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At least 145 records · Page 8

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NASA NTRS1986

Numerical solutions of the complete Navier-Stokes equations

Using ideas from the kinetic theory, the Navier-Stokes equations are modified in such a way that they can be cast as a set of first order hyperbolic equations. This is achieved by incorporating time dependent terms into the definition of the stress tensor and the heat flux vectors. The boundary conditions are then determined from the theory of characteristics. Because the resulting equations reduce to the traditional Navier-Stokes equations when the steady state is reached, the present approach provides a straightforward scheme for the determination of inflow and outflow boundary conditions. The method is validated by comparing its predictions with known exact solutions of the steady Navier-Stokes equations.

Hassan, H. A.↗

NASA NTRS1974

Relative motion of orbiting particles under the influence of perturbing forces. Volume 2: Analytical results

The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.

Eades, J. B., Jr.↗

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 NTRS1988

Choice of implicit and explicit operators for the upwind differencing method

The flux-vector and flux-difference splittings of Steger-Warming, van Leer and Roe are tested in all possible combinations on the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust; it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Liou, Meng-Sing↗

NASA NTRS1988

Choice of implicit and explicit operators for the upwind differencing method

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe's splitting, as anticipated, is found to uniformly yield the most accurate results. On the other hand, an approximate Roe splitting of the implicit operator (the complete Roe splitting is too complicated for practical use) proves to be the least robust with regard to convergence to the steady state. In this respect, the Steger-Warming splitting is the most robust: it leads to convergence when combined with any of the splittings in the explicit operator, although not necessarily in the most efficient way.

Liou, Meng-Sing↗

NASA NTRS1977

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

Models of the Jovian interiors based on theoretical equations of state of hydrogen and helium supported by a few experimental points and on observed parameters such as oblateness, gravitational coefficients, heat emission, magnetic fields, are discussed. The models fall into three categories: (1) those that 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 that take into account the lack of complete miscibility of the two elements in the condensed state. It appears now also that within the limits of error the planet is in a hydrostatic equilibrium. The large heat emission and the need for an efficient source of internal heat are confirmed, but the results do not indicate which one of the various possible mechanisms is favored, although new evolutionary models suggest that the primordial heat may be insufficient. A new red spot has been discovered. Finally, the presence of a highly eccentric and inclined magnetic field poses new problems related to the pattern of internal convection and to the possibility of a north-south asymmetry of the interior. Further analysis of the available data may throw additional light on these questions.

Smoluchowski, R.↗

NASA NTRS1978

A steady-state stratospheric aerosol model

This paper deals with the development of a one-dimensional steady-state stratospheric aerosol model and the subsequent perturbations caused by including the expected Space Shuttle particulate effluents in the model. Two approaches to the basic modeling effort have been made: in one, enough simplifying assumptions were introduced so that a more or less exact solution to the descriptive equations could be obtained; in the other, very few simplifications were made and a computer technique was used to solve the equations. The most complete form of the model contains the effects of sedimentation, diffusion, particle growth and coagulation. The results indicate that the model is capable of describing many aspects of the stratospheric aerosol layer, such as size distribution and the vertical profile of particles greater than 0.3 micron diameter.

Rosen, J. M.↗

NASA NTRS1991

A Martian global groundwater model

A global groundwater flow model was constructed for Mars to study hydrologic response under a variety of scenarios, improving and extending earlier simple cross sectional models. The model is capable of treating both steady state and transient flow as well as permeability that is anisotropic in the horizontal dimensions. A single near surface confining layer may be included (representing in these simulations a coherent permafrost layer). Furthermore, in unconfined flow, locations of complete saturation and seepage are determined. The flow model assumes that groundwater gradients are sufficiently low that DuPuit conditions are satisfied and the flow component perpendicular to the ground surface is negligible. The flow equations were solved using a finite difference method employing 10 deg spacing of latitude and longitude.

Howard, Alan D.↗

NASA NTRS1995

New model atmospheres for very cool white dwarfs with mixed H/He and pure He compositions

New model atmosphere calculations for very cool white dwarfs with mixed H/He and pure He compositions are presented. The hydrogen-rich models incorporate improved cross section calculations of the collision-induced absorption by molecular hydrogen due to collisions with H2, H, and He. The effects associated with variations in the effective temperature (T(sub eff) greater than or equal to 4000 and less than or equal to 10,000 K), the surface gravity (log g greater than or equal to 7.5 and less than or equal to 9.5), and the chemical composition (N(He)/N(H) greater than or equal to O and less than or equal to 100) are investigated. Results from earlier calculations are confirmed qualitatively, but a more detailed comparison reveals large quantitative deviations. Cool white dwarfs with mixed H/He chemical compositions are shown to be easily recognizable from their predicted strong infrared flux deficiency. Pure helium model calculations are described as well. These include a modified version of the recently developed equation of state of D. Saumon and G. Chabrier. Nonideal effects brought about by various equations of state are explored in detail. For the purpose of this analysis, a model of pressure ionization based on an accurate description of the interactions in a mostly atomic helium fluid is developed. The effects of pressure ionization are shown to be the most important issue in the model calculations. A critical discussion of previous generations of pure helium model calculations is presented. Finally, broadband color indices are provided for the complete model grid.

Bergeron, P.↗

NASA NTRS1975

Investigation A: Numerical solutions of driven vortices of binary fluid in a cylindrical geometry

The steady state laminar motion of a viscous, incompressible and binary fluid is studied for a rotating flow in a cylindrical geometry. The mathematical model employed is a cold flow simulation of the fluid mechanics of the light-bulb concept of the gaseous core nuclear engine. A numerical treatment is developed for the rotating flow which includes a description of the nuclear fuel addition. The problem is formulated with the complete Navier-Stokes equations in order to show the interaction between the fuel addition, the main flow, and the boundary layer flow in an accurate manner. The results presented show holdup of the nuclear fuel for the case of steady fuel addition.

Shin, Y. W.↗

NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗

NASA NTRS1979

Boundary conditions for implicit solutions to the compressible Navier-Stokes equations in finite computational domains

The admissible boundary conditions for the unsteady Navier-Stokes equations are insufficient to determine completely the flow variables at grid points on the boundaries of a finite computational domain. A general method is presented in which the boundary conditions are supplemented by conservatively differenced forms of the flow equations. For implicit algorithms, the method provides a fully implicit coupling between boundary and interior points. Implicit boundary-point computation schemes are given for most types of flow boundary encountered in internal and external flow problems. Convergence to steady state is generally faster than with locally explicit boundary-point schemes.

Thomas, P. D.↗

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 NTRS1991

Combustion of liquid fuel droplets in supercritical conditions

A comprehensive analysis of liquid-fuel droplet combustion in both sub- and super-critical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influences on the fluid transport, gas/liquid interface thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibits a significant variation near the critical burning pressure, mainly as a result of reduced mass-diffusion rate and latent heat of vaporization with increased pressure. The influence of droplet size on the burning characteristics is also noted.

Shuen, J. S.↗

NASA NTRS1991

Vaporization and combustion of fuel droplets at supercritical conditions

Vaporization and combustion liquid-fuel droplets in both sub- and super-critical environments have been examined. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. In addition, the dynamic responses of droplet vaporization and combustion to ambient-pressure oscillations are investigated. Results indicate that the droplet gasification and burning mechanisms depend greatly on the ambient pressure. In particular, a rapid enlargement of the vaporization and combustion responses occurs when the droplet surface reaches its critical point, mainly due to the strong variations of latent heat of vaporization and thermophysical properties at the critical state.

Yang, Vigor↗

NASA NTRS1986

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 percent 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 NTRS1992

Combustion of liquid-fuel droplets in supercritical conditions

A comprehensive analysis of liquid-fuel droplet combustion in both subcritical and supercritical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates variable thermophysical properties, finite-rate chemical kinetics, and a full treatment of liquid-vapor phase equilibrium at the drop surface. The governing equations and associated interfacial boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures in the range of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influence on fluid transport, gas-liquid interfacial thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibit a considerable change in the combustion mechanism at the critical pressure, mainly as a result of reduced mass diffusivity and latent heat of vaporization with increased pressure.

Shuen, J. S.↗

NASA NTRS2003

Self-Consistent Model of Magnetospheric Ring Current and Electromagnetic Ion Cyclotron Waves: The 2-7 May 1998 Storm

A complete description of a self-consistent model of magnetospheric ring current interacting with electromagnetic ion cyclotron waves is presented. The model is based on the system of two kinetic equations; one equation describes the ring current ion dynamics, and another equation describes the wave evolution. The effects on ring current ions interacting with electromagnetic ion cyclotron waves and back on waves are considered self-consistently by solving both equations on a global magnetospheric scale under nonsteady state conditions. The developed model is employed to simulate the entire 2-7 May 1998 storm period. First, the trapped number fluxes of the ring current protons are calculated and presented along with comparison with the data measured by the three- dimensional hot plasma instrument Polar/HYDRA. Incorporating in the model the wave-particle interaction leads to much better agreement between the experimental data and the model results. Second, examining of the wave (MLT, L shell) distributions produced by the model during the storm progress reveals an essential intensification of the wave emission about 2 days after the main phase of the storm. This result is well consistent with the earlier ground-based observations. Finally, the theoretical shapes and the occurrence rates of the wave power spectral densities are studied. It is found that about 2 days after the storm s main phase on 4 May, mainly non-Gaussian shapes of power spectral densities are produced.

Khazanov, G. V.↗