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NASA NTRS1984

Universal binding energy relations in metallic adhesion

Rose, Smith, and Ferrante have discovered scaling relations which map the adhesive binding energy calculated by Ferrante and Smith onto a single universal binding energy curve. These binding energies are calculated for all combinations of Al(111), Zn(0001), Mg(0001), and Na(110) in contact. The scaling involves normalizing the energy by the maximum binding energy and normalizing distances by a suitable combination of Thomas-Fermi screening lengths. Rose et al. have also found that the calculated cohesive energies of K, Ba, Cu, Mo, and Sm scale by similar simple relations, suggesting the universal relation may be more general than for the simple free electron metals for which it was derived. In addition, the scaling length was defined more generally in order to relate it to measurable physical properties. Further this universality can be extended to chemisorption. A simple and yet quite accurate prediction of a zero temperature equation of state (volume as a function of pressure for metals and alloys) is presented. Thermal expansion coefficients and melting temperatures are predicted by simple, analytic expressions, and results compare favorably with experiment for a broad range of metals.

Ferrante, J.↗

NASA NTRS1984

Dynamic compression and volatile release of carbonates

Particle velocity profiles upon shock compression and isentropic releases were measured for polycrystalline calcite. The Solenhofen limestone release paths lie, close to the Hugoniot. Calcite 3 to 2 transition, upon release, was observed, but rarefaction shocks were not detected. The equation of state is used to predict the fraction of material devolatilized upon isentropic release as a function of shock pressure. The effect of ambient partial pressure of CO2 on the calculations is demonstrated and considered in models of atmospheric evolution by impact induced mineral devolatilization. The radiative characteristics of shocked calcite indicate that localization of thermal energy occurs under shock compression. Shock entropy calculations result in a minimum estimate of 90% devolatilization upon complete release from 10 GPa. Isentropic release paths from calculated continuum Hugoniot temperatures cross into the CaO (solid) + CO2 (vapor) field at improbably low pressures. It is found that release paths from measured shock temperatures cross into the melt plus vapor field at pressures greater than .5 GPa, which suggests that devolatilization is initiated at the shear banding sites.

Tyburczy, J. A.↗

NASA NTRS1984

Numerical simulations of fission

Hydrodynamic simulation techniques to the fission problem of the lunar origin were applied. It is indicated that, for fluids with the compressibility of stars, dynamic fission instabilities lead to spiral arm ejection of mass and angular momentum in the form of a ring or disk of debris, not as a single body. Some quantitative aspects of these results seem favorable to lunar origin by fission. Fission instabilities in fluid objects with a smaller degree of compressibility, more closely approximating terrestrial material are considered. Although the qualitative features are similar, there are significant quantitative differences for the stiffer equation of state. The implications of the results for the fission hypothesis of lunar origin are discussed. Evolutions illustrating possible approaches to instability are presented.

Durisen, R. H.↗

NASA NTRS1984

Tidal disruption and the origin of the Moon

The dynamic problem of the tidal disruption of a rocky planetismal was solved by a direct integration of the fully three-dimensional, nonlinear equations of motion. The hypothesis that any object that passes within the Roche limit is disrupted was disproven. A time dependent solution was performed numerically, treating the planetismal as a fluid with a Murnaghan equation of state in the solid regions and zero pressure otherwise. Calculations show that a rocky body which passes by the Earth on a parabolic orbit with a perigee within the Roche limit is not tidally disrupted. Objects on hyperbolic orbits would experience even less tidal disruption. The results herein do not apply to bodies with very low viscosity. It is shown, however, that tidal disruption can be ruled out as a mechanism for reducing planetismal masses. Mechanisms for forming the Moon which rely upon tidal disruption are unlikely to be correct.

Mizuno, H.↗

NASA NTRS1985

Impact Cratering Calculations

Impact cratering, both normal and oblique, on planetary surfaces is discussed and energy partitioning, ejecta distribution, (both with regard to size, velocity, energy content, and size sorting), the condensation physics of impact induced vapor, and the loss of planetary atmospheres during accretion of terrestrial and icy planets are considered. The possible origin of SNC meteorites, impact into porous regolith, equation of state of water and ice, and a possible model for the accretion of the Jovian and Saturnian satellites are examined.

Ahrens, T. J.↗

NASA NTRS1985

Shock Compression of Liquid Helium to 56 GPa (560) Kbar

Shock-wave data are presented for liquid helium which has been compressed to densities up to five times greater than the normal liquid. The helium was heated to temperatures up to 21,000 K, while the maximum pressure attained was 56 GPa. The properties of helium and hydrogen are important for modeling the giant planets Saturn and Jupiter where these elements are the major constituents. Conditions on Saturn are of particular interest because studies have suggested that this planet has an internal energy source which is associated with unmixing and gravitational separation the hydrogen-helium fluid at pressures below 1 TPa. The existence of this phase transition depends very sensitively on the hydrogen and helium equation of state. In the experiments, strong shock waves were generated by the impact of planar projectiles into cryogenic specimen holders.

Nellis, W. J.↗

NASA NTRS1985

Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field

An analytical method has been developed to estimate the unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.

Norman, T.↗

NASA NTRS1984

The Stability of the Low Degree 5 Minute Solar Oscillations

The decay rate for many of the low degree p modes observed as 5 minute oscillations of the Sun is discussed and decay rates for modes ranging from radial (l=0) to the nonradial ones with l=5 for overtones 10 through 28. Parameters needed for he solar model are given and the hydrogen mass fraction composition structure is shown as well as the structure given by Christensen-Dalsgaard (1982) for an evolved solar model. The special equation of state and opacity table with X=0.74 for the hydrogen mass fraction in the outer 0.40 of the mass needs slightly more hydrogen in the central regions than obtained by Christensen-Dalsgaard in order to give a complete and consistent model. The difference in helium production between these two models is about 10%, meaning that the total energy radiated by the Sun during its lifetime thus far agrees satisfactorily with accurately calculated evolution sequences.

Kidman, R. B.↗

NASA NTRS1985

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗

NASA NTRS1985

Scalar/Vector potential formulation for compressible viscous unsteady flows

A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.

Morino, L.↗

NASA NTRS1984

Sum rules and static local-field corrections of electron liquids in two and three dimensions

The dielectric functions of electron liquids which take into account short-range electron-electron correlations via the static local-field corrections are examined in the light of the frequency-moment sum rules. The formation is given for degenerate as well as classical electron liquids in arbitrary (d) spatial dimensions, which is suitable for comparison between the two- and three-dimensional cases. By using the virial equations of state it is shown that such dielectric functions cannot satisfy the compressibility sum rule and the third-frequency-moment sum rule simultaneously. In the degenerate case, the plasmon, single-pair, and multipair contributions to the sum rules are analyzed, and the reason for this incompatibility is discussed.

Iwamoto, N.↗

NASA NTRS1985

Thermal phases of interstellar and quasar gas

Interstellar gas may be in a variety of thermal phases, depending on how it is heated and ionized; here a unified picture of the equation of state of interstellar and quasar gas is presented for a variety of such mechanisms over a broad range of temperatures, densities, and column densities of absorbing matter. It is found that for select ranges of gas pressure, photoionizing flux, and heating, three thermally stable phases are allowed: coronal gas (T above 100,000 K); warm gas (T about 10,000 K); and cold gas (T less than 100 K). With attenuation of ultraviolet and X-ray radiation, the cold phase may undergo a transition to molecules. In quasar broad-line clouds, this transition occurs at column density N(H) = about 10 to the 23rd/sq cm and could result in warm molecular cores and observable emission from H2 and OH. The underlying atomic physics behind each of these phase transitions and their relevance to interstellar matter and quasars are discussed.

Lepp, S.↗

NASA NTRS1985

Classical hard-sphere fluid in infinitely many dimensions

The equation of state of the fluid phase of the classical hard-sphere system in infinitely many dimensions has been obtained exactly. Only the first two virial coefficients are nonvanishing. The upper bound for the coefficients of the Mayer series for nonnegative interaction potentials is reached by this system.

Frisch, H. L.↗

NASA NTRS1985

Disturbance-accommodating tracking maneuvers of flexible spacecraft

In this paper the problem of maneuvering a flexible spacecraft through a large angle is considered, where the disturbance-accommodating feedback control tracks a desired output state. The desired output state is provided from an open-loop solution for the linear system model. The components of the disturbance vector are assumed to be represented in terms of Fourier series. Closed-form solutions are provided for the Ricati, prefilter, state trajectory, and residual state trajectory equations which define the optimal control. Example maneuvers are presented where control-rate penalties have been included in the performance index for frequency-shaping, in order to smooth both the open- and closed-loop control commands.

Turner, J. D.↗

NASA NTRS1985

Emerging monochromatic fluxes and colors of red degenerate stars

The emerging monochromatic fluxes and the B-V, V-I, J-H, and V-K color indices are presented for red degenerate stars with helium atmospheres which were calculated using an equation of state and opacities based on a hot Thomas-Fermi model of the helium gas. The effective temperature range is 4500-2500 K. It is found that although the emerging fluxes resemble blackbody curves, red degenerates emit more radiation than blackbodies in the short wavelength range and less in the long wavelength range. Thus, red degenerates appear bluer than blackbodies of the same temperature. The calculated colors of these models are compared to the colors of some of the coolest known non-DA degenerate stars. In particular it is found that the B-V and V-I colors of the cool white dwarf VB 11, whose temperature had been previously estimated to be higher than 4000 K, suggest a temperature of 3750 K. If this result is correct, then VB 11 is probably the coolest known white dwarf.

Kapranidis, S.↗

NASA NTRS1985

An MHD model of the earth's magnetosphere

It is pointed out that the earth's magnetosphere arises from the interaction of the solar wind with the earth's geomagnetic field. A global magnetohydrodynamics (MHD) model of the earth's magnetosphere has drawn much attention in recent years. In this model, MHD equations are used to describe the solar wind interaction with the magnetosphere. In the present paper, some numerical aspects of the model are considered. Attention is given to the ideal MHD equations, an equation of state for the plasma, the model as an initial- and boundary-value problem, the shock capturing technique, computational requirements and techniques for global MHD modeling, a three-dimensional mesh system employed in the global MHD model, and some computational results.

Wu, C. C.↗

NASA NTRS1985

Dynamic fission instability of dissipative protoplanets

Analytical and numerical approaches are taken to consider if a rapidly rotating, viscous protoearth would have lost mass by a fission process and thereby given birth to the moon. The fast rotation is assumed as the source of the instability in the dissipative liquid protoearth. Governing hydrodynamic equations are defined for the evolution of the protoearth. Account is taken of viscous dissipation, the pressure equation of state for the atmospheric material sent on a ballistic trajectory, and the effective viscosity. The results indicate that dynamic fission was probably not the process by which the protomoon came into existence.

Boss, A. P.↗

NASA NTRS1986

A model for the influence of pressure on the bulk modulus and the influence of temperature on the solidification pressure for liquid lubricants

Two pressure chambers, for compression experiments with liquids from zero to 2.2 GPa pressure, are described. The experimentally measured compressions are then compared to theoretical values given by an isothermal model of equation of state recently introduced for solids. The model describes the pressure and bulk modulus as a function of compression for different types of lubricants with a very high accuracy up to the pressure limit of the high pressure chamber used (2.2 GPa). In addition the influence of temperature on static solidification pressure was found to be a simple function of the thermal expansion of the fluid.

Jacobson, B. O.↗