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NASA NTRS1985

Boundary to Constructive Solid Geometry Mappings: a Focus on 2-D Issues

The problem of converting boundary representation (B-rep) to constructive solid geometry representation (CSG-rep) (and vice versa) is discussed in two phases. The first phase entails finding a CSG-rep that defines the region bounded by a polygonal profile curve. The second phase utilizes the results of the first phase to find a CSG-rep for many non-polygonal profile curves. A mathematically concise representation of a region bounded by a polygonal is presented. Namely, any polygonal region bounded by an n sided polygon may be represented by a binary tree which has at most n planar halfspaces as leaves. A structure for this representation and an algorithm for calculating is discussed.

Peterson, D. P.↗

NASA NTRS1985

Experimental investigations on airfoils with different geometries in the domain of high angles of attack-flow separation

Wind tunnel tests were conducted on airfoil models in order to study the flow separation phenomena occurring for high angles of attack. Pressure distribution on wings of different geometries were measured. Results show that for three-dimensional airfoils layout and span lift play a role. Separation effects on airfoils with moderate extension are three-dimensional. The flow domains separated from the air foil must be treated three-dimensionally. The rolling-up of separated vortex layers increases with angle in intensity and induction effect and shows strong nonlinearities. Boundary layer material moves perpendicularly to the flow direction due to the pressure gradients at the airfoil; this has a stabilizing effect. The separation starts earlier with increasing pointed profiles.

Keil, J.↗

NASA NTRS1984

Basis set limit geometries for ammonia at the SCF and MP2 levels of theory

The controversy over the Hartree-Fock bond angle of NH3 is resolved and the convergence of the geometry for the molecule as the basis set is systematically improved with both SCF and correlated MP2 wave functions. The results of the geometrical optimizations, carried out in four stages with a series of uncontracted bases sets, are shown. The obtained structure for NH3 supports the results of Radom and Rodwell (1980) that the Hartree-Fock limit angle is significantly greater than was previously believed.

Defrees, D. J.↗

NASA NTRS1984

Finite difference solutions of heat conduction problems in multi-layered bodies with complex geometries

A numerical procedure is presented for analyzing a wide variety of heat conduction problems in multilayered bodies having complex geometry. The method is based on a finite difference solution of the heat conduction equation using a body fitted coordinate system transformation. Solution techniques are described for steady and transient problems with and without internal energy generation. Results are found to compare favorably with several well known solutions.

Masiulaniec, K. C.↗

NASA NTRS1985

Effect of solar-cell junction geometry on open-circuit voltage

Simple analytical models have been found that adequately describe the voltage behavior of both the stripe junction and dot junction grating cells as a function of junction area. While the voltage in the former case is found to be insensitive to junction area reduction, significant voltage increases are shown to be possible for the dot junction cell. With regard to cells in which the junction area has been increased in a quest for better performance, it was found that (1) texturation does not affect the average saturation current density J0, indicating that the texturation process is equivalent to a simple extension of junction area by a factor of square root of 3 and (2) the vertical junction cell geometry produces a sizable decrease in J0 that, unfortunately, is more than offset by the effects of attendant areal increases.

Weizer, V. G.↗

NASA NTRS1986

Effects of Gear-Cutter Geometry on Performance

Bending stress reduced by improving tooth-fillet design. Using optimized gear-cutter design technology, gear designer reduces bending stresses by up to 20 percent. Reduction in bending stress is result of improved geometry of tooth fillet, which, in turn, results in significant improvement in horsepower-per-pound ratio. Gears run quieter and smoother than spur-gear system.

Folenta, D.↗

NASA NTRS1985

A simple, first step to the optimization of regenerator geometry

This paper presents a simplified set of equations for calculating and optimizing regenerator geometries. A number of competing parameters must be accounted for in the design of a regenerator. To obtain high values of effectiveness, there is need for a large surface area for heat transfer and high heat capacity. The void volume should be small to maintain the pressure ratio in the entire system. Moreover, the pressure drop should be small compared to the absolute pressure. With the assumptions made here, the calculations can be done with a hand calculator. The equations show that the optimum regenerator length, hydraulic radius, and porosity are independent of mass flow rate and the gas cross sectional area is proportional to the mass flow rate. It is shown that using gas gaps between parallel plates produces a significantly better regenerator than is possible with packed spheres or screens, particularly at temperatures below approximately 50%.

Radebaugh, R.↗

NASA NTRS1985

Geometry of miocene extensional deformation, lower Colorado River Region, Southeastern California and Southwestern Arizona: Evidence for the presence of a regional low-angle normal fault

The geometry of Miocene extensional deformation, which changes along a 120 km-long, northeast-trending transect from the southestern Chocolate Mountains, southeastern California, to the Trigo and southern Dome Rock Mountains, southwestern Arizona is discussed. Based upon regional differences in the structural response to extension and estimated extensional strain, the transet can be divided into three northwesterly-trending structural domains. From southwest to northeast, these domains are: (1) southestern Chocolate-southernmost Trigo Mountains; (2) central to northern Trigo Mountains; and (3) Trigo Peaks-southern Dome Rock Mountains. All structures formed during the deformation are brittle in style; fault rocks are composed of gouge, cohesive gouge, and local microbreccia. In each structural domain, exposed lithologic units are composed of Mesozoic crystalline rocks unconformably overlain by Oligocene to Early Miocene volcanic and minor interbedded sedimentary rocks. Breccia, conglomerate, and sandstone deposited synchronously with regional extension locally overlie the volcanic rocks. Extensional deformation largely postdated the main phase of volcanic activity, but rare rhyolitic tuff and flows interbedded with the syndeformational clastic rocks suggest that deformation began during the waning stages of valcanism. K-Ar isotopic ages indicate that deformation occurred in Miocene time, between about 22 and m.y. ago.

Tosdal, R. M.↗

NASA NTRS1985

The synchrotron-self-Compton process in spherical geometries. I - Theoretical framework

Both spatial and spectral accuracies are stressed in the present method for the calculation of the synchrotron-self-Compton model in spherical geometries, especially in the partially opaque regime of the synchrotron spectrum of inhomogeneous sources that can span a few frequency decades and contribute a significant portion of the scattered flux. A formalism is developed that permits accurate calculation of incident photon density throughout an optically thin sphere. An approximation to the Klein-Nishina cross section is used to model the effects of variable electron and incident photon cutoffs, as well as the decrease in the cross section at high energies. General results are derived for the case of inhomogeneous sources with power law profiles in both electron density and magnetic field.

Band, D. L.↗

NASA NTRS1985

Scattering of acoustic waves into Tollmien-Schlichting waves by small streamwise variations in surface geometry

By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) it is shown that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. O(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien-Schlichting wave. The analysis provides a qualitative explanation of the Leehey and Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin and Poliakov (1979) experiment. It may also explain why small 'trip wires' can promote early transition.

Goldstein, M. E.↗

NASA NTRS1986

Experimental study of effects of forebody geometry on high angle of attack static and dynamic stability

A series of low speed wind tunnel tests on a generic fighter model with a cylindrical fuselage were made to investigate the effects of forebody shape on static and dynamic lateral/directional stability. Five forebodies, including a chine nose of unconventional cross-sectional shape, were tested. Conventional force tests were conducted to determine static stability characteristics and single degree-of-freedom free-to-roll tests were used to study the wing rock susceptibility of the model with the various forebodies. Flow visualization data were obtained to aid in analysis of the complex flow phenomena involved. The results show that forebody cross-sectional shape can strongly effect both static and dynamic (roll) stability at high angles of attack. Large variations in stability were obtained for the various forebody geometries. These characteristics result from the impact of cross-sectional shape on forebody vortex development, the behavior of the vortices at sideslip conditions, and their interaction with the wing and empennage flow fields.

Brandon, J. M.↗

NASA NTRS1986

An isoparametric spectral element method for solution of the Navier-Stokes equations in complex geometry

High-order (p-type) finite element methods combine the geometric flexibility of standard low-order finite element (or finite volume) techniques with the rapid convergence properties of spectral methods. Various p-type schemes have been proposed for elliptic problems. However, an application of p-type methods to more complex equations, in particular the passive scalar or Navier-Stokes equations, is complicated by the nature of the equations and by efficiency considerations as regards the solution procedure. Patera (1984) has proposed a p-type method for the Navier-Stokes equations, taking into account the arising additional complications. The present study is concerned with an isoparametric spectral element discretization for the solution of flow problems in fully general, curvy geometries. Attention is given to the isoparametric formulation for elliptic equations and a time-splitting scheme for the Navier-Stokes equations.

Korczak, K. Z.↗

NASA NTRS1986

62-dB-gain multiple-pass slab geometry Nd:YAG amplifier

A flash-lamp-pumped slab Nd:YAG laser amplifier with 62 dB of gain is demonstrated. The amplifier remains linear for energy extraction up to 12 mJ, and the beam spatial quality remains good at repetition rates up to 10 Hz. The slab geometry provides for gain averaging in the zigzag dimension, thus eliminating the undesirable effects of nonuniform pumping. This averaging and the necessity for only a single compact gain element are valuable attributes that may allow for eventual laser-diode array pumping of the slab Nd:YAG amplifier.

Kane, T. J.↗

NASA NTRS1985

Hovering rotor airload prediction using a full potential flow analysis with realistic wake geometry

A three-dimensional, full potential flow analysis with realistic hover wake geometry is presented for the prediction of hovering rotor airloads. The method of analysis is based on the concept of matching inner and outer domain solutions in three dimensions. The inner domain nonlinear solution is obtained using a finite difference analysis and the outer domain solution is based on prescribed wake methodology. This formulation which includes three-dimensional wake influence, was initially validated using a fixed-wing analysis, and has been extended to hovering rotor flight. Detailed chordwise and spanwise loading results are compared with subsonic and transonic test results from two rotor configurations to illustrate the predictive capabilities of the analysis. The extension of the method to steady-level forward flight is also discussed.

Egolf, T. A.↗

NASA NTRS1986

BUNVIS-RG - An exact buckling and vibration program for lattice structures, with repetitive geometry and substructuring options

The exact FORTRAN computer program BUNVIS-RG which uses an exact stiffness matrix method to find eigenvalues and modes of three-dimensional planes, is presented in detail. It is shown that BUNVIS-RG solution times can be predicted fairly accurately from two computer dependent constants, the number of nodes and members in the frame, and the maximum node number difference of any pair of connected nodes. The program's use of repetitive geometry, stayed column substructures and nonuniform member options was found to enhance efficiency and range of application.

Anderson, M. S.↗

NASA NTRS1986

Statistical characterization of sea surface geometry for a wave slope field discontinuous in the mean square

Statistics of two-dimensional wave groups, of steep wave events, and of a cascade pattern manifested in the surface geometry in a developed sea state are derived. A systematic view is presented of the spectral moment problem, highlighting its physical meaning and showing its relationship with the theory of random fields. A solution of this problem is suggested that is appropriate to the case of wind-generated surface waves. The solution method treats the surface elevation field as specified on a spatial (temporal) running grid, developing an averaging procedure which employs the Taylor microscale as the mesh size. The technique is illustrated by first exposing errors in direct calculations of the effective surface impedance for a coherently reflected L-band radio wave. The technique is then used to study wave groups and steep waves for a Gaussian, two-dimensional, time-varying surface. Finally, the theory is applied to estimate breaking wave statistics,

Glazman, R. E.↗

NASA NTRS1985

The geometric properties of Landsat-5 Thematic Mapper data and their conformity to Landsat-4 data and to earth's surface geometry

The geometry of two TIPS processed Landsat-5 Thematic Mapper scenes was analyzed and compared with that of SCROUNGE processed Landsat-4 data. Swath-to-swath and band-to-band registration of Washington, DC, and northeastern Iowa scenes was found to be similar to or better than that of Landsat-4 data. Results indicate a high degree of geometric conformity between the images produced by the different systems. The geometric conformity of the TIPS processed images to the Space Oblique Mercator projection, however, proved to be less accurate than the targeted processing error of 15 meters.

Walker, R. E.↗

NASA NTRS1986

Rotor tip vortex geometry measurements using the wide-field shadowgraph technique

Rotor tip vortex geometry data have been acquired using the wide-field shadowgraph technique. Shadowgraphs were taken of the wakes of two model main-rotor systems in hover. These shadowgraphs provided detailed tip vortex trajectories from which axial and radial vortex coordinates were measured. Using these coordinates, prescribed-wake parameters were determined and input into a hover-performance prediction code. The resultant predictions were compared with experimental performance data to help assess the capabilities of this code. Another result of the experimental work was the development of a method to predict the visibility of rotor tip vortices on shadowgraphs. Using this method, the ability of the shadowgraph technique to visualize tip vortices in the rotor wake was quantified.

Norman, T. R.↗