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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1984

Natural convection in an enclosed cavity

The problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated is addressed. An application of the dynamic A.D.I. method to obtain numerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid. Previously announced in STAR as N83-25433

Phillips, T. N.↗
NASA NTRS1984

Convection experiments in a centrifuge and the generation of plumes in a very viscous fluid

In this paper, experiments are described for which inertial effects are negligible. A small aspect-ratio tank filled with a very viscous fluid (Pr = 10 to the 6th) is used to observe the behavior of convection for Rayleigh numbers up to 6.3 x 10 to the 5th. These high values are reached by conducting the experiment in a centrifuge which provides a 130-fold increase in apparent gravity. Rotational effects are small, but cannot be totally dismissed. In this geometry, thermal boundary layer instabilities are indeed observed, and are found to be very similar to their lower Prandtl number counterparts. It is tentatively concluded that once given a certain degree of 'vulnerability' convection can develop 'plume' like instabilities, even when the Prandtl number is infinite. The concept is applied to the earth's mantle and it is speculated that 'plumes' could well be the dominant mode of small-scale convection under the lithospheric plates.

Nataf, H.-C.↗
NASA NTRS1984

Penetrative cellular convection in a stratified atmosphere

In the present investigation of penetrative convection within a simple compressible model, the middle one of the three layers of differing stratification prior to the onset of convection is a convectively unstable polytrope bounded above and below by two stably stratified polytropes. One- and two-mode steady solutions with hexagonal planforms have been studied for Rayleigh numbers up to aobut 1000 times critical, and for a range of Prandtl numbers, horizontal wavenumbers, and stratifications. These indicate that the penetration into the lower stable layer by downward plumes is substantially larger in a stratified medium than in a Boussinesq fluid, and produces an extended region of adiabatic stratification. The strong asymmetry between upward and downward penetration in compressible media has major implications for the mixing of stable regions above and below stellar convection zones.

Massaguer, J. M.↗
NASA NTRS1986

Simulation of the turbulent Rayleigh-Benard problem using a spectral/finite difference technique

The three-dimensional, incompressible Navier-Stokes and energy equations with the Bousinesq assumption have been directly simulated at a Rayleigh number of 3.8 x 10 to the 5th power and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were used. A spectral/finite difference numerical method was used to simulate the flow. The flow at these conditions is turbulent and a sufficiently fine mesh was used to capture all relevant flow scales. The results of the simulation are compared to experimental data to justify the conclusion that the small scale motion is adequately resolved.

Eidson, T. M.↗
NASA NTRS1985

Surface deformation and geoid anomalies over single and double-layered convective systems

Using a primitive variable formulation of the finite-element method, the differences in the surface observables, such as topography and geoid, produced by single- and double-layered thermal convection, were compared. Both constant and depth-dependent viscosities have been considered. For the same Rayleigh number, larger surface perturbations are produced by single-cell convection. For the same Nusselt number, the magnitudes of the surface observables are greater for double-layered convection. For the same surface heat-flux, surface topographies have similar magnitudes, but the relative amplitudes of geoid anomalies depend greatly on the style of viscosity stratification. This difference in the geoid between the two systems increases with greater surface heat-flow, regardless of viscosity structure.

Koch, M.↗
NASA NTRS1985

Effect of enclosure shape on natural convection velocities in microgravity

Natural convection velocities within two-dimensional enclosures of various shapes are estimated with reasonable accuracy, for Rayleigh numbers up to at least 5000, by considering the area to be equivalent to a circle of equal area. For the class of figures including the square, upright half-circle, and upright 2 x 1 aspect ratio rectangle, excellent agreement is obtained by considering the temperature difference across the maximum horizontal dimension to be equal to that across the equal area circle horizontal diameter. The agreement of two upright oblong shapes indicates probable agreement for any similar upright oblong shape of roughly the same aspect ratio. The horizontal oblong shapes have natural convection velocities approximately one-half that estimated based on the equal area circle, with the temperature difference across the maximum horizontal dimension taken to be equal to that across the equal area circle diameter.

Robertson, S. J.↗
NASA NTRS1986

Convection in the vertical midplane of a horizontal cylinder Comparison of two-dimensional approximations with three-dimensional results

Experimental results and numerical data on the flow characteristics of core-driven and boundary-layer-driven regimes (CDRs) and (BLDRs) are compared to two-dimensional solutions for heated convective flow in the vertical midplane of a horizontal cylinder. The data were obtained from laser Doppler velocimetry (LDA) measurements and from three-dimensional numerical solutions. It is shown that the approximate solutions gave the correct Rayleigh-number-dependences and distributions for the velocities in the CDR and BLDR regimes. However, the transition between the CDR and the BLDR, as well as the magnitude of the distribution of velocity components, were found to be dependent on the type of two-dimensional approximation selected. In the case of CDR, core velocities were overestimated by as much as 30 percent by the two-dimensional approximations; and in the case of BLDR, the core velocities were overestimated by 40-50 percent as compared to the measured velocities. A schematic illustration of the flow patterns in the cylinder is provided.

Bontoux, P.↗
NASA NTRS1986

Interaction of flows with the crystal-melt interface

The coupling between a crystal-melt interface and fluid flow is investigated. The solidification boundary conditions at the crystal-melt interface are described. The influences of morphological and double-diffusive instabilities during directional solidification on the interface are studied. The experiments by Glicksman and Mickalonis (1982) and Fang et al. (1985) which examine the relationship between the hydrodynamic state of the phase melt and phase-change interface are analyzed. The Rayleigh-Benard problem, and the effect of crystal-melt interaction on the Rayleigh number are examined. Various applications for melt-flow interactions with solid-liquid interface to engineering and welding are discussed.

Glicksman, M. E.↗
NASA NTRS1985

Theoretical and experimental studies in support of the geophysical fluid flow experiment

Meteorologists and astrophysicists interested in large scale planetary and solar circulations have come to recognize the importance of rotation and stratification in determining the character of these flows. In particular, the effect of latitude-dependent Coriolis force on nonlinear convection is thought to play a crucial role in such phenomena as differential rotation on the Sun, cloud band orientation on Jupiter, and the generation of magnetic fields in thermally driven dynamos. The continuous low-gravity environment of the orbiting space shuttle offers a unique opportunity to make laboratory studies of such large-scale thermally driven flows under the constraint imposed by rotation and sphericity. This is possible because polarization forces in a dielectric liquid, which are linearly dependent on fluid temperature, give rise to an effectively radial buoyancy force when a radial electrostatic field is imposed. The Geophysical Fluid Flow Cell (GFFC) is an implementation of this ideal in which fluid is contained between two rotating hemispheres that are differentially heated and stressed with a large a-c voltage. The experiment, to be flown on Spacelab III (currently set for launch April 29, 1985), will explore non-linear mode selection and high Rayleigh number turbulence in a rotating convecting spherical shell of liquid. Experiments will be carried out in a low driving parameter range where some limited numerical experimentation is currently feasible, as well as in a parameter range significantly beyond numerical computation for many years.

Hart, J.↗
NASA NTRS1987

The delineation and interpretation of the Earth's gravity field

The geoid and topographic fields of the central Pacific were delineated and shown to correlate closely at intermediate wavelengths (500 to 2500 km). The associated admittance shows that anomalies having wavelengths less than about 1000 km are probably supported by the elastic strength of the lithosphere. Larger wavelength anomalies are due to dynamic effects in the sublithosphere. Direct modeling of small scale convection in the asthenosphere shows that the amplitudes of observed geoid and topographic anomalies can be independently matched, but that the observed admittance cannot. Only by imposing an initial regional variation in the thermal regime is it possible to match the admittance. It is proposed that this variation may be due to differences in the onset time of convection beneath the lithosphere of different ages. That is, convection beneath thickening lithosphere is strongly dependent on the rate of thickening (V) relative to the rise time for convection. The critical Rayleigh number contains the length scale K/V, where K is thermal diffusivity. Young, fast growing lithosphere stabilizes the underlying asthenosphere unless it has an unusually low viscosity. Lithosphere of different age, separated by fracture zones, will go unstable at different times, producing regional horizontal temperature gradient that may strongly influence convection. Laboratory and numerical experiments are proposed to study this form of convection and its influence on the geoid.

Marsh, Bruce D.↗
NASA NTRS1986

High spatial resolution models of time-dependent, layered mantle convection

Time-dependent models of Boussinesq convection are analyzed in order to determine the potential existence of the transient phase of multiple layered convection initially described by Ross and Sacks (1982, 1984). The initial thermal profile for subsolidus mantle convection is examined in terms of an adiabatic or a conductive profile. The effects of varied spatial resolution, aspect ratio, Rayleigh number, initial buoyancy, and supersolidus temperature cutoffs on mantle convection are investigated. It is observed that the data supports the existence of the transient phase of multiple layered convection.

Boss, A. P.↗
NASA NTRS1987

Thermosolutal convection during directional solidification. II - Flow transitions

The influence of thermosolutal convection on solute segregation in crystals grown by vertical directional solidification of binary metallic alloys or semiconductors is studied. Finite differences are used in a two-dimensional time-dependent model which assumes a planar crystal-melt interface to obtain numerical results. It is assumed that the configuration is periodic in the horizontal direction. Consideration is given to the possibility of multiple flow states sharing the same period. The results are represented in bifurcation diagrams of the nonlinear states associated with the critical points of linear theory. Variations of the solutal Rayleigh number can lead to the occurrence of multiple steady states, time-periodic states, and quasi-periodic states. This case is compared to that of thermosolutal convection with linear vertical gradients and stress-free boundaries.

Mcfadden, G. B.↗
NASA NTRS1987

The effect of a shallow low viscosity zone on the apparent compensation of midplate swells

A model for midplate swells is assumed where the swell topography is dynamically maintained by convection beneath a conducting lid. Using an idealized viscosity structure consisting of a low viscosity layer underneath the lid and overlying a constant viscosity region, the effect of the low viscosities, the layer thickness, and the Rayleigh number on the flow and on the inference of a compensation mechanism from the associated gravity, geoid, and topography anomalies is investigated. The calculations show that a simple plume model with stratified viscosity variations of less than two orders of magnitude near the surface can produce the range of depths of compensation seen at midplate swells. Shallow depths of compensation, therefore, cannot be used to argue against dynamic models for the formation of hot spot swells.

Robinson, Elizabeth M.↗
NASA NTRS1985

Three-dimensional convection in horizontal cylinders - Numerical solutions and comparison with experimental and analytical results

The results of a three-dimensional numerical simulation of Boussinesq free convection in a horizontal differentially heated cylinder are presented. The computation was based on a Samarskii-Andreyev scheme (described by Leong, 1981) and a false-transient advancement in time, with vorticity, velocity, and temperature as dependent variables. Solutions for velocity and temperature distributions were obtained for Rayleigh numbers (based on the radius) Ra = 74-18,700, thus covering the core- and boundary-layer-driven regimes. Numerical solutions are compared with asymptotic analytical solutions and experimental data. The numerical results well represent the complex three-dimensional flows found experimentally.

Smutek, C.↗
NASA NTRS1988

Magnetic fields interacting with nonlinear compressible convection

Two-dimensional numerical simulations are used to study fully compressible convection in the presence of an imposed magnetic field. Highly nonlinear flows are considered that span multiple density scale heights. The convection tends to sweep the initially uniform vertical magnetic field into concentrated flux sheets with significant magnetic pressures. These flux sheets are partially evacuated, and effects of buoyancy and Lorentz forces there can serve to suppress motions. The flux sheets can be surrounded by a sheath of descending flow. If the imposed magnetic field is sufficiently strong, the convection can become oscillatory. The unstably stratified fluid layer has an initial density ratio (bottom to top of layer) of 11. Surveys of solutions at fixed Rayleigh number sample Chandrasekhar numbers from 1 to 1000 and magnetic Prandtl numbers from 1/16 to 1. These nonlinear simulations utilize a two-dimensional numerical scheme based on a modified two-step Lax-Wendroff method.

Hulburt, Neal E.↗
NASA NTRS1988

Effect of a shallow low-viscosity zone on the formation of midplate swells

A finite-element numerical method is used here to analyze the effect of a low-viscosity zone on convection driven by heating from below in the upper mantle, in particular on the formation of midplate swells. The convective temperature and velocity solutions are calculated for different combinations of the viscosity in the top layer, the fluid layer thicknesses, and the Rayleigh number based on the viscosity in the bottom layer. The temperature solutions are used to calculate the geoid, topography, and heat flow anomalies, the elastic plate thickness, the depth of compensation, and an upper bound on the uplift time that result from the flow. The results are compared to data at the Hawaii, Bermuda, Cape Verde, and Marquesas swells. The magnitudes and the trend with age are consistent with theoretical and other estimates of the viscosity variation in the shallow upper mantle. Convective models can therefore explain the uplift and observed anomalies at midplate swells.

Robinson, E. M.↗
NASA NTRS1988

The effect of a shallow low-viscosity zone on the mantle flow, the geoid anomalies and the geoid and depth-age relationships at fracture zones

A two-dimensional FEM is used to investigate the flow driven by the horizontal temperature gradient at a fracture zone and to calculate the resulting geoid and topography anomalies. Using a three-layered viscosity structure for the upper mantle, results are presented for the effects of varying: (1) the viscosity contrast between the fluid layers: (2) the Rayleigh number based on the viscosity of the bottom layer; and (3) the thickness of the low-viscosity channel. Good agreement is obtained with the results of geoid anomalies over the Udintsev fracture zone when the viscosity of the top layer is greater than one order of magnitude less than post-glacial rebound values.

Robinson, Elizabeth M.↗
NASA NTRS1988

Channel formation in Pb-Sn, Pb-Sb, and Pb-Sn-Sb alloy ingots and comparison with the system NH4Cl-H2O

The formation of segregation channels during the unidirectional solidification of base chilled ingots has been studied as a function of composition in binary Pb-Sn and Pb-Sb and ternary Pb-Sn-Sb alloys. The patterns of channel distribution were characterized in the binary and ternary systems and are described as functions of temperature gradients, growth rates, dendrite spacings, and interdendritic permeabilities. Channels appear to nucleate at random across a dendritic front and subsequently to interact as they propagate, decreasing in density across the front. Assuming that the interdendritic spacing is the characteristic distance for a liquid perturbation, yields critical effective Rayleigh numbers which lie within a factor of x 40 for both metallic and aqueous systems. This correlation is close, considering the sensitivity to any assumed dimension and the range of material properties involved, and is taken to support a model for channel nucleation occurring close to the dendritic growth front.

Hellawell, A.↗