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NASA NTRS1958

Elliptic Cones Alone and with Wings at Supersonic Speed

To help fill the gap in the knowledge of aerodynamics of shapes intermediate between bodies of revolution and flat triangular wings, force and moment characteristics for elliptic cones have been experimentally determined for Mach numbers of 1.97 and 2.94. Elliptic cones having cross-sectional axis ratios from 1 through 6 and with lengths and base areas equal to circular cones of fineness ratios 3.67 and 5 have been studied for angles of bank of 0 degree and 90 degrees. Elliptic and circular cones in combination with triangular wings of aspect ratios 1 and 1.5 also have been considered. The angle-of-attack range was from 0 degree to about 16 degrees, and the Reynolds number was 8 x 10(6), based on model length. In addition to the forces and moments at angle of attack, pressure distributions for elliptic cones at zero angle of attack have been determined. The results of this investigation indicate that there are distinct aerodynamic advantages to the use of elliptic cones.

Jorgensen, Leland H↗

NASA NTRS1994

Far-infrared mapping of dusty elliptical galaxies

Preliminary results from a program to map the thermal far-infrared emission from cool dust in elliptical galaxies using the Yerkes 60-Channel Camera on the Kuiper Airborne Observatory (KAO) are presented. The 160 micron emission from the elliptical NGC 6542 is apparently extended over the optical galaxy whereas the 100 micron emission is unresolved. This implies a dust temperature gradient consistent with that expected for dust with Galactic properties exposed to the general interstellar radiation field of the elliptical galaxy. Observations of the elliptical NGC 5666 and the NGC 7463/4/5 compact group (consisting of the elliptical NGC 7464, the S0 NGC 7465, and the spiral NGC 7463) are also discussed.

Lees, Joanna F.↗

NASA NTRS1995

Multilevel elliptic smoothing of large three-dimensional grids

Elliptic grid generation methods have been used for many years to smooth and improve grids generated by algebraic interpolation schemes. However, the elliptic system that must be solved is nonlinear and convergence is generally very slow for large grids. In an attempt to make elliptic methods practical for large three-dimensional grids, a two-stage implementation is developed where the overall grid point locations are set using a coarse grid generated by the elliptic system. The coarse grid is then interpolated to generate a finer grid which is smoothed using only a few iterations of the elliptic system.

Mastin, C. Wayne↗

NASA NTRS1994

The richness of the globular cluster system of NGC 3923: Clues to elliptical galaxy formation

We present new data on the globular cluster system of the elliptical galaxy NGC 3923 which show that it has the most globular clusters per unit luminosity of any noncluster elliptical yet observed, with S(sub N) = 6.4 +/- 1.4. NGC 3923 is also among the brightest ellipticals outside of a galaxy cluster for which the number of globular clusters has been determined. Our observation of a large number of clusters per unit luminosity (high S(sub N)-value) for a bright elliptical in a sparse environment is consistent with the suggestion of Djorgovski and Santiago that the number of globular clusters is a power-law function of the luminosity with an exponent greater than 1. We relate this higher specific frequency of globular clusters in more luminous galaxies to other observations which indicate that the physical conditions within elliptical galaxies at the time of their formation were dependent on galaxy mass.

Zepf, Stephen E.↗

NASA NTRS2002

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Kaul, Upender K.↗

NASA NTRS2008

Spatially Resolved Imaging at 350 Micrometers of Cold Dust in Nearby Elliptical Galaxies

Continuum observations at 350 micrometers of seven nearby elliptical galaxies for which CO gas disks have recently been resolved with interferometry mapping are presented. These SHARC II mapping results provide the first clearly resolved far-infrared (FIR)-to-submillimeter continuum emission from cold dust (with temperatures 31 K is approximately greater than T approximately greater than 23 K) of any elliptical galaxy at a distance greater than 40 Mpc. The measured FIR excess shows that the most likely and dominant heating source of this dust is not dilute stellar radiation or cooling flows, but rather star formation that could have been triggered by an accretion or merger event and fueled by dust-rich material that has settled in a dense region cospatial with the central CO gas disks. The dust is detected even in two cluster ellipticals that are deficient in H (sub I), showing that, unlike H (sub I), cold dust and CO in ellipticals can survive in the presence of hot X-ray gas, even in galaxy clusters. No dust cooler than 20 K, either distributed outside the CO disks or cospatial with and heated by the entire dilute stellar optical galaxy (or very extended H (sub I)), is currently evident.

photometry↗

NASA NTRS1978

Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication

The film-parameter equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic of low-elastic-modulus materials, or isoviscous-elastic; and elastohydrodynamic, or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The film-parameter equations for the respective regimes come from earlier theoretical studies by the authors on elastohydrodynamic and hydrodynamic lubrication of elliptical conjunctions. These equations are restated and the results are presented as a map of the lubrication regimes, with film-thickness contours on a log-log grid of the viscosity and elasticity parameters for five values of the ellipticity parameter. The results present a complete theoretical film-parameter solution for elliptical contacts in the four lubrication regimes.

Hamrock, B. J.↗

NASA NTRS1978

On the rotation of elliptical galaxies

The tensor virial theorem is applied to models of early-type galaxies. First the theorem is applied to rotating elliptical galaxies whose constant-density surfaces are similar ellipsoids. A relationship is obtained between the observed rotations and the forms of generally triaxial galaxies. By applying the results of Robert (1962) to the evaluation of the components of the Chandrasekhar tensor which occurs in this relationship, it is found that the form of a galaxy that lacks global velocity anisotropy uniquely determines the ratio of its rotational and random kinetic energies independently of the radial density profile of that galaxy. A distribution of three-dimensional prolate spheroids is derived which accounts for the observed distribution of ellipticities reported by Sandage, Freeman, and Stokes (1970). This is then used to derive curves giving the expected frequency of occurrence of galaxies of given rotational velocities for each of a number of different apparent elongations on the sky. It is found that if elliptical galaxies are prolate, there should be little correlation between apparent ellipticity and rotation velocity.

Binney, J.↗

NASA NTRS1982

Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies is introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The lineaar stabilities of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable.

Kwok, J. H.↗

NASA NTRS1983

Elastohydrodynamics of elliptical contacts for materials of low elastic modulus

The influence of the ellipticity parameter k and the dimensionless speed U, load W, and materials G parameters on minimum film thickness for materials of low elastic modulus was investigated. The ellipticity parameter was varied from 1 (a ball-on-plane configuration) to 12 (a configuration approaching a line contact); U and W were each varied by one order of magnitude. Seventeen cases were used to generate the minimum- and central-film-thickness relations. The influence of lubricant starvation on minimum film thickness in starved elliptical, elastohydrodynamic configurations was also investigated for materials of low elastic modulus. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction in the numerical solutions. Contour plots of pressure and film thickness in and around the contact were presented for both fully flooded and starved lubrication conditions. It is evident from these figures that the inlet pressure contours become less circular and closer to the edge of the Hertzian contact zone and that the film thickness decreases substantially as the serverity of starvation increases. The results presented reveal the essential features of both fully flooded and starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus.

Hamrock, B. J.↗

NASA NTRS1985

Downwash in the plane of symmetry of an elliptically loaded wing

A closed-form solution for the downwash in the plane of symmetry of an elliptically loaded line is given. This theoretical result is derived from Prandtl's lifting-line theory and assumes that: (1) a three-dimensional wing can be replaced by a straight lifting line, (2) this line is elliptically loaded, and (3) the trailing wake is a flat-sheet which does not roll up. The first assumption is reasonable for distances greater than about 1 chord from the wing aerodynamic center. The second assumption is satisfied by any combination of wing twist, spanwise camber variation, or planform that approximates elliptic loading. The third assumption is justified only for high-aspect-ratio wings at low lift coefficients and downstream distances less than about 1 span from the aerodynamic center. It is shown, however, that assuming the wake to be fully rolled up gives downwash values reasonably close to those of the flat-sheet solution derived in this paper. The wing can therefore be modeled as a single horseshoe vortex with the same lift and total circulation as the equivalent ellipticity loaded line, and the predicted downwash will be a close approximation independent of aspect ratio and lift coefficient. The flat-sheet equation and the fully rolled up wake equation are both one-line formulas that predict the upwash field in front of the wing, as well as the downwash field behind it. These formulas are useful for preliminary estimates of the complex aerodynamic interaction between two wings (i.e., canard, tandem wing, and conventional aircraft) including the effects of gap and stagger.

Phillips, J. D.↗

NASA NTRS1986

Regularity estimates up to the boundary for elliptic systems of difference equations

Regularity estimates up to the boundary for solutions of elliptic systems of finite difference equations were proved. The regularity estimates, obtained for boundary fitted coordinate systems on domains with smooth boundary, involve discrete Sobolev norms and are proved using pseudo-difference operators to treat systems with variable coefficients. The elliptic systems of difference equations and the boundary conditions which are considered are very general in form. The regularity of a regular elliptic system of difference equations was proved equivalent to the nonexistence of eigensolutions. The regularity estimates obtained are analogous to those in the theory of elliptic systems of partial differential equations, and to the results of Gustafsson, Kreiss, and Sundstrom (1972) and others for hyperbolic difference equations.

Strikwerda, J. C.↗

NASA NTRS1985

Boxy isophotes, discs and dust lanes in elliptical galaxies

CCD images of 42 elliptical and S0 galaxies are examined for low-contrast structures or subtle distortions of the isophotes from perfect ellipses. 75 percent of the galaxies have isophotes completely describable as concentric ellipses to within the photometry errors. 'Boxy' isophotes, stellar discs, and dust lanes are detected in the remaining 25 percent of the sample. The boxy elliptical galaxies appear dynamically indistinguishable from normal ellipticals and are therefore different from boxy bulges, which rotate rapidly. Most of the galaxies with faint discs, however, appear dynamically similar to S0 galaxies. Nearly edge-on dust lanes are found in four galaxies, which suggests that dust lanes may commonly occur in elliptical galaxies.

Lauer, T. R.↗

NASA NTRS1986

Effects of initial condition on circular and elliptic jet noise

Noise produced by cold elliptic jets was studied experimentally using a 4 cm air jet in an anechoic chamber by varying the aspect ratio, nozzle exit boundary layer, and Mach number. Elliptic geometry is found to accentuate the sound produced by pairing of the shear layer vortices in the laminar boundary jet. Calculation of the pressure field produced by the pairing of elliptic vortex rings shows that the ratio of sound intensities produced by the pairing of inviscid elliptic vortex filament rings should be equal to their aspect ratio, the minor axis producing greater sound. Tripping the nozzle boundary layer changes the instability of the shear layer and removes the laminar vortices. If the sound produced by pairing and/or breakdown is considered to be the difference between laminar and turbulent jet noise, the pairing mechanism is seen to be very significant in laminar boundary layer jets.

Bridges, J. E.↗

NASA NTRS1990

The evolution of the interstellar medium in elliptical galaxies. I - The early wind phase

The evolving mass loss rates from type I and II SNe, stellar winds, and PN and the associated evolution of the mass-averaged temperature of the stellar ejecta are calculated. At early times, the mass-averaged temperature of the ejecta is found to be much greater than the central escape temperature from even very luminous elliptical galaxies due to the high frequency of type II SNe. The amount of oxygen and iron that can be injected into the intracluster medium from type II SN-driven winds in elliptical galaxies is calculated and the results are compared with observations. The gas ejected during this early wind phase is very hot and can heat the cluster gas to temperatures greater than that produced by gravitational heating alone. Two numerical simulations concerning the evolution of the ISM in an elliptical galaxy model with L(B) = 10 to the 11th solar are presented which confirm the existence of an early type II SN-driven wind phase and reproduce the observed X-ray properties of bright elliptical galaxies in the present epoch.

David, L. P.↗

NASA NTRS1992

Molecular gas in elliptical galaxies with dust lanes

We have searched for CO(1-0) line emission in eight dust lane elliptical and lenticular galaxies using the Nobeyama 45 m telescope. Five of the eight galaxies, including the well-studied elliptical NGC 1052, have CO emission at above the 5-sigma level, with inferred molecular gas masses ranging from 10 exp 8 to a few times 10 exp 9 solar masses. Our selection criterion differs from previous surveys in that it does not depend on the FIR fluxes, and thus is less sensitive to the sizes and distances of the host galaxies or to the degree to which dust is heated. The relatively high detection rate of CO in these ellipticals suggests a close correlation between molecular mass and cold dust. Compared with previously studied samples of FIR selected early-type galaxies, our sample has on average four times more CO emission per unit FIR (40-120 microns) luminosity. If the intrinsic gas-to-dust ratio of these galaxies as similar to that of the Milky Way, then only about 5 percent of the dust mass in dust lane ellipticals radiates substantially at 60 and 100 microns, and the remaining dust must be colder than about 30 K.

Wang, Zhong↗

NASA NTRS1992

The noise from supersonic elliptic jets

This paper presents calculations of the noise radiated by a supersonic elliptic jet. The large scale structures in the jet, that are the predominant source of noise in the downstream direction, are modeled as instability waves. The evolution of the instability waves is determined by a local, linear, inviscid analysis. An expression is derived for the acoustic field outside the jet and the far field directivity associated with each instability wave. Calculations are performed for a Mach 1.5 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 3:1. The mean flow development is taken from experimental results. Comparisons are made with far field acoustic measurements.

Morris, Philip J.↗

NASA NTRS1994

Modeling near wall effects in second moment closures by elliptic relaxation

The elliptic relaxation model of Durbin (1993) for modeling near-wall turbulence using second moment closures (SMC) is compared to DNS data for a channel flow at Re(sub t) = 395. The agreement for second order statistics and even the terms in their balance equation is quite satisfactory, confirming that very little viscous effects (via Kolmogoroff scales) need to be added to the high Reynolds versions of SMC for near-wall-turbulence. The essential near-wall feature is thus the kinematic blocking effect that a solid wall exerts on the turbulence through the fluctuating pressure, which is best modeled by an elliptic operator. Above the transition layer, the effect of the original elliptic operator decays rapidly, and it is suggested that the log-layer is better reproduced by adding a non-homogeneous reduction of the return to isotropy, the gradient of the turbulent length scale being used as a measure of the inhomogeneity of the log-layer. The elliptic operator was quite easily applied to the non-linear Craft & Launder pressure-strain model yielding an improved distinction between the spanwise and wall normal stresses, although at higher Reynolds number (Re) and away from the wall, the streamwise component is severely underpredicted, as well as the transition in the mean velocity from the log to the wake profiles. In this area a significant change of behavior was observed in the DNS pressure-strain term, entirely ignored in the models.

Laurence, D.↗