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At least 109 records · Page 6

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NASA NTRS2006

Free-jet Testing of a REST Scramjet at Off-Design Conditions

Scramjet flowpaths employing elliptical combustors have the potential to improve structural efficiency and performance relative to those using planar geometries. NASA Langley has developed a scramjet flowpath integrated into a lifting body vehicle, while transitioning from a rectangular capture area to both an elliptical throat and combustor. This Rectangular-to-Elliptical Shape Transition (REST) scramjet, has a design point of Mach 7.1, and is intended to operate with fixed-geometry between Mach 4.5 and 8.0. This paper describes initial free-jet testing of the heat-sink REST scramjet engine model at conditions simulating Mach 5.3 flight. Combustion of gaseous hydrogen fuel at equivalence ratios between 0.5 and 1.5 generated robust performance after ignition with a silane-hydrogen pilot. Facility model interactions were experienced for fuel equivalence ratios above 1.1, yet despite this, the flowpath was not unstarted by fuel addition at the Mach 5.3 test condition. Combustion tests at reduced stagnation enthalpy indicated that the engine self-started following termination of the fuel injection. Engine data is presented for the largest fuel equivalence ratio tested without facility interaction. These results indicate that this class of three-dimensional scramjet engine operates successfully at off-design conditions.

Smart, Michael K.↗

NASA NTRS1995

Calculated coupling efficiency between an elliptical-core optical fiber and an optical waveguide over temperature

To determine the feasibility of coupling the output of a single-mode optical fiber into a single-mode rib waveguide in a temperature varying environment, a theoretical calculation of the coupling efficiency between the two was investigated. Due to the complex geometry of the rib guide, there is no analytical solution to the wave equation for the guided modes, thus, approximation and/or numerical techniques must be utilized to determine the field patterns of the guide. In this study, three solution methods were used for both the fiber and guide fields; the effective-index method (EIM), Marcatili's approximation, and a Fourier method. These methods were utilized independently to calculate the electric field profile of each component at two temperatures, 20 C and 300 C, representing a nominal and high temperature. Using the electric field profile calculated from each method, the theoretical coupling efficiency between an elliptical-core optical fiber and a rib waveguide was calculated using the overlap integral and the results were compared. It was determined that a high coupling efficiency can be achieved when the two components are aligned. The coupling efficiency was more sensitive to alignment offsets in the y direction than the x, due to the elliptical modal field profile of both components. Changes in the coupling efficiency over temperature were found to be minimal.

Tuma, Margaret L.↗

NASA NTRS1972

On the elliptic restricted three-body problem.

This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.

Broucke, R.↗

NASA NTRS1988

Boundary element method for 3-D cracks in a plate

Fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a three-dimensional BEM for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations. Part-through elliptic cracks in an elastic plate with traction-free surfaces are analyzed and the SIF values along the crack front are found to compare favorably with the numerical SIF results of Raju and Newman (1979).

Fares, N.↗

NASA NTRS2003

Mach 4 Performance of a Fixed-Geometry Hypersonic Inlet with Rectangular-to-Elliptical Shape Transition

Wind-tunnel testing of a hypersonic inlet with rectangular-to-elliptical shape transition has been conducted at Mach 4.0. These tests were performed to investigate the starting and back-pressure limits of this fixed-geometry inlet at conditions well below the Mach 5.7 design point. Results showed that the inlet required side spillage holes in order to self-start at Mach 4.0. Once started, the inlet generated a compression ratio of 12.6, captured almost 80% of available air and withstood a back-pressure ratio of 30.3 relative to tunnel static pressure. The spillage penalty for self-starting was estimated to be 4% of available air. These experimental results, along with previous experimental results at Mach 6.2 indicate that fixed-geometry inlets with rectangular-to-elliptical shape transition are a viable configuration for airframe-integrated scramjets that operate over a significant Mach number range. Nomenclature

Smart, Michael K.↗

NASA NTRS1993

What do you gain from deconvolution? - Observing faint galaxies with the Hubble Space Telescope Wide Field Camera

We describe experiments with deconvolutions of simulations of deep HST Wide Field Camera images containing faint, compact galaxies to determine under what circumstances there is a quantitative advantage to image deconvolution, and explore whether it is (1) helpful for distinguishing between stars and compact galaxies, or between spiral and elliptical galaxies, and whether it (2) improves the accuracy with which characteristic radii and integrated magnitudes may be determined. The Maximum Entropy and Richardson-Lucy deconvolution algorithms give the same results. For medium and low S/N images, deconvolution does not significantly improve our ability to distinguish between faint stars and compact galaxies, nor between spiral and elliptical galaxies. Measurements from both raw and deconvolved images are biased and must be corrected; it is easier to quantify and remove the biases for cases that have not been deconvolved. We find no benefit from deconvolution for measuring luminosity profiles, but these results are limited to low S/N images of very compact (often undersampled) galaxies.

Schade, David J.↗

DOE OSTI2024

Measured dynamic aperture and detuning of nonlinear integrable optics

One of the most promising advantages of nonlinear integrable optics is strong amplitude dependent tune shift without degrading the dynamic aperture. The integrable optics test accelerator (IOTA) at Fermilab is constructed around nonlinear lattice elements of the elliptical type as described by Danilov and Nagaitsev. Detuning and dynamic aperture scans in IOTA were performed using a fast dipole kicker and a low emittance electron beam. The evolution of the dynamic aperture and detuning for different configurations of the integrable optics lattice are presented.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Measured Dynamic Aperture and Detuning of Nonlinear Integrable Optics

43 PARTICLE ACCELERATORS↗

NASA NTRS1973

Analysis of embedded shock waves calculated by relaxation methods.

The requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies. A mathematical analysis shows that sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator. The latter results in a consistency condition on the integral equations, rather than the differential, at these points. Calculated jump conditions for several embedded and detached shock waves are analyzed in the physical and hodograph planes. Comparisons are made with previous results, a time-dependent calculation, and data.

Murman, E. M.↗

NASA NTRS1976

Multivariate normal integration

Monte Carlo program evaluates integrals over rectangular regions for dimensions less than six and over elliptical regions in bivariate case. Program gives positive definite symmetric variance/covariance matrix factorization and calculates reciprocal of lower triangular matrix and product of diagonal elements of triangular matrix.

Falls, L. W.↗

NASA NTRS1983

Numerical predictions of residence times behind a rearward facing step with transverse injection

A numerical investigation of the two-dimensional recirculation zone formed between a rear-ward facing step and a transverse hydrogen jet in a supersonic flow is presented. Calculations were made using an elliptic flow computer code with a time-relaxation finite difference integration algorithm. Cases were examined for jet static pressures between 2 and 5 times mainstream with jets located 3 to 7 step heights downstream of the step. Nominal mainstream flow conditions were Mach 2.4 air at 1 atm pressure and 1000K (1800R) static temperature. Results in the form of mean properties in the recirculation zone and residence time are presented. Calculations of the decay of hydrogen mass from the steady state are presented for selected cases. The combustion potential for each case is assessed by comparison of computed conditions in the recirculation zone with the results from a well-stirred reactor theory.

Rogers, R. C.↗

NASA NTRS1983

Numerical predictions of residence times behind a rearward facing step with transverse injection

A numerical investigation of the two-dimensional recirculation zone formed between a rearward facing step and a transverse hydrogen jet in a supersonic flow is presented. Calculations were made using an elliptic flow computer code with a time-relaxation finite difference integration algorithm. Cases were examined for jet static pressures between 2 and 5 times mainstream with jets located 3 to 7 step heights downstream of the step. Nominal mainstream flow conditions were Mach 2.4 air at 1 atm pressure and 1000 K (1800 R) static temperature. Results in the form of mean properties in the recirculation zone and residence time are presented. Calculations of the decay of hydrogen mass from the steady state are presented for selected cases. The combustion potential for each case is assessed by comparison of computed conditions in the recirculation zone with the results from a well-stirred reactor theory.

Rogers, R. C.↗

NASA NTRS2005

Image of Fomalhaut Dust Ring at 350 Microns: The Relative Column Density Map Shows Pericenter-Apocenter Asymmetry

We have imaged the circumstellar disk of Fomalhaut at 350 mm wavelength, using SHARC II (Submillimeter High Angular Resolution Camera II) at the Caltech Submillimeter Observatory. The spatial resolution of the raw images (9") has been enhanced by a factor of 3 using the HiRes deconvolution procedure. We find that at this wavelength and signal-to-noise ratio (approx.12), the observed morphology is that of a simple inclined ring (i approx. 70 deg), with little or no other apparent structure--this is the first observation that shows clearly the ring morphology of the disk. We have combined our 350 mm data with Spitzer Space Telescope images at 24, 70, and 160 mm in order to estimate the two-dimensional spatial variation of relative column density ("tau map") using our DISKFIT procedure. The tau map is based on the following physical assumptions: (1) the wavelength variation of opacity is the same throughout the disk, (2) the radial variation of dust temperature is dictated by the energy balance of individual grains in the stellar radiation field, and (3) the vertical scale height of the disk follows a power-law radial variation. The results confirm the ringlike morphology but also show that the geometric center is displaced from the star by about 8 AU and that the ring has an apocentric enhancement of approximately 14% in integrated column density. If we interpret the displacement in terms of elliptical orbital motion due to gravitational perturbation by an unseen planet, then the implied forced eccentricity is ~0.06; dynamical modeling then predicts an apocentric density enhancement consistent with that inferred from the tau map.

Fomalhaut↗

NASA NTRS1986

Three-dimensional grids as solutions of elliptic systems

An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.

Hartwich, P.-M.↗

NASA NTRS1994

The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries

Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.

Sharobeam, Monir H.↗

NASA NTRS1986

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

Sidi, A.↗

NASA NTRS2008

Limits to Open Class Performance?

This presentation discusses open or unlimited class aircraft performance limitations and design solutions. Limitations in this class of aircraft include slow climbing flight which requires low wing loading, high cruise speed which requires high wing loading, gains in induced or viscous drag alone which result in only half the gain overall and other structural problems (yaw inertia and spins, flutter and static loads integrity). Design solutions include introducing minimum induced drag for a given span (elliptical span load or winglets) and introducing minimum induced drag for a bell shaped span load. It is concluded that open class performance limits (under current rules and technologies) is very close to absolute limits, though some gains remain to be made from unexplored areas and new technologies.

Bowers, Albion H.↗

NASA NTRS1985

Design study of an integrated aerobraking orbital transfer vehicle

An aerobraking orbital transfer vehicle (AOTV) concept, which has an aerobrake structure that is integrated with the propulsion stage, is discussed. The concept vehicle is to be assembled in space and is space-based. The advantages of aeroassist over an all propulsive vehicle are discussed and it is shown that the vehicle considered is very competitive with inflatable and deployable concepts from mass and performance aspects. The aerobrake geometry is an ellipsoidally blunted, raked-off, elliptical wide-angle cone with a toroidal skirt. Propellant tanks, engines, and subsystems are integrated into a closed, isogrid aerobrake structure which provides rigidity. The vehicle has two side-firing, gimbaled RL-10 type engines and carries 38,000 kg of useable propellant. The trajectory during aerobraking is determined from an adaptive guidance logic, and the heating is determined from engineering correlations as well as 3-D Navier-Stokes solutions. The AOTV is capable of placing 13,500 kg payload into geosynchronous Earth orbit (GEO) or carrying a LEO-GEO-LEO round-trip payload of 7100 kg. A two-stage version considered for lunar missions results in a lunar surface delivery capability of 18,000 kg or a round-trip capability of 6800 kg with 3860 kg delivery-only capability.

Scott, C. D.↗