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NASA NTRS1988

A numerical study of viscous vortex rings using a spectral method

Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.

Stanaway, S. K.↗

NASA NTRS1995

Hydrodynamics of coalescing binary neutron stars: Ellipsoidal treatment

We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.

Lai, Dong↗

NASA NTRS1993

Collisions and close encounters between massive main-sequence stars

Smooth-particle hydrodynamics is used to investigate collisions and close encounters between two massive main-sequence stars. Approximate scaling relations and fitting formulas are given for the amount of mass loss and for the critical impact parameters for capture or merging. The more massive stars, which have smaller ratios of specific binding energy to the square of escape velocity, are more easily disrupted in collisions. As the relative velocity increases, the orbital energy of the colliding stars can only be dissipated by shock heating, and the critical capture radius decreases much faster than predicted by linear theory. The average fractional mass loss per collision in a cluster is found not to depend sensitively on the stellar velocity dispersion.

Lai, Dong↗

NASA NTRS1997

Modeling of Water Injection into a Vacuum

A loosely coupled two-phase vacuum water plume model has been developed. This model consists of a source flow model to describe the expansion of water vapor, and the Lagrangian equations of motion for particle trajectories. Gas/Particle interaction is modeled through the drag force induced by the relative velocities. Particles are assumed traveling along streamlines. The equations of motion are integrated to obtain particle velocity along the streamline. This model has been used to predict the mass flux in a 5 meter radius hemispherical domain resulting from the burst of a water jet of 1.5 mm in diameter, mass flow rate of 24.2 g/s, and stagnation pressure of 21.0 psia, which is the nominal Orbiter water dump condition. The result is compared with an empirical water plume model deduced from a video image of the STS-29 water dump. To further improve the model, work has begun to numerically simulate the bubble formation and bursting present in a liquid stream injected into a vacuum. The technique of smoothed particle hydrodynamics was used to formulate this simulation. A status and results of the on-going effort are presented and compared to results from the literature.

Alred, John W.↗

NASA NTRS2020

On the Maximum Stellar Rotation to Form a Black Hole without an Accompanying Luminous Transient

The collapse of a massive star with low angular momentum content is commonly argued to result in the formation of a black hole without an accompanying bright transient. Our goal in this Letter is to understand the flow in and around a newly-formed black hole, involving accretion and rotation, via general relativistic hydrodynamics simulations aimed at studying the conditions under which infalling material can accrete without forming a centrifugally supported structure and, as a result, generate no effective feedback. If the feedback from the black hole is, on the other hand, significant, the collapse would be halted and we suggest that the event is likely to be followed by a bright transient. We find that feedback is only efficient if the specific angular momentum of the infalling material at the innermost stable circular orbit exceeds that of geodesic circular flow at that radius by at least≈20%. We use the results of our simulations to constrain the maximal stellar rotation rates of the disappearing massive progenitors PHL293B-LBV and N6946-BH1, and to provide an estimate of the overall rate of disappearing massive stars. We find that about a few percent of single O-type stars with measured rotational velocities are expected to spin below the critical value before collapse and are thus predicted to vanish without a trace.

Scott C Noble↗

NASA NTRS1998

High-Velocity Ly(Alpha) Emission from SMR 1987A

The high-velocity Ly(Alpha) emission from SN 1987A observed with the Space Telescope Imaging Spectrograph (STIS) evidently comes from a reverse shock formed where the outer envelope of SN 1987A strikes ionized gas inside the inner circumstellar ring. The observations can be explained by a simple kinematic model, in which the Ly(Alpha) emission comes from hydrogen atoms with radial velocity approximately 15,000 km s(exp -1) crossing a reverse shock in the shape of a slightly prolate ellipsoid with equatorial radius 4.8 x 10(exp 17) cm or approximately 80% of the distance to the inner surface of the inner ring. N v double Lambda 1239, 1243 emission, if present, has a net luminosity approximately less than 30% times that of the Ly(Alpha) emission. Future STIS observations should enable us to predict the time of impact with the inner ring and to determine unambiguously whether or not N v emission is present. These observations will offer a unique opportunity to probe the structure of SN 1987A's circumstellar environment and the hydrodynamics and kinetics of very fast shocks.

Michael, Eli↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. III - Aerodynamic lift

The aerodynamic lift exerted on a magnetic flux tube by the asymmetric flow around the two sides of the tube is calculated as part of an investigation of the physics of solar flux tubes. The general hydrodynamic forces on a rigid circular cylinder in a nonuniform flow of an ideal fluid are derived from the first derivatives of the velocity field. Aerodynamic lift in a radial nonuniform flow is found to act in the direction of the flow, toward the region of increased flow velocity, while in a shear flow, lift is perpendicular to the free stream and directed toward increasing flow velocity. For a general, three dimensional, large-scale stationary incompressible equilibrium flow, an expression is also derived relating the lift per unit length to the dynamical pressure, cylinder radius and the gradient of the free-stream velocity. Evidence from an asymmetric airfoil in a uniform flow indicates that lift is enhanced in a real fluid in the presence of turbulence.

Parker, E. N.↗

NASA NTRS2001

Formation and Early Evolution of Solar and Extra-Solar Giant Planets

This project investigates the origin of giant planets, both in the Solar System and around other stars. It is assumed that the planets form by the core accretion process: small solid particles in a disk surrounding a young star gradually coagulate into objects of a few kilometers in size, known as planetesimals, which then accumulate into solid protoplanetary cores. Once the cores have become large enough, they are able to attract gas from the surrounding disk to form the deep gaseous envelope of the giant planet. Our code simulates giant planet growth in a spherical approximation, and it has been quite successful in addressing a number of basic planetary properties. Further improvements to the code have been made to achieve a more realistic understanding of planetary formation. The computations of the models were based on an earlier version of our code and were stopped at the onset of runaway gas accretion. Now, improved boundary conditions have been incorporated into the code to allow for hydrodynamic inflow of gas and to handle the late stages of evolution when the planet evolves at constant mass. These changes were made to the version of the code that uses a constant accretion rate and to the version that uses a self-consistent method for calculating both the solid and gas accretion rates. The equation of state has been updated to incorporate the detailed tables of Saumon, Chabrier, and Van Horn. The opacities were updated to include the results of Alexander and Ferguson. The outer boundary conditions were modified. During the accretion phase when the planet's radius is between the accretion radius and the tidal radius, we set the outer boundary at a 'modified' accretion radius, which is the point where thermal energy is enough to bring gas to the edge of the Hill sphere.

Bodenheimer, P. H.↗

NASA NTRS2016

Migration of Accreting Planets in Radiative Discs From Dynamical Torques

We present the results of hydrodynamical simulations of the orbital evolution of planets undergoing runaway gas accretion in radiative discs. We consider accreting disc models with constant mass flux through the disc, and where radiative cooling balances the effect of viscous heating and stellar irradiation. We assume that 20–30 M(sub ⨁) giant planet cores are formed in the region where viscous heating dominates and migrate outward under the action of a strong entropy-related corotation torque. In the case where gas accretion is neglected and for an α viscous stress parameter α = 2 × 10(exp -3), we find evidence for strong dynamical torques in accreting discs with accretion rates M ̇ ≳ 7 × 10(exsp -8)M(sub ⨀) yr(exp -1). Their main effect is to increase outward migration rates by a factor of ∼2 typically. In the presence of gas accretion, however, runaway outward migration is observed with the planet passing through the zero-torque radius and the transition between the viscous heating and stellar heating dominated regimes. The ability for an accreting planet to enter a fast migration regime is found to depend strongly on the planet growth rate but can occur for values of the mass flux through the disc of M ̇ ≳ 5 × 10(exp -8)M(sub ⨀) yr(exp -1).We find that an episode of runaway outward migration can cause an accreting planet formed in the 5–10 au region to temporarily orbit at star–planet separations as large as∼60–70 au. However, increase in the amplitude of the Lindblad torque associated with planet growth plus change in the streamline topology near the planet systematically cause the direction of migration to be reversed. Subsequent evolution corresponds to the planet migrating inward rapidly until it becomes massive enough to open a gap in the disc and migrate in the type II regime. Our results indicate that a planet can reach large orbital distances under the combined effect of dynamical torques and gas accretion, but an alternative mechanism is required to explain the presence of massive planets on wide orbits.

Accretion↗

NASA NTRS1982

A wind tunnel investigation of the shape of uncharged raindrops in the presence of an external, electric field

Results of a wind tunnel experiment in which electrically uncharged water drops of 500 to 3000 microns equivalent radius are freely suspended in the vertical air stream of the UCLA cloud tunnel are presented. During this suspension the drops were exposed to external vertical electric fields of 500 to 8,000 volts/cm. The change in drop shape with drop size and electric field strength was noted and is discussed in the light of theoretical work cited in the literature which unfortunately does not take into account the effects of air flow past the drop. The wind tunnel study is documented by stills from a 16 mm film record that demonstrates the shape of water drops in response to both hydrodynamic and electric forces.

Pruppacher, H. R.↗

NASA NTRS1995

Using X-rays to determine which compact groups are illusory

If the large-scale galaxy distribution is filamentary, as suggested by some observations and recent hydrodynamical simulations, then lengthwise views of filaments will apparently produce compact groups (CGs) that are in reality stretched out along the line of sight. This possibility has been advocated recently by Hernquist, Katz, & Weinberg (1995). Here we propose a test for this hypothesis using X-ray emission from CGs. The observable quantity Q identical with L(sub x)a(sup 3)(sup p)/(L(sup 2)(sup g))T(sup 1/2)(sub x) should be proportional to the axis ratio of the group, a/c, where a and c are the short and long axes of a prolate distribution, a(sub p) is the radius of the group projected onto the sky, L(sub x) is the bolometric X-ray luminosity, L(sub g) is the group blue luminosity, and T(sub x) is the gas temperature. We find that the distribution of Q is consistent with the notion that many CGs with unusually small values of a/c are frauds, i.e., that the values of Q are anomalously small. Absent other information, it is equally possible that CGs are very gas-poor relative to rich clusters; however, this can be tested using the Sunyaev-Zeldovich effect. If the groups have a close to normal ratio of gas to total mass, but are simply stretched out along the line of sight, a Sunyaev-Zeldovich signal should be detectable.

Ostriker, Jeremiah P.↗

NASA NTRS1993

The sand bag model of the dispersion of the cosmic body in the atmosphere

The strength of the extraterrestrial bodies depends on their structure, composition, dimensions, and the history of this body. The fragmentation of the body due to aerodynamic stresses begins at sufficiently large heights above the surface of the Earth. The process of fragmentation and dispersion of the fragments usually is studied by the hydrodynamic or even gasdynamic models. If the fragmentation process begins due to the initial cracks and faults of the body, or this body consists of large boulders glued by ice, the strength of these boulders after fragmentation remains higher than the aerodynamic stresses exerted at the remaining part of the body. It is supposed that fragmentation occurs at initial moment t = 0 at some height z(sub o) above the surface of the air, these fragments remain solid. The possibility of further fragmentation during the remaining part of the trajectory is not taken into account. If the number of these parts is large enough and their size is small in comparison to the initial radius of the body than we can use the sand bag model proposed in qualitative form.

Teterev, A. V.↗

NASA NTRS1979

The structure and appearance of winds from supercritical accretion disks. I - Numerical models

Equations for the structure and appearance of supercritical accretion disks and the radiation-driven winds which emanate from them are derived and solved by a steady-state hydrodynamic computer code with a relaxation technique used in stellar structure problems. The present model takes into account the mass of the accreting star, the total accretion rate, a generalization of the disk alpha parameter which accounts for heating by processes in addition to viscosity, and the ratio of the total luminosity to the Eddington luminosity. Solutions indicate that for accretion onto a hard-surfaced star, steady, optically thick winds result for even slightly supercritical accretion, and the object will appear as a supergiant star with a high mass loss rate and a nonblackbody spectrum. Winds from black hole accretion disks are expected to depend on the form of the accretion interior to the critical radius, possibly consisting of no ejection at all, a wind similar to that of a hard-surfaced star, or a column of material ejected from a hole in the accretion disk.

Meier, D. L.↗

NASA NTRS1994

The heating of nova ejecta by radioactive decays of the beta-unstable nuclei

Recent nucleosynthesis and hydrodynamic calculations of the consequences of accretion onto massive ONeMg white dwarf stars show that under certain circumstances significant amounts of the beta-unstable nuclei can be produced and ejected by the resulting explosion. We use these calculations as a guide in order to obtain the conditions under which the heating of the ejected material by the nonthermal electrons and positrons produced by the decays of the beta-unstable nuclei is sufficient to overcome the cooling from adiabatic expansion and lead to the production of X-ray-emitting coronal gas. These conditions are as follows: (1) a mass fraction for Na-22 of the order of 10(exp -3) or greater, (2) an expansion velocity in the range approximately 10(exp 2) - 10(exp 3) km/s, (3) a photospheric radius of approximately 10(exp 14) cm, (4) if the density distribution in the atmosphere satisfies a power law, then the exponent must be less than 3 for heating to overcome adiabatic cooling. Both the simulations of the outburst and the model atmosphere fits to the observed energy distributions, however, imply that the exponent is greater than or = 3 during the early phases of the outburst. Nevertheless, for a value of the exponent of 2, we predict the time when hot coronal gas can form during the expansion phases of the envelope.

Pistinner, Shlomi↗

NASA NTRS2021

VLTI-MATISSE Chromatic Aperture-Synthesis Imaging of η Carinae’s Stellar Wind Across the Brα Line: Periastron Passage Observations in February 2020

Context: Eta Carinae is a highly eccentric, massive binary system (semimajor axis∼15.5 au) with powerful stellar winds and a phase-dependent wind-wind collision (WWC) zone. The primary star, ηCar A, is a luminous blue variable (LBV); the secondary, η Car B, is a Wolf-Rayet or O star with a faster but less dense wind. Aperture-synthesis imaging allows us to study the mass loss from the enigmatic LBV η Car. Understanding LBVs is a crucial step toward improving our knowledge about massive stars and their evolution. Aims: Our aim is to study the intensity distribution and kinematics of η Car’s WWC zone. Methods: Using the VLTI-MATISSE mid-infrared interferometry instrument, we perform Brα imaging of η Car’s distorted wind. Results: We present the first VLTI-MATISSE aperture-synthesis images of η Car A’s stellar wind in several spectral channels distributed across the Brα 4.052 μm line (spectral resolving power R∼960). Our observations were performed close to periastron passage in February 2020 (orbital phase∼14.0022). The reconstructed iso-velocity images show the dependence of the primary stellar wind on wavelength or line-of-sight (LOS) velocity with a spatial resolution of 6 mas (∼14 au). The radius of the faintest outer wind regions is∼26 mas (∼60 au). At several negative LOS velocities, the primary stellar wind is less extended to the northwest than in other directions. This asymmetry is most likely caused by the WWC. Therefore, we see both the velocity field of the undisturbed primary wind and the WWC cavity. In continuum spectral channels, the primary star wind is more compact than in line channels. A fit of the observed continuum visibilities with the visibilities of a stellar wind CMFGEN model (CMFGEN is an atmosphere code developed to model the spectra of a variety of objects) provides a full width at half maximum fit diameter of the primary stellar wind of 2.84±0.06 mas (6.54±0.14 au). We compare the derived intensity distributions with the CMFGEN stellar wind model and hydrodynamic WWC models.

G Weigelt↗

NASA NTRS1995

Gaseous Vortices in Barred Spiral Galaxies

During the course of examining many two-dimensional, as well as a smaller sample of three-dimensional, models of gas flows in barred spiral galaxies, we have been impressed by the ubiquitous presence fo vortex pairs, oriented roughly perpendicular to their bars, with one vortex on each side. The vortices are obvious only when viewed in the bar frame, and the centers of their velocity fields usually are near Lagrangian points L(sub 4,5). In all models that we have studied, the vortices form on essentially the same time scale as that for the development of gaseous spiral arms, typically two bar rotations. Usually the corotation radius, r(sub c), lies slightly beyond the end of the bar. Depending upon the mass distributions of the various components, gas spirals either into, or out of, the vortices: In the former case, the vortices become regions of high density, whereas the opposite is true if the gas spirals out of a vortex. The models described in this paper have low-density vortices, as do most of the models we have studied. Moreover, usually the vortex centers lie approximately within +/- 15 deg of L(sub 4,5). In the stellar dynamic limit, when pressure and viscous forces are absent, short-period orbits exist, centered on L(sub 4,5). These orbits need not cross and therefore their morphology is that of gas streamlines, that is, vortices. We believe that the gas vortices in our models are hydrodynamic analogues of closed, short-period, libration orbits centered on L(sub 4,5).

England, Martin N.↗

NASA NTRS2003

Cellular Instabilities and Self-Acceleration of Expanding Spherical Flames

In the present investigation we aim to provide experimental information on and thereby understanding of the generation and propagation of spark-ignited, outwardly propagating cellular flames, with three major focuses. The first is to unambiguously demonstrate the influence of the four most important parameters in inducing hydrodynamic and diffusional-thermal cellularities, namely thermal expansion, flame thickness, non-unity Lewis number, and global activation energy. The second is to investigate the critical state for the onset of cellularity for the stretch-affected, expanding flame. The third is to identify and consequently quantify the phenomena of self-acceleration and possibly auto-turbulization of cellular flames. Due to space limitation the effects of activation energy and the critical state for the onset of cellularity will not be discussed herein. Experiments were conducted using C3H8-air and H2-O2-N2 mixtures for their opposite influences of non-equidiffusivity. The additional system parameters varied were the chamber pressure (p) and the mixture composition including the equivalence ratio (phi). From a sequence of the flame images we can assess the propensity of cell formation, and determine the instantaneous flame radius (R), the flame propagation rate, the global stretch rate experienced by the flame, the critical flame radius at which cells start to grow, and the average cell size.

Law, C. K.↗

NASA NTRS2013

The 0.5-2.22 micrometer Scattered Light Spectrum of the Disk around TW Hya: Detection of a Partially Filled Disk Gap at 80 AU*

We present a 0.5-2.2 micrometer scattered light spectrum of the circumstellar disk around TW Hya from a combination of spatially resolved Hubble Space Telescope STIS spectroscopy and NICMOS coronagraphic images of the disk. We investigate the morphology of the disk at distances greater than 40 AU over this wide range of wavelengths, and identify the presence of a depression in surface brightness at approximately 80 AU that could be caused by a gap in the disk. Additionally, we quantify the surface brightness, azimuthal symmetry, and spectral character of the disk as a function of radius. Our analysis shows that the scattering efficiency of the dust is largely neutral to blue over the observed wavelengths. We model the disk as a steady α-disk with an ad hoc gap structure. The thermal properties of the disk are selfconsistently calculated using a three-dimensional radiative transfer code that uses ray tracing to model the heating of the disk interior and scattered light images. We find a good fit to the data over a wide range of distances from the star if we use a model disk with a partially filled gap of 30% depth at 80 AU and with a self-similar truncation knee at 100 AU. The origin of the gap is unclear, but it could arise from a transition in the nature of the disk's dust composition or the presence of a planetary companion. Based on scalings to previous hydrodynamic simulations of gap-opening criteria for embedded proto-planets, we estimate that a planetary companion forming the gap could have a mass between 6 and 28 solar mass.

radiative transfer↗