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NASA NTRS1984

Flap-lag damping of an elastic rotor blade with torsion and dynamic inflow in hover from symbolically generated equations

A program written in FORTRAN IV and coded into subroutines for subsequent numerical study is used to derive symbolically the governing equations of motion of the elastic rotor blade and the dynamic inflow equations. By rearranging the coefficients of the equations, the blade and dynamic inflow equations are converted into equations in a multiblade coordinated system. The final multiblade equations can accommodate any number of elastic blade modes. It is noted that with a given data set, the entire process, from the derivation of the equations to the numerical calculations, is computerized and requires only limited user interface. To demonstrate the usefulness of the approach, damping data in hover with and without dynamic inflow effects are presented for various rotor blade models, including flap-lag, flap-lag-torsion, quasi-static torsion, and rigid blade lag-flap.

Reddy, T. S. R.↗

NASA NTRS1984

Numerical simulation of the viscous flow fields over three-dimensional complicated geometries

A 'thin-layer' Navier-Stokes code capable of predicting steady state viscous flows is applied to complicated three-dimensional flow fields. The code is written in a generalized coordinate system, and a recently developed grid generation procedure is used for the flow-field discretization. Application is made to the vortical flow over a delta wing at high angle of attack, and the computed results are compared with experimental results. The results indicate that the present method can capture the physical phenomenon well. It is observed that a leading-edge separation vortex is formed over the wing, as is a secondary separation vortex near the leading edge. The flow field behind the trailing edge is also well described. Application is also made to the transonic flow over the Shuttle configuration. The result appears to be reasonable even though no experimental data are available for comparison. These results indicate that the present approach is capable of computing complicated three-dimensional flow fields.

Fujii, K.↗

NASA NTRS1984

Observations of the dynamics of the polar thermosphere

The dynamics of the polar thermosphere are examined by using observations made from the Dynamics Explorer 2 satellite. The results used in this study were obtained primarily from the Fabry-Perot interferometer (FPI) and the wind and temperature spectrometer (WATS) during the time period from September 1981 through January 1982. Two primary geophysical conditions were examined: these were the southern summer and the northern winter polar regions. The results support the conclusion that above 60 degrees of latitude the neutral winds are strongly controlled by ion/neutral frictional momentum transfer resulting from magnetospheric convection. This implies that the natural coordinate system within which to display the neutral winds in the high polar thermosphere is magnetic. The collected observations of this study were used to assess the validity of two of the large thermospheric general circulation models. The result of this assessment was that the models reasonably represent the vector winds at high altitudes but do not, at present, accurately simulate the thermodynamics of that regime.

Hays, P. B.↗

NASA NTRS1984

An analytic solution for the orbital perturbations of the Venus Radar Mapper due to gravitational harmonics

Hill's variational equations are solved analytically for the orbital perturbations of a spacecraft nominally in an elliptic orbit around a non-spherical body. The rotation of the central planet about its spin-axis is not considered in the analysis. The perturbations are restricted to the planetary gravitational harmonics only. An extremely simple algorithm is derived to transform the spherical harmonic potentials to the orbital coordinate system, and the resulting accelerations are shown to be simply trigonometric functions of the true anomaly. With the principal matrix solution for the differential equations of the adjoint system given in closed form, the orthogonality of the trigonometric functions makes it possible to obtain an analytic solution for the non-homogeneous problem, at intervals of 2 pi in true anomaly. The solution for orbital perturbations can be extended over several revolutions by applying well-known results from Floquet's theory. The technique is demonstrated with results presented on the spacecraft periapsis altitude for the forthcoming Venus Radar Mapper Mission.

Vijayaraghavan, A.↗

NASA NTRS1984

Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.

Rosen, M. C.↗

NASA NTRS1984

The Z3 model of Saturn's magnetic field and the Pioneer 11 vector helium magnetometer observations

Magnetic field observations obtained by the Pioneer 11 vector helium magnetometer are compared with the Z(sub 3) model magnetic field. These Pioneer 11 observations, obtained at close-in radial distances, constitute an important and independent test of the Z(sub 3) zonal harmonic model, which was derived from Voyager 1 and Voyager 2 fluxgate magnetometer observations. Differences between the Pioneer 11 magnetometer and the Z(sub 3) model field are found to be small (approximately 1 percent) and quantitatively consistent with the expected instrumental accuracy. A detailed examination of these differences in spacecraft payload coordinates shows that they are uniquely associated with the instrument frame of reference and operation. A much improved fit to the Pioneer 11 observations is obtained by rotation of the instrument coordinate system about the spacecraft spin axis by 1.4 degree. With this adjustment, possibly associated with an instrumental phase lag or roll attitude error, the Pioneer 11 vector helium magnetometer observations are fully consistent with the Voyager Z(sub 3) model.

Connerney, J. E. P.↗

NASA NTRS1986

Photo-Optical Blade-Vibration-Data Acquisition System

Techniques developed for measuring blade vibrations using optical sensors fixed in casing around bladed turbine-engine stage. Measurement system coordinates and assembles inputs of many optical probes in order to monitor all of blades on spinning stage. Several points on every blade monitored in order to develop quantitative measure of overall bladed-stage response.

Kiraly, L. J.↗

NASA NTRS1984

Stress-derivative control of keystoning deformation in finite element codes

The stress derivative technique for control of keystoning deformation in under-integrated finte elements is based on expansion of the stress in a Taylor series about the element center and retention of additional terms beyond the constant stress term. It has the advantage over other control techniques that keystoning resistance is provided by actual rather than artificial material properties. Application of this technique to the quadrilateral ring elements used for modelling solids of revolution subjected to axisymmetric loads is described. In a cylindrical coordinate system additional terms appear in the formulation which must be dealt with in arriving at a workable keystoning control scheme.

Schulz, J. C.↗

NASA NTRS1984

Supersonic nonlinear potential analysis

The NCOREL computer code was established to compute supersonic flow fields of wings and bodies. The method encompasses an implicit finite difference transonic relaxation method to solve the full potential equation in a spherical coordinate system. Two basic topic to broaden the applicability and usefulness of the present method which is encompassed within the computer code NCOREL for the treatment of supersonic flow problems were studied. The first topic is that of computing efficiency. Accelerated schemes are in use for transonic flow problems. One such scheme is the approximate factorization (AF) method and an AF scheme to the supersonic flow problem is developed. The second topic is the computation of wake flows. The proper modeling of wake flows is important for multicomponent configurations such as wing-body and multiple lifting surfaces where the wake of one lifting surface has a pronounced effect on a downstream body or other lifting surfaces.

Siclari, M. J.↗

NASA NTRS1984

SSME thrust chamber simulation using Navier-Stokes equations

The capability of the PHOENICS fluid dynamics code in predicting two-dimensional, compressible, and reacting flow in the combustion chamber and nozzle of the space shuttle main engine (SSME) was evaluated. A non-orthogonal body fitted coordinate system was used to represent the nozzle geometry. The Navier-Stokes equations were solved for the entire nozzle with a turbulence model. The wall boundary conditions were calculated based on the wall functions which account for pressure gradients. Results of the demonstration test case reveal all expected features of the transonic nozzle flows. Of particular interest are the locations of normal and barrel shocks, and regions of highest temperature gradients. Calculated performance (global) parameters such as thrust chamber flow rate, thrust, and specific impulse are also in good agreement with available data.

Przekwas, A. J.↗

NASA NTRS1985

Diffraction Analysis of Mesh Deployable Reflector Antennas

A formulation and many representative numerical results for mesh reflector antennas are presented. The reflection coefficient matrix for the prescribed mesh configuration was determined and the local coordinate system of the mesh cells at each point on the curved reflector surface was accentuated. A novel strip aperture model was used to formulate the transmission coefficient matrix for a variety of mesh cell configurations. Numerical data are tailored to the dimensions of a conceptually designed land mobile satellite system (LMSS) which employs a large mesh deployable offset parabolic antenna. Results are shown for an offset parabolic reflector with mesh surfaces similar to the mesh surface of tracking and data relay satellite system (TDRSS).

Rahmat-Samii, Y.↗

NASA NTRS1984

Desired characteristics of catalogs for cometary astrometry

Reference star catalogs for cometary astrometry have to provide an all-sky coverage with suitable stellar density and limiting magnitude on a fundamental coordinate system. A general catalog meeting all these requirements will not be available for a foreseen timescale. The suitability of various existing catalogs for cometary astrometry is discussed.

Devegt, C.↗

NASA NTRS1985

A 4-node Bilinear Isoparametric Element in Rockwell NASTRAN

The development and evaluation of the Rockwell NASTRAN four node quadrilateral (QUAD4) element is presented. The element derivation utilizes bilinear isoparametric techniques both for membrane and bending characteristics. The QUAD4 element coordinate system, membrane properties, lumped mass matrix, and treatment of warping are based upon the COSMIC/NASTRAN QDMEMI element while the bending characteristics are based on a paper by T. J. R. Hughes. The effects of warping on the bending stiffness, consistent mass, and geometric stiffness are based upon a paper by R. H. MacNeal. Numerical integration is accomplished by Gaussian quadrature on a 2 x 2 grid. Practical user support features include variable element thickness, thermal analysis and layered composite material definitions.

Liao, C.↗

NASA NTRS1985

User's manual for airfoil flow field computer code SRAIR

A two dimensional unsteady Navier-Stokes calculation procedure with specific application to the isolated airfoil problem is presented. The procedure solves the full, ensemble averaged Navier-Stokes equations with turbulence represented by a mixing length model. The equations are solved in a general nonorthogonal coordinate system which is obtained via an external source. Specific Cartesian locations of grid points are required as input for this code. The method of solution is based upon the Briley-McDonald LBI procedure. The manual discusses the analysis, flow of the program, control steam, input and output.

Shamroth, S. J.↗

NASA NTRS1985

When Is a Bernstein-bezier Curve the Graph of a Function?

The question of determining when a Bernstein-Bezier cubic curve in the plane can be represented as the graph of function in some fixed orthogonal coordinate system is considered. The notion of a curve being monotone in a given direction is introduced to aid in the analysis.

Mclaughlin, H. W.↗

NASA NTRS1985

Study of meshing of beveled gears with normally decreasing arc teeth

The meshing of beveled gears was studied by the direct and inverse approaches. Gear wheels with teeth of equal height are studied, and wheels with normally-decreasing arc teeth. Different coordinate systems are utilized to plot the determination of the rotation of the originating gear wheel and the meshing line of the gear wheel which is cut. Matrices are used to determine the equations of the originating surfaces and the unit vectors of the normals to these originating surfaces.

Litvin, F. L.↗

NASA NTRS1985

Solar physics applications of computer graphics and image processing

Computer graphics devices coupled with computers and carefully developed software provide new opportunities to achieve insight into the geometry and time evolution of scalar, vector, and tensor fields and to extract more information quickly and cheaply from the same image data. Two or more different fields which overlay in space can be calculated from the data (and the physics), then displayed from any perspective, and compared visually. The maximum regions of one field can be compared with the gradients of another. Time changing fields can also be compared. Images can be added, subtracted, transformed, noise filtered, frequency filtered, contrast enhanced, color coded, enlarged, compressed, parameterized, and histogrammed, in whole or section by section. Today it is possible to process multiple digital images to reveal spatial and temporal correlations and cross correlations. Data from different observatories taken at different times can be processed, interpolated, and transformed to a common coordinate system.

Altschuler, M. D.↗

NASA NTRS1985

Angular distribution and multiplicity of backward hadrons in hFe interactions at 0.5-5.0 TeV energies (PION Experiment)

Based on the analysis of approximates 5 X 1000 events registered on the PION installation, data are obtained on the angular distribution and multiplicity of particles, flying back into the laboratory coordinate system (LCS) that are identified mainly as hadrons produced in the reactions of hFe yield h prime X type. The inclusively produced hadron energy is 200 MeV. The experimental data are compared to the results of the cumulative particle production in hA processes observed on accelerators at lower energies.

Avakian, V. V.↗