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NASA NTRS1995

Feasibility of Coupling Between a Single-Mode Elliptical-Core Fiber and a Single Mode Rib Waveguide Over Temperature

To determine the feasibility of coupling the output of an optical fiber to a rib waveguide in a temperature environment ranging from 20 C to 300 C, a theoretical calculation of the coupling efficiency between the two was investigated. This is a significant problem which needs to be addressed to determine whether an integrated optic device can function in a harsh temperature environment. Because the behavior of the integrated-optic device is polarization sensitive, a polarization-preserving optic fiber, via its elliptical core, was used to couple light with a known polarization into the device. To couple light energy efficiently from an optical fiber into a channel waveguide, the design of both components should provide for well-matched electric field profiles. The rib waveguide analyzed was the light input channel of an integrated-optic pressure sensor. Due to the complex geometry of the rib waveguide, there is no analytical solution to the wave equation for the guided modes. Approximation or numerical techniques must be utilized to determine the propagation constants and field patterns of the guide. In this study, three solution methods were used to determine the field profiles of both the fiber and guide: the effective-index method (EIM), Marcatili's approximation, and a Fourier method. These methods were utilized independently to calculate the electric field profile of a rib channel waveguide and elliptical fiber at two temperatures, 20 C and 300 C. These temperatures were chosen to represent a nominal and a high temperature that the device would experience. Using the electric field profile calculated from each method, the theoretical coupling efficiency between the single-mode optical fiber and rib waveguide was calculated using the overlap integral and results of the techniques compared. Initially, perfect alignment was assumed and the coupling efficiency calculated. Then, the coupling efficiency calculation was repeated for a range of transverse offsets at both temperatures. Results of the calculation indicate a high coupling efficiency can be achieved when the two components were properly aligned. The coupling efficiency was more sensitive to alignment offsets in the y direction than the x, due to the elliptical modal profile of both components. Changes in the coupling efficiency over temperature were found to be minimal.

Tuma, Margaret L.↗

NASA NTRS1995

Elliptic surface grid generation on minimal and parametrized surfaces

An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.

Spekreijse, S. P.↗

NASA NTRS1998

Design of Three-Dimensional Hypersonic Inlets with Rectangular to Elliptical Shape Transition

A methodology has been devised for the design of three-dimensional hypersonic inlets which include a rectangular to elliptical shape transition. This methodology makes extensive use of inviscid streamtracing techniques to generate a smooth shape transition from a rectangular-like capture to an elliptical throat. Highly swept leading edges and a significantly notched cowl enable use of these inlets in fixed geometry configurations. The design procedure includes a three dimensional displacement thickness calculation and uses established correlations to check for boundary layer separation due to shock wave interactions. Complete details of the design procedure are presented and the characteristics of a modular inlet with rectangular to elliptical shape transition and a design point of Mach 7.1 are examined. Comparison with a classical two-dimensional inlet optimized for maximum total pressure recovery indicates that this three-dimensional inlet demonstrates good performance even well below its design point.

Smart, M. K.↗

NASA NTRS1999

A Gas-Kinetic Method for Hyperbolic-Elliptic Equations and Its Application in Two-Phase Fluid Flow

A gas-kinetic method for the hyperbolic-elliptic equations is presented in this paper. In the mixed type system, the co-existence and the phase transition between liquid and gas are described by the van der Waals-type equation of state (EOS). Due to the unstable mechanism for a fluid in the elliptic region, interface between the liquid and gas can be kept sharp through the condensation and evaporation process to remove the "averaged" numerical fluid away from the elliptic region, and the interface thickness depends on the numerical diffusion and stiffness of the phase change. A few examples are presented in this paper for both phase transition and multifluid interface problems.

Xu, Kun↗

NASA NTRS2005

An Interoperability Consideration in Selecting Domain Parameters for Elliptic Curve Cryptography

Elliptic curve cryptography (ECC) will be an important technology for electronic privacy and authentication in the near future. There are many published specifications for elliptic curve cryptosystems, most of which contain detailed descriptions of the process for the selection of domain parameters. Selecting strong domain parameters ensures that the cryptosystem is robust to attacks. Due to a limitation in several published algorithms for doubling points on elliptic curves, some ECC implementations may produce incorrect, inconsistent, and incompatible results if domain parameters are not carefully chosen under a criterion that we describe. Few documents specify the addition or doubling of points in such a manner as to avoid this problematic situation. The safety criterion we present is not listed in any ECC specification we are aware of, although several other guidelines for domain selection are discussed in the literature. We provide a simple example of how a set of domain parameters not meeting this criterion can produce catastrophic results, and outline a simple means of testing curve parameters for interoperable safety over doubling.

Ivancic, Will↗

NASA NTRS2006

Aerodynamic Comparison of Hyper-Elliptic Cambered Span (HECS) Wings with Conventional Configurations

An experimental study was conducted to examine the aerodynamic and flow field characteristics of hyper-elliptic cambered span (HECS) wings and compare results with more conventional configurations used for induced drag reduction. Previous preliminary studies, indicating improved L/D characteristics when compared to an elliptical planform prompted this more detailed experimental investigation. Balance data were acquired on a series of swept and un-swept HECS wings, a baseline elliptic planform, two winglet designs and a raked tip configuration. Seven-hole probe wake surveys were also conducted downstream of a number of the configurations. Wind tunnel results indicated aerodynamic performance levels of all but one of the HECS wings exceeded that of the other configurations. The flow field data surveys indicate the HECS configurations displaced the tip vortex farther outboard of the wing than the Baseline configuration. Minimum drag was observed on the raked tip configuration and it was noted that the winglet wake lacked the cohesive vortex structure present in the wakes of the other configurations.

Lazos, Barry S.↗

NASA NTRS2007

Enhanced Elliptic Grid Generation

An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are determined automatically as part of the solution of the defining PDEs. Depending on the shape of the boundary segments and the physical nature of the problem to be solved on the grid, the solution of the defining PDEs may provide for rates of decay to vary along and among the boundary segments and may lend itself to interpretation in terms of one or more physical quantities associated with the problem.

Kaul, Upender K.↗

NASA NTRS2016

CFD Simulations for Arc-Jet Panel Testing Capability Development Using Semi-Elliptical Nozzles

This paper reports computational simulations in support of arc-jet panel testing capability development using semi-elliptical nozzles in a high enthalpy arc-jet facility at NASA Ames Research Center. Two different semi-elliptical nozzle configurations are proposed for testing panel test articles. Computational fluid dynamics simulations are performed to provide estimates of achievable panel surface conditions and useful test area for each configuration. The present analysis comprises three-dimensional simulations of the nonequilibrium flowfields in the semi-elliptical nozzles, test box and flowfield over the panel test articles. Computations show that useful test areas for the proposed two nozzle options are 20.32 centimeters by 20.32 centimeters (8 inches by 8 inches) and 43.18 centimeters by 43.18 centimeters (17 inches by 17 inches). Estimated values of the maximum cold-wall heat flux and surface pressure are 155 watts per centimeters squared and 39 kilopascals for the smaller panel test option, and 44 watts per centimeters squared and 7 kilopascals for the larger panel test option. Other important properties of the predicted flowfields are presented, and factors that limit the useful test area in the semi-free jet test configuration are discussed.

TPS↗

NASA NTRS2016

CFD Simulations for Arc-Jet Panel Testing Capability Development Using Semi-Elliptical Nozzles

CFD↗

NASA NTRSDate not supplied

CFD Simulations of the Truncated IHF Semi-Elliptical Nozzle Flow: Convective Calibration Plate

This paper reports computational simulations of a high-enthalpy panel test facility at NASA Ames Research Center. The recently developed facility configuration uses a truncated version of an existing semi-elliptical nozzle in the 60-MW Interaction Heating Facility, and it provides testing capability for panel test articles as large as 43.2 cm x 43.2 cm (17 in x 17 in). A water-cooled calibration plate, which is attached to the semi-elliptical nozzle bottom surface and instrumented with twenty Gardon-gage heat flux calorimeters and twelve pressure gages, is used to characterize the convective heating environment over the panel test articles. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, and flowfield over panel test articles. Both laminar and turbulent simulations are performed, and the computational results are compared with the calibration plate measurements. Comparisons of computed and measured heat fluxes indicate that the boundary layer in the semi-elliptical nozzle is transitional at certain conditions (relatively higher arc-heater pressures or mass flow rates).

Arc-jets↗

NASA NTRSDate not supplied

CFD Simulations of the Truncated IHF Semi-Elliptical Nozzle Flow: Convective Calibration Plate

This paper reports computational simulations of a high-enthalpy panel test facility at NASA Ames Research Center. The recently developed facility configuration uses a truncated version of an existing semi-elliptical nozzle in the 60-MW Interaction Heating Facility, and it provides testing capability for panel test articles as large as 43.2 cm x 43.2 cm (17 in x 17 in). A water-cooled calibration plate, which is attached to the semi-elliptical nozzle bottom surface and instrumented with twenty Gardon-gage heat flux calorimeters and twelve pressure gages, is used to characterize the convective heating environment over the panel test articles. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, and the flowfields over panel test articles. Both laminar and turbulent simulations are performed, and the computational results are compared with the calibration plate measurements. Comparisons of computed and measured heat fluxes indicate that the boundary layer in the semi-elliptical nozzle is transitional at certain conditions (relatively higher arc-heater pressures or mass flow rates).

Arc-jets↗

NASA NTRSDate not supplied

On Characterization of Laminar to Turbulent Transitional Flow in the Truncated IHF Semi-Elliptical Nozzle

This paper reports computational analysis and experimental data to characterize the laminar to turbulent flow transition in a high-enthalpy panel test facility at NASA Ames Research Center. The recently developed facility configuration uses a truncated version of an existing semi-elliptical nozzle in the 60-MW Interaction Heating Facility, and it provides testing capability for panel test articles as large as 43.2 cm x 43.2 cm (17 in x 17 in). A water-cooled calibration plate, which is attached to the semi-elliptical nozzle bottom surface and instrumented with twenty Gardon-gage heat flux calorimeters and twelve pressure gages, is used to characterize the convective heating environment over the panel test articles. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, and the flowfields over panel test articles, and comparisons with the measured test data. Both laminar and turbulent simulations are performed. Constant current studies are performed: the measured data are grouped at the same arc current levels with varying mass flow rates, and they are compared with corresponding computations. For all currents studied, these studies indicate that the semi-elliptical nozzle flow is transitional at relatively higher mass flow rates within the facility operating envelope.

Arc-jets↗

NASA NTRSDate not supplied

On Characterization of Laminar to Turbulent Transitional Flow in the Truncated IHF Semi-Elliptical Nozzle

This paper reports computational analysis and experimental data to characterize the laminar to turbulent flow transition in a high-enthalpy panel test facility at NASA Ames Research Center. The recently developed facility configuration uses a truncated version of an existing semi-elliptical nozzle in the 60-MW Interaction Heating Facility, and it provides testing capability for panel test articles as large as 43.2 cm x 43.2 cm (17 in x 17 in). A water-cooled calibration plate, which is attached to the semi-elliptical nozzle bottom surface and instrumented with twenty Gardon-gage heat flux calorimeters and twelve pressure gages, is used to characterize the convective heating environment over the panel test articles. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, and the flowfields over panel test articles, and comparisons with the measured test data. Both laminar and turbulent simulations are performed. Constant current studies are conducted: the measured data are grouped at the same arc current levels with varying mass flow rates, and they are compared with corresponding computations. For all currents considered, these studies indicate that the semi-elliptical nozzle flow is transitional at relatively higher mass flow rates within the facility operating envelope. An approximate facility map for the transitional flow characterization is developed, showing laminar and transitional to turbulent flow regions.

Arc-jets↗

NASA NTRS1966

Numerical integration of periodic orbits in the elliptic restricted three-body problem

The problem of finding periodic orbits in the circular restricted three-body problem has been very extensively studied in celestial mechanics. It is well known that continuous families of periodic orbits exist, for which the period varies in a continuous way. However, all the applications which are found in the solar system correspond to cases with non-zero eccentricities, and the elliptic restricted three-body problem is thus a better approximation than the circular one. For instance, for the motion of a satellite in the Earth-Moon system, as a first approximation, we may assume that the Moon moves around the Earth in circular motion; but as a much better approximation, we can also assume that the Moon moves in an elliptic orbit around the Earth.

NUMERICAL INTEGRATION↗

NASA NTRS1972

Computer program for calculating supersonic flow about circular, elliptic, and bielliptic cones by the method of lines

A user's manual for a computer program which calculates the supersonic flow about circular, elliptic, and bielliptic cones at incidence and elliptic cones at yaw by the method of lines is presented. The program is automated to compute a case from known or easily calculated solution by changing the parameters through a sequence of steps. It provides information including the shock shape, flow field, isentropic surface properties, entropy layer, and force coefficients. A description of the program operation, sample computations, and a FORTRAN 4 listing are presented.

Klunker, E. B.↗

NASA NTRS1973

Supersonic aerodynamic characteristics of hypersonic low-wave-drag elliptical body-tail combinations as affected by changes in stabilizer configuration

An investigation has been made at Mach numbers from 1.50 to 4.63 to determine systematically the effects of the addition and position of outboard stabilizers and vertical- and vee-tail configurations on the performance and stability characteristics of a low-wave-drag elliptical body. The basic body shape was a zero-lift hypersonic minimum-wave-drag body as determined for the geometric constraints of length and volume. The elliptical cross section had an axis ratio of 2 (major axis horizontal) and an equivalent fineness ratio of 6.14. Base-mounted outboard stabilizers were at various dihedral angles from 90 deg to minus 90 deg with and without a single center-line vertical tail or a vee-tail. The angle of attack was varied from about minus 6 to 27 deg at sideslip angles of 0 and 5 deg and a constant Reynolds number of 4.58 x one million (based on body length).

Spencer, B., Jr.↗

NASA NTRS1975

Propagation of sound in elliptic ducts

The paper studies the propagation of sound in an elliptic duct, which is of considerable interest in the field of jet-engine noise reduction. The cutoff frequencies of the higher-order circumferential modes in an elliptic duct are calculated for various duct eccentricities. The results indicate that, if equal inlet area is retained, even major deformations of the inlet shape will have virtually no influence on the cutoff conditions of the radiated sound.

Lowson, M. V.↗

NASA NTRS1975

Eclipses by an elliptical torus

A general procedure for computing the effects of eclipses by a torus, including both the outer horizon and the inner or hole horizon, was developed. The procedure can be used for any of the simple figures of revolution encountered in binary-star models. That is, the thickness can be made negligible to produce a thin ring, the hole radius can be set to zero to yield a thin disk, the radius to the center of the elliptical meridian section can be brought to zero to give an ellipsoid of revolution, or the equatorial axis of the elliptical meridian section can be made to equal zero to produce a section of a right circular cylinder.

Wilson, R. E.↗