optimal control) is analyzed using singular perturbation methods. The problem is first cast in singular perturbation form and then solved to zero order by adding boundary-layer corrections to the reduced solution. For a quadratic drag law, a closed-form solution is obtained, although consideration of a numerical example indicates that this solution is not useful for practical sounding rockets. However, use of state variable transformations allows a very accurate numerical approximation to be constructed. It is concluded that application of singular perturbation methods to the well-known sounding rocket problem indicates that these methods may have utility in dealing with singular problems of optimal control.

Ardema, M. D.↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗

NASA NTRS1982

Development of a locally mass flux conservative computer code for calculating 3-D viscous flow in turbomachines

The VANS successive approximation numerical method was extended to the computation of three dimensional, viscous, transonic flows in turbomachines. A cross-sectional computer code, which conserves mass flux at each point of the cross-sectional surface of computation was developed. In the VANS numerical method, the cross-sectional computation follows a blade-to-blade calculation. Numerical calculations were made for an axial annular turbine cascade and a transonic, centrifugal impeller with splitter vanes. The subsonic turbine cascade computation was generated in blade-to-blade surface to evaluate the accuracy of the blade-to-blade mode of marching. Calculated blade pressures at the hub, mid, and tip radii of the cascade agreed with corresponding measurements. The transonic impeller computation was conducted to test the newly developed locally mass flux conservative cross-sectional computer code. Both blade-to-blade and cross sectional modes of calculation were implemented for this problem. A triplet point shock structure was computed in the inducer region of the impeller. In addition, time-averaged shroud static pressures generally agreed with measured shroud pressures. It is concluded that the blade-to-blade computation produces a useful engineering flow field in regions of subsonic relative flow; and cross-sectional computation, with a locally mass flux conservative continuity equation, is required to compute the shock waves in regions of supersonic relative flow.

Walitt, L.↗

NASA NTRS1981

Boundary layer thermal stresses in angle-ply composite laminates, part 1

Thermal boundary-layer stresses (near free edges) and displacements were determined by a an eigenfunction expansion technique and the establishment of an appropriate particular solution. Current solutions in the region away from the singular domain (free edge) are found to be excellent agreement with existing approximate numerical results. As the edge is approached, the singular term controls the near field behavior of the boundary layer. Results are presented for cases of various angle-ply graphite/epoxy laminates with (theta/-theta/theta/theta) configurations. These results show high interlaminar (through-the-thickness) stresses. Thermal boundary-layer thicknesses of different composite systems are determined by examining the strain energy density distribution in composites. It is shown that the boundary-layer thickness depends on the degree of anisotropy of each individual lamina, thermomechanical properties of each ply, and the relative thickness of adjacent layers. The interlaminar thermal stresses are compressive with increasing temperature. The corresponding residual stresses are tensile and may enhance interply delaminations.

Wang, S. S.↗

NASA NTRS1982

Boundary-layer effects in composite laminates. I - Free-edge stress singularities. II - Free-edge stress solutions and basic characteristics

The fundamental nature of the boundary-layer effect in fiber-reinforced composite laminates is formulated in terms of the theory of anisotropic elasticity. The basic structure of the boundary-layer field solution is obtained by using Lekhnitskii's stress potentials (1963). The boundary-layer stress field is found to be singular at composite laminate edges, and the exact order or strength of the boundary layer stress singularity is determined using an eigenfunction expansion method. A complete solution to the boundary-layer problem is then derived, and the convergence and accuracy of the solution are analyzed, comparing results with existing approximate numerical solutions. The solution method is demonstrated for a symmetric graphite-epoxy composite.

Wang, S. S.↗

NASA NTRS1982

Surface fitting with biharmonic and harmonic models

The physical and geometric interpretation of a surface fitting technique, multiquadric equations (MQ), is discussed. The relation of this method and its reciprocal form to biharmonic and harmonic techniques respectively, is pointed out. In both forms the solutions may be viewed as being numerical approximations of an integral equation in which an unknown density function is the physical source for disturbing potential (reciprocal-MQ) or elastic displacement (MQ).

Hardy, R. L.↗

NASA NTRS1982

Mixture densities, maximum likelihood, and the EM algorithm

The problem of estimating the parameters which determine a mixture density is reviewed as well as maximum likelihood estimation for it. A particular iterative procedure for numerically approximating maximum likelihood estimates for mixture density problems is considered. This EM algorithm, is a specialization to the mixture density context of a general algorithm of the same name used to approximate maximum likelihood estimates for incomplete data problems. The formulation and theoretical and practical properties of the EM algorithm for mixture densities are discussed focussing in particular on mixtures of densities from exponential families.

Redner, R. A.↗