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At least 937 records · Page 52

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NASA NTRS1974

The interior structure of Jupiter (consequences of Pioneer 10 data)

Models of the Jovian interiors are based on theoretical equations of state of hydrogen and helium supported by a few experimental points and an observed parameter such as oblateness, gravitational coefficients, heat emission, and magnetic fields. The models fall into three categories: (1) those which assume a uniform and rather low H2/He ratio throughout the planet, (2) those in which this ratio is solar and thus higher and (3) those which take into account the lack of complete miscibility of the two elements in the condensed state. Recent values of the observed parameters obtained by Pioneer 10 permit improvements of the first two models but also pose new questions. In the first category of models the new data indicate that the amount of hydrogen has to be increased, while in the solar models which have a heavy core (made of SiO2, MgO, Fe and Ni), the abundance of hydrogen has to be decreased, both changes pointing in the direction of incomplete miscibility present in the third category of models.

Smoluchowski, R.↗

NASA NTRS1975

Thermodynamics and phase separation of dense fully-ionized hydrogen-helium fluid mixtures

The free energy of a hydrogen-helium fluid mixture is evaluated for the temperatures and densities appropriate to the deep interior of a giant planet such as Jupiter. The electrons are assumed to be fully pressure-ionized and degenerate. In this regime, an appropriate first approximation to the ionic distribution functions can be found by assuming hard sphere interactions. Corrections to this approximation are incorporated by means of the perturbation theory of Anderson and Chandler. Approximations for the three-body interactions and the nonlinear response of the electron gas to the ions are included. It is predicted that a hydrogen-helium mixture, containing 10% by number of helium ions, separates into hydrogen-rich and helium-rich phases below about 8000 K, at the pressures relevant to Jupiter (4-40 Megabars). It is also predicted that the alloy occupies less volume per ion than the separated phases. The equations of state and other thermodynamic derivatives are tabulated. Implications of these results are discussed.

Stevenson, D. J.↗

NASA NTRS1974

Strongly magnetized classical plasma models

Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).

Montgomery, D.↗

NASA NTRS1974

The interaction of interstellar gas with stellar density wave packets

We have numerically studied the interaction between interstellar gas and a gravitational perturbation produced by a fluctuation in the stellar mass distribution. For a simple equation of state, shock waves develop even if the gravitational perturbation is aperiodic and transient. In a medium which can change thermal phase, shocks do not form and the gas makes a transition directly to the cold, dense phase. The cold material has an anomalous velocity imparted to it by the gravitational perturbation and it becomes an accretion front moving through the hot gas and capturing it. The accretion fronts trigger thermal phase change on a large scale and can reproduce the extent of observed cold clouds. Furthermore their high mass is favorable to gravitational instability and subsequent star formation.

Baker, P. L.↗

NASA NTRS1975

The structure and evolution of Jupiter - The fluid contraction stage

The complete evolution of a contracting star of Jovian mass consisting of a convective adiabatic homogeneous fluid is determined using stellar structure methods, improved model atmosphere calculations, and substantially improved thermodynamic properties for hydrogen and hydrogen-helium fluids. The model atmospheres are calculated in the form of time-averaged vertical temperature structures, including all relevant sources of opacity and a solar energy deposition component, and the thermodynamic properties are modified to obtain better agreement with Monte Carlo results for metallic fluids. The resultant gravitationally contracting evolutionary models are found to have two phases: an early stellar phase similar to a typical low-mass pre-main-sequence body and a later phase constituting an approach to a degenerate-dwarf cooling curve. The first phase is shown to have high luminosities and internal temperatures, while the second gives excellent agreement with the observed radius and luminosity of Jupiter. Analysis indicates that the equation of state and superadiabaticity have the strongest influence on evolution over planetary time scales.

Graboske, H. C., Jr.↗

NASA NTRS1975

The distribution of stars in galactic nuclei - Loaded polytropes

We consider the structure of a galactic nucleus in which a compact supermassive object (e.g., a black hole or spinar) is embedded. The surrounding stars are assumed to satisfy a polytropic or isothermal equation of state. The density distribution of these loaded polytropes has a sharp central spike in which the time scale for stellar collisions can be short. Other properties of loaded polytropes, such as their masses, radii, projected density distribution, relaxation times, and stability, can also differ significantly from those of normal polytropes.

Huntley, J. M.↗

NASA NTRS1975

FCAP - A new tool for the evaluation of active control technology

A computer program has been developed for the evaluation of flight control systems designed for flexible aircraft. This Flight Control Analysis Program (FCAP) is designed in a modular fashion to incorporate sensor, actuator, and control logic element dynamics as well as aircraft dynamics and aerodynamics for complex configurations. Formulation of the total aircraft dynamic system is accomplished in matrix form by casting the equations in state vector format. The system stability and performance are determined in either the frequency or time domain using classical analysis techniques. The aerodynamic method used also permits evaluation of the flutter characteristics of the aircraft.

Noll, R. B.↗

NASA NTRS1975

Further investigations of Jupiter models

It is noted that previously calculated models of Jupiter, in which the H/He ratio is assumed to be solar, required the inclusion of considerable additional mass in the form of volatilized condensates in the atmosphere and excess mass in the central core. Several additional models are considered in this paper which take into account the stricter constraints imposed by Pioneer 10 measurements of Jupiter's gravitational moments. These measurements have indicated that the mass of the excess volatilized condensates (assumed to be water) relative to the core mass (assumed to be rock) exceeds the relevant solar ratio. The present models are tested for sensitivity to variations in the H/He ratio, in the softness of the equation of state for water, in the treatment of the internal adiabat, in departures from an internal adiabat, and in temperature at the one-bar level. The preliminary results indicate that the ratio of excess water to rock in Jupiter is considerably in excess of the solar value.

Podolak, M.↗

NASA NTRS1976

Diatomic molecule variations

The rotational energy is separated from vibrational energy in the two-particle, steady-state wave equation and to first order the solutions are harmonic oscillator functions. The classical phase integral gives a partition function valid only at high temperature, but the quantum summation is easily performed to give analytic expressions for all the thermodynamic properties of the harmonic oscillator at all temperatures. Anharmonic effects are treated by small perturbation solutions to the wave equation and the relation between energy levels and a series expansion of the perturbation potential is derived. Next, the quantum solutions for an oscillator with a Morse-function potential are derived in terms of Laguerre polynomials.

Source record↗

NASA NTRS1976

Equilibrium properties of chemically reacting gases

The equilibrium energy, enthalpy, entropy, specific heat at constant volume and constant pressure, and the equation of state of the gas are all derived for chemically reacting gas mixtures in terms of the compressibility, the mol fractions, the thermodynamic properties of the pure gas components, and the change in zero point energy due to reaction. Results are illustrated for a simple diatomic dissociation reaction and nitrogen is used as an example. Next, a gas mixture resulting from combined diatomic dissociation and atomic ionization reactions is treated and, again, nitrogen is used as an example. A short discussion is given of the additional complexities involved when precise solutions for high-temperature air are desired, including effects caused by NO produced in shuffle reactions and by other trace species formed from CO2, H2O and Ar found in normal air.

Source record↗

NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1976

Analysis of surface tension driven flow in floating zone melting

Surface tension driven flow in a cylindrical melt suspended between two rods was investigated by numerical solution of the steady state differential equations for heat and momentum transfer. Radiation heating and electron beam heating were considered approximately. For small values of the driving force, one rotating ring was formed in the top half of the zone, and its mirror image in the bottom half. At larger driving forces, secondary cells form which probably would undergo oscillatory motion. The influence of Prandtl number, zone movement, and buoyancy on the convection was also studied. The primary resistance to mass transfer in the laminar regime was in the center of the zone rather than at the solid-liquid interfaces.

Chang, C. E.↗

NASA NTRS1976

Interior structure of Jupiter - Theory of gravity sounding

Using relatively simple interior models and a fourth-order theory of figures, it is found that there are basically two extremes of interior structure which agree with current gravity data. One extreme is a 'solar'-composition envelope with 10 to 15 earth masses of heavy material in a core; the other extreme has nearly uniform 'solar' composition but with approximately an additional 30 earth masses of heavy material distributed essentially uniformly. Thus, Jupiter is not of 'solar' composition. It is shown how additional gravity data and improvement in knowledge of the molecular hydrogen equation of state will permit a significant reduction in the number of possible models.

Hubbard, W. B.↗

NASA NTRS1977

Accretion of rotating fluids by barytropes - Numerical results for white-dwarf models

Numerical sequences of rotating axisymmetric nonmagnetic equilibrium models are constructed which represent the evolution of a barytropic star as it accretes material from a rotating medium. Two accretion geometries are considered - one approximating accretion from a rotating cloud and the other, accretion from a Keplerian disk. It is assumed that some process, such as Ekman spin-up or nonequilibrium oscillations, maintains nearly constant angular velocity along cylinders about the rotation axis. Transport of angular momentum in the cylindrically radial direction by viscosity is included. Fluid instabilities and other physical processes leading to enhancement of this transport are discussed. Particular application is made to zero-temperature white-dwarf models, using the degenerate electron equation of state. An initially nonrotating 0.566-solar-mass white dwarf is followed during the accretion of more than one solar mass of material. Applications to degenerate stellar cores, to mass-transfer binary systems containing white dwarfs, such as novae and dwarf novae, to Type I supernovae, and to galactic X-ray sources are considered.

Durisen, R. H.↗

NASA NTRS1977

FCAP - A new tool for the performance and structural analysis for complex flexible aircraft with active control

A very general formulation has been developed for the analysis of complex flexible-aircraft configurations in presence of active control. The formulation is incorporated into a computer program, Flight Control Analysis Program (FCAP), which is designed in a modular fashion to incorporate aircraft dynamics and aerodynamics for complex configurations, as well as sensor, actuator and control logic element dynamics. Formulation of the total aircraft dynamic system is accomplished in matrix form by casting equations in state vector format. The system stability and performance are determined in either the frequency or time domain using classical analysis techniques. Fully unsteady aerodynamics is used for the evaluation of the flutter characteristics as well as the gust response of the aircraft.

Morino, L.↗

NASA NTRS1976

Impact ejecta on the moon

The response of a lunar-sized object to the impact of meteoroids no more than about 100 km in radius is studied by means of a numerical model. The partitioning of impact energy into the kinetic and internal energy of the ejecta is obtained by using the conservation of mass, momentum, and energy conservation equations in finite-difference form within an Eulerian framework with approximate equations of state. The calculations are performed for a 15 km/sec impact of an iron object 5 cm in radius on a gabbroic anorthosite surface. Ejecta ballistic analysis is then performed. Most of the material lost escaping the moon is lunar crust material. Only 0.2% of the meteoroid escapes, all in the vapor phase.

Okeefe, J. D.↗

NASA NTRS1977

Study of igniter design and applications to low smoke solid rockets

A simple analysis of igniter design is described which is sufficiently general to be applicable to any 'basket'-type housing containing one or more charges. The gas equation of state is used in conjunction with the experimentally determined propellant burning-rate law to predict the pressure-time histories in the igniter housing and the rocket motor. Typical numerical results are presented for three cases which represent three experimental conditions tested in a project on low-smoke motors where the requirements on the exhaust were sufficiently stringent to preclude condensible matter from the igniter. Pressure was measured continuously in time at two locations in the igniter housing and at the head end of the motor case. The agreement between theoretical and experimental results is felt to be encouraging considering the complexity of the problem and the many simplifications in the analysis.

Ramohalli, K.↗

NASA NTRS1977

Very massive neutron stars in Ni's theory of gravity

It is shown that in Ni's theory of gravity, which is identical to general relativity in the post-Newtonian limit, neutron stars of arbitrarily large mass are possible. This result is independent, within reasonable bounds, of the equation of state of matter at supernuclear densities.

Mikkelsen, D. R.↗