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NASA NTRS1988

Igneous proceses and closed system evolution of the Tharsis region of Mars

A quantitative petrologic model for the evolution of the Tharsis region on Mars is presented, which is consistent with global gravity and topography data. It is demonstrated that it is possible to form and support the topographic relief of the Tharsis plateau by a closed-system mass-conservative nearly isostatic process involving generation of magmas from a mantle source region. Extrusion and/or intrusion (or underplating) of such magmas allows low-pressure solidification, with a consequent increase in volume relative to that which would be possible in the high-pressure source region, leading to elevated topology. The distribution of densities with depth obtained by the model is quantitatively consistent with the isostatic models of Sleep and Phillips (1979, 1985).

Finnerty, A. A.↗
NASA NTRS1989

The free-wake prediction of rotor hover performance using a vortex embedding method

A method is developed to predict the rotor hover performance. This method solves the compressible mass conservation equation much like current full potential codes and can therefore predict the transonic flows on a rotor. However, the newly developed approach also allows for the free convection of shed vorticity and permits the computation of the entire hover wake system. The method uses a vortex embedding scheme in potential flow and has been implemented in a computer code, HELIX -I. To predict power we implement a simple boundary layer and two different induced-drag integration schemes. The induced-drag is obtained from surface pressure integration and an energy flux integral. Comparisons between computations and experiment show good agreement for the prediction of power polars, surface pressure distribution, and tip vortex geometry.

Ramachandran, K.↗
NASA NTRS1989

The ultraviolet variability of HD 45166 (qWR + B8 V) - Evidence for stellar wind radiative instabilities

High-resolution IUE spectroscopy of the low-mass qWR star HD 45166, obtained at several epochs during 1980-1988, reveals a complex pattern of variability in its stellar wind emission lines, P Cygni profiles, and highly ionized photospheric absorption spectrum. The most intensive observations, obtained during a 36 hr continuous run in February 1988, show the presence of discrete absorption components (DACs) in the C IV 1550 resonance doublet. These DACs can blend to give the appearance of a well-developed P Cygni absorption profile seen at some other times, roughly doubling the column density of the ground state C(3+) ions in the wind. In the 1988 spectra, two principal features are seen, at about -950 km/s and -750 km/s, with column densities of about 14.0 and 14.7 dex/sq cm, respectively. Both features migrate in velocity with accelerations of about 140 cm/sq sec, implying a recurrence time scale of about 1.6 days and a lifetime of about 3 days for the DACs. A striking characteristic of the acceleration is its slowness. The pattern of DAC variability in HD 45166 is similar to that found for O-type stars and provides further evidence that the DACs are not mass-conserving features but rather that a given feature is formed by different material at different times. It is concluded that the C IV DAC variability observed in HD 45166 results from structural changes in the wind arising from radiative instabilities.

Willis, Allan J.↗
NASA NTRS1989

A complete spherical harmonic approach to luni-solar tides

In this work a spherical harmonic theory of ocean tides is presented. The theory is based on Laplace tide equations modified to include turbulence with constant eddy viscosity, linearized bottom friction, and oceanic loading and self-gravitation. Variable bathymetry is also treated in harmonic terms, and no-flow boundary conditions are applied at continental coastlines. The tide and boundary constraint equations are reduced to matrix form and solved by a weighted least-squares procedure. Five zonal luni-solar tides, ranging in period from 14 days to 18.6 yr, are investigated using the theory; such tides have typically been difficult to compute using traditional numerical approaches. The polar motion and changes in the length of day induced by these long-period tides are calculated. Tidal solutions are compared extensively with results from other tidal theories and from recent satellite and sea-level observations. The greatest limitation to accurate prediction of zonal tides - for any theory - appears to be the marginal failure of all tide theories to conserve mass globally; the use of additional mass constraints may be warranted.

Dickman, S. R.↗
NASA NTRS1990

Relativistic winds from pulsar and black hole magnetospheres

The present consideration of the extraction of the rotational energy stored in a Kerr black hole by a large-scale MHD wind as a possible source for AGN jet energy proceeds by viewing both the ingoing and outgoing winds as propagating toward asymptotic infinities and transporting the conserved mass, angular momentum, and energy fluxes established by the source region. It is judged that the field-line rotation rate or total voltage drop across the system must also be determined by the dissipative process that injects plasma onto the magnetospheric field lines.

Punsly, Brian↗
NASA NTRS1991

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.

Thompson, C. P.↗
NASA NTRS1991

Ion dynamics in the Venus ionosphere

Measurement data on the ion velocity in the Venus ionosphere (mainly from the Pioneer Venus Orbiter Retarding Potential Analyzer) are summarized, and theoretical models developed to explain them are reviewed. Data and theoretical predictions are compared in extensive graphs and diagrams and discussed in detail. It is shown that the predominant flow is away from the subsolar point, at up to 3 km/sec in the terminator region. A model of axisymmetric flow based on momentum, energy, and mass conservation laws is found to reproduce the observed ion velocities at solar zenith angles less than about 140 deg, but not the high velocities and chaotic behavior seen near the antisolar point. Also discussed are significant differences between the flow above and below about 400 km and the effects of changes in the dynamic pressure of the solar wind.

Miller, K. L.↗
NASA NTRS1991

The turbomachine blading design using S2-S1 approach

The boundary conditions corresponding to the design problem when the blades being simulated by the bound vorticity distribution are presented. The 3D flow is analyzed by the two steps S2 - S1 approach. In the first step, the number of blades is supposed to be infinite, the vortex distribution is transformed into an axisymmetric one, so that the flow field can be analyzed in a meridional plane. The thickness distribution of the blade producing the flow channel striction is taken into account by the modification of metric tensor in the continuity equation. Using the meridional stream function to define the flow field, the mass conservation is satisfied automatically. The governing equation is deduced from the relation between the azimuthal component of the vorticity and the meridional velocity. The value of the azimuthal component of the vorticity is provided by the hub to shroud equilibrium condition. This step leads to the determination of the axisymmetric stream sheets as well as the approximate camber surface of the blade. In the second step, the finite number of blades is taken into account, the inverse problem corresponding to the blade to blade flow confined in each stream sheet is analyzed. The momentum equation implies that the free vortex of the absolute velocity must be tangential to the stream sheet. The governing equation for the blade to blade flow stream function is deduced from this condition. At the beginning, the upper and the lower surfaces of the blades are created from the camber surface obtained from the first step with the assigned thickness distribution. The bound vorticity distribution and the penetrating flux conservation applied on the presumed blade surface constitute the boundary conditions of the inverse problem. The detection of this flux leads to the rectification of the geometry of the blades.

Luu, T. S.↗
NASA NTRS1991

Ocean tide models for satellite geodesy and Earth rotation

A theory is presented which predicts tides in turbulent, self-gravitating, and loading oceans possessing linearized bottom friction, realistic bathymetry, and continents (at coastal boundaries no-flow conditions are imposed). The theory is phrased in terms of spherical harmonics, which allows the tide equations to be reduced to linear matrix equations. This approach also allows an ocean-wide mass conservation constraint to be applied. Solutions were obtained for 32 long and short period luni-solar tidal constituents (and the pole tide), including the tidal velocities in addition to the tide height. Calibrating the intensity of bottom friction produces reasonable phase lags for all constituents; however, tidal amplitudes compare well with those from observation and other theories only for long-period constituents. In the most recent stage of grant research, traditional theory (Liouville equations) for determining the effects of angular momentum exchange on Earth's rotation were extended to encompass high-frequency excitations (such as short-period tides).

Dickman, Steven R.↗
NASA NTRS1992

Estimation of excitation energy of diatomic molecules in expanding nonequilibrium flows

The energy contained in the highly excited vibrational and rotational states in a diatomic gas in a thermochemical nonequilibrium state during expansion is estimated. The estimation is made on the assumption that the populations of the vibrational and rotational states, when normalized by their respective equilibrium values, are describable by simple functions containing no more than four arbitrary parameters. A cubic polynomial, a logarithmic-cubic polynomial, and a bimodal step function are used for this purpose. The four parameters are determined by imposing conditions known at the ground state and the dissociation limit and the mass conservation law. The energy in excess of that accounted for by assuming a Boltzmann distribution of these states, defined here as excess excitation energy, is calculated for N2, O2, NO, CO, OH, and H2. A calculation made for a typical nozzle flow shows that the excess energy may reach 6 percent of the total enthalpy of the flow, and that the flow velocity may decrease by as much as 4 percent due to the nonequilibrium excitation phenomenon.

Park, Chul↗
NASA NTRS1992

Navier-Stokes solutions with surface catalysis for Martian atmospheric entry

In this study numerical solutions have been obtained for two-dimensional axisymmetric hypersonic nonequilibrium CO2 flow over a high angle blunt cone with appropriate surface boundary conditions to account for energy and mass conservation at the body surface. The flowfield is described by the Navier-Stokes equations and multicomponent conservation laws which account for both translational and internal vibrational nonequilibrium effects. Complete forebody solutions have been obtained for the peak heating point of the Mars entry trajectory specified in the proposed NASA MESUR (Mars Environmental Survey) project. In these solutions, radiative equilibrium wall temperature and surface heating distributions are determined over the MESUR aeroshell forebody for entry velocity equal to 7 km/sec with varying degrees of surface catalysis. The effects of gas kinetics, surface catalysis, transport properties, and vibrational relaxation times on the surface heating are examined. The results identify some important issues in the prediction of surface heating for flows in thermochemical nonequilibrium and show that the Navier-Stokes code used herein is effective for thermal protection system design and materials selection.

Chen, Y.-K.↗
NASA NTRS1992

Adaptive multigrid domain decomposition solutions for viscous interacting flows

Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.

Rubin, Stanley G.↗
NASA NTRS1992

Segmented multigrid domain decomposition procedure for incompressible viscous flows

In this paper, the Navier-Stokes (NS) equations are approximated with a reduced NS system, that represents the lowest-order terms in an asymptotic Re expansion. This system allows for simplified boundary conditions, more generality in the location of the outflow boundary, and insures mass conservation in all subdomain grid interfaces, and also at the outflow boundary. The higher-order NS diffusion terms are included through a deferred corrector, in chosen subdomains, when required.

Srinivasan, Kumar↗
NASA NTRS1991

A microcomputer program for estimating low altitude wind and turbulence fields

Past efforts to develop methods for objective wind analysis and to provide turbulence estimates to pilots are reviewed. The present approach involves a wind module and a turbulence module. The wind module extends the critical dividing streamline concept and past developments in mass-conserving wind interpolation schemes. The turbulence module is based on recent efforts to develop practical atmospheric turbulence parameterization schemes based on lapse rate, wind shear, surface heating, and surface roughness. The lapse rate and wind shear are readily obtained from the wind module. Surface roughness and heating come from land use information and net radiation estimates derived from cloud cover, terrain slope, local time, and latitude. This system is argued to have considerable potential for providing useful online information for many kinds of aircraft operations.

Ludwig, F. L.↗
NASA NTRS1993

Analysis of hypersonic arcjet flow fields and surface heating of blunt bodies

A Gauss-Seidel implicit aerothermodynamic Navier-Stokes computational CFD code with thermochemical surface conditions (GIANTS) and with appropriate boundary conditions was developed for the analysis of hypersonic arcjet flows over large angle blunt bodies. Two-dimensional axisymmetric multicomponent full Navier-Stokes equations were solved, together with boundary conditions, to account for the surface slip, surface catalysis, and energy and mass conservation at the body surface. It is shown that the predictions for isothermal, noncatalytic, and no-slip surface conditions which are made using the GIANTS code with simple boundary conditions agree with those of the LAURA code, and the predicted normalized heating distributions over the forebody surface with boundary conditions for various cone angles are consistent with the trends of data from arcjet experiments.

Chen, Y.-K.↗
NASA NTRS1993

Heat Transfer from Radiatively Heated Material in a Low Reynolds Number Microgravity Environment

A mathematical model of the transient three-dimensional heat transfer between a slowly moving ambient gas stream and a thermally thick or thin flat surface heated by external radiation in a microgravity environment is presented. The problem is motivated in part by fire safety issues in spacecraft. The gas phase is represented by variable property convection-diffusion energy and mass conservation equations valid at low Reynolds numbers. The absence of gravity and low Reynolds number together permit the flow to be represented by a self-consistent velocity potential determined by the ambient velocity and the thermal expansion in the gas. The solid exchanges energy with the gas by conduction/convection and with the surroundings by surface absorption and re-emission of radiation. Heat conduction in the solid is assumed to be one dimensional at each point on the surface as a consequence of the limited times (of order of 10 seconds) of interest in these simulations. Despite the apparent simplicity of the model, the results show a complex thermally induced flow near the heated surface. The thermal exchange between the gas and solid produces an outward sourcelike flow upstream of the center of the irradiated area and a sinklike flow downstream. The responses of the temperature fields and the associated flows to changes in the intensity of the external radiation and the ambient velocity are discussed.

Yamashita, H.↗
NASA NTRS1993

Segmented multigrid domain decomposition solutions for three dimensional viscous recirculating flows

A segmented multigrid domain decomposition strategy is combined with a pressure-based form of flux-vector discretization for 3D incompressible and compressible viscous flow applications. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes (NS) equations, which are represented by an implicit lowest-order reduced NS system and a purely diffusive higher-order deferred corrector. A trapezoidal or boxlike form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable nonstaggered grid computation. Improvements in gridding strategy are presented by allowing for disjoint subdomains that provide optimal resolution of disparate flow features.

Srinivasan, Kumar↗
NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗