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NASA NTRS1988

An efficient high-frequency analysis of modal reflection and transmission coefficients for a class of waveguide discontinuities

A high-frequency analysis of electromagnetic modal reflection and transmission coefficients is presented for waveguide discontinuities formed by joining different waveguide sections. The analysis uses an extended version of the concept of geometrical theory of diffraction based equivalent edge currents in conjunction with the reciprocity theorem to describe interior scattering effects. If the waveguide modes and their associated modal rays can be found explicitly, general two- and three-dimensional waveguide geometries can be analyzed. Expressions are developed for two-dimensional reflection and transmission coefficients. Numerical results are given for a flanged, semi-infinite parallel plate waveguide and for the junction between two linearly tapered waveguides.

Pathak, P. H.↗

NASA NTRS1989

Ray analysis of modal reflection for three-dimensional open-ended waveguides

An efficient high-frequency ray analysis, which combines the geometrical theory of diffraction (GTD) with the equivalent current method, is used for evaluating modal reflection at the open ends of three-dimensional waveguides. After reviewing a method used for the two-dimensional case and introducing some extensions necessary for evaluating modal reflection of open-ended three-dimensional waveguides, the modal reflection coefficients are then given for open-ended circular and rectangular waveguides. Numerical results calculated using these expressions agree favorably with those obtained by a different analytical technique and by experiment.

Chuang, C. W.↗

NASA NTRS1989

Numerical algorithms for steady and unsteady incompressible Navier-Stokes equations

The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.

Hafez, Mohammed↗

NASA NTRS1990

Extension of a three-dimensional viscous wing flow analysis user's manual: VISTA 3-D code

Three-dimensional unsteady viscous effects can significantly influence the performance of fixed and rotary wing aircraft. These effects are important in both flows about helicopter rotors in forward flight and flows about three-dimensional (swept and tapered) supercritical wings. A computational procedure for calculating such flow field was developed. The procedure is based upon an alternating direction technique employing the Linearized Block Implicit method for solving three-dimensional viscous flow problems. In order to demonstrate the viability of this method, two- and three-dimensional problems are computed. These include the flow over a two-dimensional NACA 0012 airfoil under steady and oscillating conditions, and the steady, skewed, three-dimensional flow on a flat plate. Although actual three-dimensional flows over wings were not obtained, the ground work was laid for considering such flows. In this report a description of the computer code is given.

Weinberg, Bernard C.↗

NASA NTRS1990

Velocity filtering applied to optical flow calculations

Optical flow is a method by which a stream of two-dimensional images obtained from a forward-looking passive sensor is used to map the three-dimensional volume in front of a moving vehicle. Passive ranging via optical flow is applied here to the helicopter obstacle-avoidance problem. Velocity filtering is used as a field-based method to determine range to all pixels in the initial image. The theoretical understanding and performance analysis of velocity filtering as applied to optical flow is expanded and experimental results are presented.

Barniv, Yair↗

NASA NTRS1989

Three-dimensional aspects of plasticity-induced fatigue crack closure

A three-dimensional elastoplastic finite element analysis of fatigue crack growth and closure in a center-crack tension specimen was performed in order to investigate the crack opening stress as a function of specimen thickness under constant amplitude loading conditions. Elastic-perfectly plastic conditions were assumed and cycle loading was kept at R = 0.1. Firstly, by imposing proper boundary conditions on the three-dimensional model, a plane strain analysis was carried out. The ratio of stabilized opening stress over the maximum applied stress under plane strain conditions was found to be 0.28. Secondly, the model thickness was varied under fully three-dimensional conditions, and crack-opening stresses were determined for each specimen thickness. The crack-opening stress is found to vary through the thickness for the center crack tension specimen. On the specimen surface and in the midplane the crack-opening stress levels tend to two-dimensional solutions for plane stress and plane strain conditions, respectively.

Chermahini, R. G.↗

NASA NTRS1989

Analysis of finite phased arrays of circular microstrip patches

A method is presented for analyzing a finite planar array of circular microstrip patches fed by coaxial probes. The self- and mutual impedances between array elements are calculated using the method of moments with the dyadic Green's function for a dielectric layer on a ground plane. The patch circuits are determined by using the reaction integral equation. The active input impedance as well as the active element pattern of the array are computed from a knowledge of the resultant patch currents. The calculated results for two-element and eight-element linear arrays are in good agreement with experimental data. The active reflection coefficient and element pattern for the center and edge elements of a two-dimensional array as a function of scan angle are also presented.

Deshpande, Manohar D.↗

NASA NTRS1989

Finite element analysis of the Space Shuttle Main Engine (SSME) high pressure fuel turbopump turbine blade (HPFTP)

Cracking of the turbine blades of the SSME HPFTP is studied using two- and three-dimensional finite element analysis. The development and composition of the two- and three-dimensional models are described. Analyses are conducted under the speed, pressure, and thermal load conditions that occur during the full power level of the engine. The effects of friction on the two-dimensional model are examined. The strain and life cycle data reveal that the LCF cracking in the first stage is not probable unless the effects of fit-up tolerance between the blade and rotor are present, and for the second stage it is predicted that hydrogen assisted LCF cracking will occur under the present thermal environment. Design modifications to alleviate this cracking are discussed.

Lee, H. M.↗

NASA NTRS1990

Unsteady analysis of hot streak migration in a turbine stage

Two- and three-dimensional Navier-Stokes analyses are used to predict unsteady viscous rotor-stator interacting flow in the presence of a combustor hot streak. Predicted results are presented for a two-dimensional three-stator/four-rotor, a two-dimensional one-stator/one-rotor, and a three-dimensional one-stator/one-rotor simulation of hot streak migration through a turbine stage. Comparison of these results with experimental data demonstrates the capability of the three-dimensional procedure to capture most of the flow physics associated with hot streak migration including the effects of combustor hot streaks on turbine rotor surface temperatures. It is noted that blade count ratio has little effect on predicted time-averaged surface pressure and temperature distributions, but a substantial effect on the unsteady flow characteristics. It is shown that high-temperature hot streak fluid accumulates on the pressure surface of the rotor blades, resulting in a high time-averaged surface temperature 'hot spots'.

Dorney, Daniel J.↗

NASA NTRS1989

Analysis of the transient compressible vapor flow in heat pipes

The transient compressible one-dimensional vapor flow dynamics in a heat pipe is modeled. The numerical results are obtained by using the implicit non-iterative Beam-Warming finite difference method. The model is tested for simulated heat pipe vapor flow and actual vapor flow in cylindrical heat pipes. A good comparison of the present transient results for the simulated heat pipe vapor flow with the previous results of a two-dimensional numerical model is achieved and the steady state results are in agreement with the existing experimental data. The transient behavior of the vapor flow under subsonic, sonic, and supersonic speeds and high mass flow rates are successfully predicted. The one-dimensional model also describes the vapor flow dynamics in cylindrical heat pipes at high temperatures.

Jang, J. H.↗

NASA NTRS1990

An empirical study of FORTRAN programs for parallelizing compilers

Some results are reported from an empirical study of program characteristics that are important in parallelizing compiler writers, especially in the area of data dependence analysis and program transformations. The state of the art in data dependence analysis and some parallel execution techniques are examined. The major findings are included. Many subscripts contain symbolic terms with unknown values. A few methods of determining their values at compile time are evaluated. Array references with coupled subscripts appear quite frequently; these subscripts must be handled simultaneously in a dependence test, rather than being handled separately as in current test algorithms. Nonzero coefficients of loop indexes in most subscripts are found to be simple: they are either 1 or -1. This allows an exact real-valued test to be as accurate as an exact integer-valued test for one-dimensional or two-dimensional arrays. Dependencies with uncertain distance are found to be rather common, and one of the main reasons is the frequent appearance of symbolic terms with unknown values.

Shen, Zhiyu↗

NASA NTRS1990

Domain decomposition methods in aerodynamics

Compressible Euler equations are solved for two-dimensional problems by a preconditioned conjugate gradient-like technique. An approximate Riemann solver is used to compute the numerical fluxes to second order accuracy in space. Two ways to achieve parallelism are tested, one which makes use of parallelism inherent in triangular solves and the other which employs domain decomposition techniques. The vectorization/parallelism in triangular solves is realized by the use of a recording technique called wavefront ordering. This process involves the interpretation of the triangular matrix as a directed graph and the analysis of the data dependencies. It is noted that the factorization can also be done in parallel with the wave front ordering. The performances of two ways of partitioning the domain, strips and slabs, are compared. Results on Cray YMP are reported for an inviscid transonic test case. The performances of linear algebra kernels are also reported.

Venkatakrishnan, V.↗

NASA NTRS1990

Real-time motion tracking of three-dimensional objects

The problem in which the three-dimensional motion of an object corresponding to a known polyhedral model is to be computed using only the motion of edge features in a continuous stream of two-dimensional images is considered. Advantage is taken of the spatiotemporal density of the input signal and the limitations of long-range trajectory-prediction methods are avoided. Two parallel algorithms which use feature-based, short-range (spatiotemporally local) motion processes to achieve real-time tracking of modeled objects are presented. Both algorithms have been implemented and tested on a tightly coupled multiprocessor system consisting of an Aspex Pipe for low-level, image-feature computations and a Sequent Symmetry for high-level, model-based computations. An analysis is given of the actual performance limits of each method using the current hardware configuration.

Verghese, Gilbert↗

NASA NTRS1990

Three-dimensional potential flows from functions of a 3D complex variable

Potential, or ideal, flow velocities can be found from the gradient of an harmonic function. An ordinary complex valued analytic function can be written as the sum of two real valued functions, both of which are harmonic. Thus, 2D complex valued functions serve as a source of functions that describe two-dimensional potential flows. However, this use of complex variables has been limited to two-dimensions. Recently, a new system of three-dimensional complex variables has been developed at the NASA Ames Research Center. As a step toward application of this theory to the analysis of 3D potential flow, several functions of a three-dimensional complex variable have been investigated. The results for two such functions, the 3D exponential and 3D logarithm, are presented in this paper. Potential flows found from these functions are investigated. Important characteristics of these flows fields are noted.

Kelly, Patrick↗

NASA NTRS1990

Two- and three-dimensional blade vortex interactions

A three-dimensional time dependent Navier-Stokes analysis was applied to the rotor blade vortex interaction (BVI) problem. The numerical procedure is an iterative implicit procedure using three point central differences to represent spatial derivatives. A series of calculations were made to determine the time steps, pseudo-time steps, iterations, artificial dissipation level, etc. required to maintain a nondissipative vortex. Results show the chosen method to have excellent non-dissipative properties provided the correct parameters are chosen. This study was used to set parameters for both two- and three-dimensional blade vortex interaction studies. The two-dimensional study considered the interaction between a vortex and a NACA0012 airfoil. The results showed the detailed physics during the interaction including the pressure pulse propagating from the blade. The simulated flow physics was qualitatively similar to that experimentally observed. The 2-D BVI phenomena is the result of the buildup and violent collapse of the shock waves and local supersonic pockets on the blade surfaces. The resulting pressure pulse build-up appears to be centered at the blade leading edge. The three-dimensional interaction study considered the case of a vortex at 20 deg incidence to the blade leading edge. Although the qualitative results were similar to that of the two-dimensional interaction, details clearly showed the three-dimensional nature of the interaction process.

Davoudzadeh, F.↗

NASA NTRS1951

Flow through cascades in tandem

An exact treatment of the problem of finding the incompressible, inviscid two-dimensional flow around two cascades in tandem is presented. The analysis includes solutions of both the direct and the inverse problems. These problems are solved by conformally mapping the tandem cascade onto the region between two concentric circles in which region there are suitably placed flow singularities. Formulas for the velocity and the potential in the annular region are presented in a closed form by means of elliptic functions. The equations are presented in a form suitable for computation.

Spraglin, William E↗

NASA NTRS1989

Space vehicle approach velocity judgments under simulated visual space conditions

There were 35 volunteers who responded when they first perceived an increase in apparent size of a collimated, two-dimensional perspective image of an Orbiter vehicle. The variables of interest included the presence (or absence) of a fixed reticle within the field of view (FOV), background starfield velocity, initial range to the vehicle and vehicle closure velocity. It was found that: 1) increasing vehicle approach velocity yielded a very small (but significant) effect of faster detection of vehicle movement, nevertheless, response variability was relatively large; 2) including the fixed reticle in the FOV produced significantly slower detection of vehicle radial movement, however this occurred only at the largest range and the magnitude of the effect was only about 15% of the one sigma value; and 3) increasing background star velocity during this judgment led to slower detection of vehicle movement. While statistically significant, this effect was small and occurred primarily at the largest range. A possible explanation for the last two findings is that other static and dynamic objects within the visual field may compete for available attention which otherwise would be available for judging image expansion; thus, the target's retinal image has to expand more than otherwise for its movement to be detected. This study also showed that the Proximity Operations Research Mockup at NASA/Ames can be used effectively to investigate a variety of visual judgment questions related to future space operations. These findings are discussed in relation to previous research and possible underlying mechanisms.

Space Flight↗

NASA NTRS1948

Theoretical Analysis of Stationary Potential Flows and Boundary Layers at High Speed

The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.

Oswaititsch, K.↗