Engineering topics

Benz, Willy

Publications and source records attributed to Benz, Willy.

11 records

NASA NTRS1995

A method of smoothed particle hydrodynamics using spheroidal kernels

We present a new method of three-dimensional smoothed particle hydrodynamics (SPH) designed to model systems dominated by deformation along a preferential axis. These systems cause severe problems for SPH codes using spherical kernels, which are best suited for modeling systems which retain rough spherical symmetry. Our method allows the smoothing length in the direction of the deformation to evolve independently of the smoothing length in the perpendicular plane, resulting in a kernel with a spheroidal shape. As a result the spatial resolution in the direction of deformation is significantly improved. As a test case we present the one-dimensional homologous collapse of a zero-temperature, uniform-density cloud, which serves to demonstrate the advantages of spheroidal kernels. We also present new results on the problem of the tidal disruption of a star by a massive black hole.

Fulbright, Michael S.↗

NASA NTRS1994

Inside the supernova: A powerful convective engine

We present an extensive study of the inception of supernova explosions by following the evolution of the cores of two massive stars (15 and 25 Solar mass) in multidimension. Our calculations begin at the onset of core collapse and stop several hundred milliseconds after the bounce, at which time successful explosions of the appropriate magnitude have been obtained. Similar to the classical delayed explosion mechanism of Wilson, the explosion is powered by the heating of the envelope due to neutrinos emitted by the protoneutron star as it radiates the gravitational energy liberated by the collapse. However, as was shown by Herant, Benz, & Colgate, this heating generates strong convection outside the neutrinosphere, which we demonstrate to be critical to the explosion. By breaking a purely stratified hydrostatic equilibrium, convection moves the nascent supernova away from a delicate radiative equilibrium between neutrino emission and absorption, Thus, unlike what has been observed in one-dimensional calculations, explosions are rendered quite insensitive to the details of the physical input parameters such as neutrino cross sections or nuclear equation of state parameters. As a confirmation, our comparative one-dimensional calculations with identical microphysics, but in which convection cannot occur, lead to dramatic failures. Guided by our numerical results, we have developed a paradigm for the supernova explosion mechanism. We view a supernova as an open cycle thermodynamic engine in which a reservoir of low-entropy matter (the envelope) is thermally coupled and physically connected to a hot bath (the protoneutron star) by a neutrino flux, and by hydrodynamic instabilities. This paradigm does not invoke new or modified physics over previous treatments, but relies on compellingly straightforward thermodynamic arguments. It provides a robust and self-regulated explosion mechanism to power supernovae that is effective under a wide range of physical parameters.

Herant, Marc↗

NASA NTRS1994

The Disruption and Demise of Periodic Comet Shoemaker-Levy 9

The impact of the fragmented comet Shoemaker-Levy 9 (SL9) into Jupiter this July promises to change our understanding of the outer solar system. More than twenty mountain-sized conglomerates of ice and rock will hit the atmosphere at approx. 50 km/s over the course of a week beginning July 16, releasing approx. 10(exp 4) to 10(exp8) megatons of energy per burst, and providing unique and perhaps pivotal clues to the properties of comets and the physics of massive atmospheres. Because the fragments will strike the far side of Jupiter, data acquisition, analysis and interpretation will be quite sensitive to the actual size and energy of the fragments. We therefore examine an event which took place two summers ago, unnoticed and unobserved: the disruption of SL9 into a "string of pearls' as it passed within the Roche limit at perijove. We first demonstrate, on the basis of timescales of tidal interaction, that the comet could not have broken into 20+ fragments through a hierarchy of brittle fracture events. Next, noting that the tidal stress was too weak to have even fragmented an uncompressed mass of freshly fallen snow, we run models for a strengthless comet held together only by self-gravity. We explore the initial size, density, and rotation. We conclude that a 4 km diameter comet (smaller if a prograde rotator) of density approx. 0.5 g/cu cm disrupts and disperses into a chain of fragments similar to Shoemaker-Levy 9, whether we begin with 21, 85, 169, 700 or 2000 sub-grains. Gravitational reaccumulation is evidently the answer, and there is no need to invoke the presence of 21 "cometesimals" as the subscale of the comet. To explain how a comet can be weaker than uncompacted snow, we show that the ring-plane crossing prior to perijove could have caused total damage. Finally, we compute the tidal stress on impactors as they approach Jupiter this July. Objects of various density are moderately distorted but not disrupted by the time they strike the planet.

Asphaug, Erik↗

NASA NTRS1992

Giant impacts on a primitive Uranus

Simulations of collisions are conducted between a model of the primitive Uranus and 1-3 earth-mass impactors, using smooth-particle hydrodynamics. A series of collisions was simulated for each impactor while varying the total angular momentum of the system. Most of the simulation runs left ices in orbit; a subset of the runs also left rock or iron (from the impactor). It is concluded on the basis of these results that there is a wide range of giant impacts which could have produced the current period and inclination of the spin axis relative to the plane of the ecliptic. A subset of these could have deposited the material in orbit from which the regular satellites of Uranus were assembled.

Slattery, Wayne L.↗

NASA NTRS1992

Postcollapse hydrodynamics of SN 1987A - Two-dimensional simulations of the early evolution

The first few seconds of the explosion of SN 1987A are modeled here using a 2D cylindrical geometry smooth particle hydrodynamics code. The success of the explosion is determined to be sensitive to the duration of the infall, the timing of the bounce, and the subsequent neutrino heating. A semianalytical model for the initial structure of the collapsed object is used to present two simulations that differ by the mass that has been allowed to collapse into a neutron star prior to the bounce. In the case of a short initial infall, the explosion fails due to excessive cooling. For a longer initial infall, the cooling is less and the explosion is successful although relatively weak. It is shown that in this case, a successful explosion is brought about by the presence of an entropy gradient which, combined with the gravitational pull of the neutron star, leads to extremely strong instabilities. The critical importance of the global circulation for the success of the explosion is demonstrated.

Herant, Marc↗

NASA NTRS1992

Postexplosion hydrodynamics of SN 1987A

A comprehensive study is presented of the postexplosion hydrodynamics of the ejecta of SN 1987A encompassing the Rayleigh-Taylor instabilities at the shell interfaces and the dynamical effects of the energy input due to the radioactive decay of Ni-56 and Co-56. The dependence of the hydrodynamical behavior on progenitor structure, initial perturbations, explosion energy, and dimensionality of the numerical simulation is investigated in order to explain the observed high-velocity wings of the iron line of SN 1987A. It is shown that none of these factors leads to the required high-velocity tail of iron. When nickel is artificially premixed in the initial model, it is found that this early mixing has to affect the inner 1.5 solar mass of the ejecta to reproduce the high-velocity wings at a time of 90 d. It is argued that the high-entropy bubble associated with the delayed mechanism is responsible for this premixing by driving convective motions early in the explosion.

Herant, Marc↗

NASA NTRS1991

Hydrodynamical instabilities and mixing in SN 1987A - Two-dimensional simulations of the first 3 months

Results are presented from numerical simulations of the early stages of the explosion of SN 1987A. Using a two-dimensional cylindrical geometry version of a smooth particle hydrodynamics code, the explosion is followed for three months to investigate both the early hydrodynamical instabilities and the effect of the subsequent radioactive decay of Ni-56 and Co-56 with half-lives of 6.1 and 77.8 days, respectively. It is shown that the mixing induced by hydrodynamical instabilities occurring during the first few hours is substantially modified at later time by the radioactive decay of Ni-56 and Co-56. The inner cavity of the expanding supernova remnant fills up with nickel, its decay products thus forming a giant 'nickel bubble'. The peak velocity of the nickel increases by approximately 30 percent after the decays. While these results adequately model the core of the observed Fe line profiles, they fail to reproduce the high velocity wings of the spectra.

Herant, Marc↗

NASA NTRS1990

Convective instabilities in SN 1987A

Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.

Benz, Willy↗

NASA NTRS1988

Collisional stripping of Mercury's mantle

A three-dimensional smoothed-particle hydrocode is the basis of the present numerical simulations of conditions under which a giant collision between a proto-Mercury and a planet one-sixth its size would lead to the loss of most of the silicate mantle of Mercury and thereby account for its anomalously high density. A head-on collision at 20 km/sec, and an off-axis impact parameter of half the radius of the proto-Mercury at 35 km/sec, are approximately equal in damage yielded; both will yield a remnant whose characteristics are those of the present Mercury.

Benz, Willy↗

NASA NTRS1988

The strange density of Mercury - Theoretical considerations

Two classes of models which have been advanced to explain the high density of Mercury are reviewed and contrasted. These models invoke either the differing volatilities of iron and silicates or disruptive collisions to fractionate the two phases. Also contrasted are equilibrium condensation and planetary vaporization models, both of which fall within the first broad class considered. Results indicate that equilibrium condensation models are unable to account for the observed high density of Mercury without invoking special mechanisms such as unrealistically narrow planetary accretion zones. However, it is found that distinctive chemical differences, which are potentially testable by spacecraft experiments, provide means for distinguishing between planetary vaporization and large impact scenarios.

Cameron, A. G. W.↗

NASA NTRS1987

Three-dimensional hydrodynamical simulations of stellar collisions. I - Equal-mass main-sequence stars

Two distinct mass-loss mechanisms are noted in the present, fully three-dimensional calculations of collisions between identical stars. While strong shocks in nearly head-on collisions lead to high-velocity jets perpendicular to the collision axis, with increasing mass loss as impact velocity at infinity increases from zero to 2.3 times the escape velocity from the stellar surface, low velocity encounters lead to a sharp increase in mass loss at impact parameters that correspond to nearly-grazing collisions in a two-stage process. In the first stage, the two stars become gravitationally bound due to the encounter's energy dissipation; these binary components then violently coalesce during subsequent periastron passage.

Benz, Willy↗