SEARCH · Search NASA

Results for “RAYLEIGH NUMBER”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

NASA NTRS1992

Time-dependent three dimensional compressible convection with depth-dependent properties

Using a spectral code, we have studied the time-dependent regime of three-dimensional anelastic compressible convection with depth-dependent thermal expansivity, viscosity and thermal conductivity in a wide box of size 5 x 5 x 1. Surface Rayleigh numbers up to 5 x 10 exp 6 have been considered. Very few cylindrical plumes are developed at the bottom but they join up collectively to form strong upwellings, which pulsate chaotically. Major descending flows occur in sheets which form rectangular planform at the top. The thermal and flow fields are dominated by large-scale features. The bottom 20 percent of the convecting layer is found to be superadiabatic.

Balachandar, S.↗

NASA NTRS1992

Axisymmetric spherical shell models of mantle convection with variable properties and free and rigid lids

Axisymmetric spherical shell numerical simulations of mantle convection were carried out to investigate the influence of two end-member surface stress conditions: stress-free and rigid. These correspond approximately to a subducting or a rigid lithosphere and can be seen as end-member models of the surface of Venus. Our model assumed an effective Rayleigh number of 3 x 10 exp 6, similar to that for earth, and included uniform internal heating and depth-dependent thermal expansivity and thermal conductivity. The simulations utilized a Newtonian viscosity which was constant or varied with depth and/or temperature. We show how the temperature, speed, and vorticity fields change qualitatively and quantitatively with surface temperature, surface stress condition, internal heating and viscosity distribution. We find that a rigid lid and viscosity which increases with depth both promote steady large-scale circulation with smaller-scale circulation in the upper mantle.

Leitch, A. M.↗

NASA NTRS1992

Macrosegregation During Steady-State Arrayed Growth of Dendrites in Directionally Solidified Pb-Sn Alloys

The paper examines the growth parameter dependence of the longitudinal macrosegregation due to interdendritic thermosolutal convection during directional solidification of Pb-Sn alloys with a steady-state dendritic arrayed morphology. The experimentally observed longitudinal macrosegregation can be described by an empirical parameter, effective partition coefficient (kE), obtained from Cs = kEC0(1 - fs) super KI-1, where the original tin content is C0 and that corresponding to the fraction distance solidified (Fs) is Cs. Channel formation is strongly associated with the onset of thermosolutal convection in the interdendritic melt. The critical effective Rayleigh number for the onset of channel formation is about 0.07.

Tewari, S. N.↗

NASA NTRS1991

Development of a laser-Doppler system for measurement of velocity fields in PVT crystal growth systems

A laser-Doppler velocimetry (LDV) system capable of measuring velocities as low as 10 exp -5 m/s is presented, and a calibration system for determining the accuracy of the LDV system at these velocities is described. The results obtained in mercurous chloride crystal grown in cylindrical ampoules at 300 C, using physical vapor transport (PVT) methods, are presented. It is concluded that the overall flow pattern observed is a unicellular, asymmetric pattern between Rayleigh number of 125 and 250.

Jones, O. C.↗

NASA NTRS1993

Constraints on the thermal evolution of Venus inferred from Magellan data

One interpretation of the Magellan data suggests that the cratering record on Venus was erased by a global resurfacing event, or events, the latest ending about 500 m.y. ago. In this global-resurfacing model the resurfacing was followed by minor volcanism and tectonism that has been concentrated primarily in the equatorial highland regions characterized by extensive fracture belts and rifts. A thermal evolution model of Venus that can explain these observations is one in which a deformable lithosphere, capable of being incorporated in mantle circulations, provides an almost stress-free condition at the surface. Mantle convection with an almost stress-free boundary at the surface cools the interior more efficiently. Rapid cooling decreases the Rayleigh number of mantle convection below a transition value required for oscillatory convection, and the vigor of convection diminishes as the mantle changes to a quasi-steady circulation after about 500 m.y. ago.

Arkani-Hamed, J.↗

NASA NTRS1992

Convective effects during the physical vapor transport process. I - Thermal convection

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra(T) ranging from 1.80 to 1.92 x 10 exp 6. Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is 10 increase the threshold of instability. For typical ground based conditions time dependent oscillatory convection can occur. This results in nonuniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows regions of both periodic and quasi-periodic states. Low gravity conditions can effectively reduce convective effects, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗

NASA NTRS1993

Phase transitions and 2D spherical convection in a large icy satellite

Three ice phase transitions, based on experimental and theoretical results, were incorporated into a 2D spherical convection model. These phase transitions are the exothermic Ice 1-2, the endothermic Ice 2-6, and the exothermic Ice 6-8 phase transitions. The fluid is assumed isoviscous and the anelastic liquid formulation was used. The object is an icy satellite whose physical characteristics resemble those of Ganymede or Callisto. Structural models, similar to those of Mueller and McKinnon, with different core sizes, i.e. with different degree of differentiation were studied. The shells, i.e. the mantle of the satellite, is heated both internally and from below to account for the decaying radiogenic heating and the heat flow from the solid core. The lower boundary of the mantle is rigid and isothermal, the upper boundary is isothermal. Calculations with rigid and shear stress free upper boundary are carried out in order to assess the role of the different boundary conditions. Two different Rayleigh numbers, depending on the assumed value of the viscosity, were used in the calculations and the thermal evolution of the satellite was studied. The suit of calculations presented demonstrates that phase transition cannot be ignored when the thermal evolution of a large icy satellite has to be studied. The importance of the construction of the realistic phase diagram for ice was also documented. On the other hand the degree of differentiation, simulated with the structures with different core's radius does not seem to drastically influence the overall behavior of the convective activity. Within the limits of our simulations, the post-accretional evolution seems to be independent on the degree of primordial differentiation.

Forni, O.↗

NASA NTRS1993

Convection effects on radial segregation and crystal melt interface in vertical Bridgman growth

We analytically study the influence of convection caused by horizontal heat transfer through the sides of a vertical Bridgman apparatus. We consider the case when the heat transfer across the side walls is small so that the resulting interfacial deformation and fluid velocities are also small. This allows us to linearize the Navier-Stokes equations and express the interfacial conditions about a planar interface through a Taylor expansion. Using a no tangential stress conditions on the side walls, asymptotic expressions for both the interfacial slope, and radial segregation at the crystal-melt interface are obtained in closed form in the limit of large thermal Rayleigh number. It is suggested that these can be reduced by appropriately controlling a specific heat transfer property at the edge of the insulation zone in the solid side.

Tanveer, S.↗

NASA NTRS1993

Expectations for the Martian core magnetic field

In the traditional view of planetary magnetism, a planet either has a core dynamo (Earth, Jupiter, Saturn, Uranus, Neptune, maybe Mercury) or does not (Mars, Venus, Moon...) I argue that this view is simplistic in two respects. First, mantle convection in terrestrial planets is invariably ata high enough Rayleigh number that it is time variable; this leads to the intermittent arrival of mantle 'cold fingers' at the core-mantle boundary promoting at least local core convection and dynamo action even when the planetary core is stably stratified on average. Thus, I predict an intermittent dynamo regime in addition to the simple dynamo-on (Earth) and dynamo-off regimes. Second, the mantle convection-driven horizontal temperature gradients just below the core-mantle boundary can lead to unstable flows that will convert thermoelectric or electrochemical toroidal fields into externally detectable poloidal fields, even when a dynamo is not possible. It is likely that Mars possesses an interesting core magnetic field of the latter kind, complex but with a dipole that might be approximately aligned with the rotation axis and a surface field of a few to tens of gammas.

Stevenson, D. J.↗

NASA NTRS1993

Linear and nonlinear pattern selection in Rayleigh-Benard stability problems

A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.

Davis, Sanford S.↗

NASA NTRS1994

Onset of hexagons in surface-tension-driven Benard convection

High resolution laboratory experiments with large aspect ratio are being conducted for thin fluid layers heated from below and bounded from above by a free surface. The fluid depths are chosen sufficiently small (less than 0.06 cm) so that surface tension is the dominant driving mechanisms; the Rayleigh number is less than 5 for the results reported here. Shadowgraph visualization reveals that the primary instability leading to hexagons is slightly hysteretic (approximately 1 percent). Preliminary measurements of the convection amplitude using infrared imaging are also presented.

Schatz, Michael F.↗

NASA NTRS1995

Studies of planetary scale waves and instabilities in support of the geophysical fluid flow cell experiment on USML-2

High resolution numerical simulations of thermal convection in a rapidly rotating channel with gravity perpendicular to the rotation vector are described. The convecting columns are subject to a beta-effect resulting from cross-channel topographic vortex stretching. The symmetries of the problem allow many invariant wavenumber sets, and this property is associated with the existence of stable multiple-equilibria at modest supercriticality. The transition to chaotic behavior involves the production of intermittent unstable orbits off a two-torus in energy space. At very high Rayleigh number (of order 10(exp 6) to 10(exp 7)) the motion can be turbulent, depending on the size of beta. However, the turbulence is usually characterized by an almost-periodic formation of patches of small scale convection that cause regular pulsations in the accompanying strong zonal jets. The processes maintaining these flows may be related to those responsible for the zonal currents on Jupiter and for cyclic variability on the Sun.

Hart, J. E.↗

NASA NTRS1993

The onset of electrohydrodynamic instability in isoelectric focusing

The onset of electrohydrodynamic motion associated with the imposition of an electric field across a thin layer of liquid has been investigated for the case in which the electrical conductivity varies linearly over the depth of the layer. The variation of the conductivity is due to concentration gradients in the charge-carrying solutes and its spatio-temporal evolution is represented by a convective-diffusion equation. When the viscous relaxation time is long compared to the time for charge relaxation, the analysis reveals that the neutral stability curves for the layer can be characterized by three dimensionless parameters: Ra(sub e) is equivalent to d(epsilon)E(sup 2, sub 0) Delta sigma/mu K(sub eff) sigma(sub 0), an electrical Rayleigh number; delta sigma/sigma(sub 0), the relative conductivity increment; and alpha, the transverse wave number of the disturbance. Here d is the thickness, epsilon is the dielectric constant, and mu is the viscosity of layer, E(sub 0) is the applied field strength at the lower conductivity boundary, and K(sub eff) is an effective diffusivity associated with the Brownian motion of the charge-carrying solutes. With viscous-stress-free boundaries, at which the electrical conductivity and the normal component of the electric field are prescribed, the critical Ra(sub e) is 1.504 x 10(exp 4) at a critical transverse wave number of 1.97 when Delta sigma/sigma(sub 0) is 10. As Delta sigma/sigma(sub 0) increases, the critical Ra(sub e) increases and shifts to shorter wavelength disturbances; the critical imposed field strength, however, passes through a minimum because the lower-conductivity boundary exerts a considerable stabilizing influence in the presence of steep conductivity gradients. Similar trends were obtained for liquid layers with rigid boundaries.

Baygents, James C.↗

NASA NTRS1995

Thermal and chemical convection in planetary mantles

Melting of the upper mantle and extraction of melt result in the formation of a less dense depleted mantle. This paper describes series of two-dimensional models that investigate the effects of chemical buoyancy induced by these density variations. A tracer particles method has been set up to follow as closely as possible the chemical state of the mantle and to model the chemical buoyant force at each grid point. Each series of models provides the evolution with time of magma production, crustal thickness, surface heat flux, and thermal and chemical state of the mantle. First, models that do not take into account the displacement of plates at the surface of Earth demonstrate that chemical buoyancy has an important effect on the geometry of convection. Then models include horizontal motion of plates 5000 km wide. Recycling of crust is taken into account. For a sufficiently high plate velocity which depends on the thermal Rayleigh number, the cell's size is strongly coupled with the plate's size. Plate motion forces chemically buoyant material to sink into the mantle. Then the positive chemical buoyancy yields upwelling as depleted mantle reaches the interface between the upper and the lower mantle. This process is very efficient in mixing the depleted and undepleted mantle at the scale of the grid spacing since these zones of upwelling disrupt the large convective flow. At low spreading rates, zones of upwelling develop quickly, melting occurs, and the model predicts intraplate volcanism by melting of subducted crust. At fast spreading rates, depleted mantle also favors the formation of these zones of upwelling, but they are not strong enough to yield partial melting. Their rapid displacement toward the ridge contributes to faster large-scale homogenization.

Dupeyrat, L.↗

NASA NTRS1994

Linear stability of a layered fluid with mobile surface plates

We develop a general method of calculating the linear stability of a fluid with homogeneous layers that is heated from below. The method employs a propagator technique to obtain expressions for the fluid velocity, stress, and temperature. The principal advantage of the method is the ease with which solutions are adapted to a wide variety of boundary conditions and fluid properties. We demonstrate the utility of the method using three examples which quantify the effects of (1) rheological layering, (2) mobile plates at the surface, and (3) multiple phase transitions. Each example is presented in the context of Earth's mantle. In the first example, we predict that convection becomes confined to the upper mantle once the viscosity increase between the upper and lower mantle exceeds a factor of 2000, consistent with the nonlinear calculations of Davies (1977). In the second example we find that the heat flux variations in a convecting fluid with variably sized, surface plates can be attributed, in part, to changes in the critical Rayleigh number. The linear stability of a fluid with multiple phase transitions is significantly affects by the locations of the transitions. We find that phase transitions have their largest effect when they are located at the center of the fluid layer and become much less important when they are located near the exterior boundaries.

Buffett, B. A.↗

NASA NTRS1996

Experiments on Thermal Convection in Rotating Spherical Shells With Radial Gravity: The Geophysical Fluid Flow Cell

Experiments designed to study the fluid dynamics of buoyancy driven circulations in rotating spherical shells were conducted on the United States Microgravity Laboratory 2 spacelab mission. These experiments address several aspects of prototypical global convection relevant to large scale motions on the Sun, Earth, and on the giant planets. The key feature is the consistent modeling of radially directed gravity in spherical geometry by using dielectric polarization forces. Imagery of the planforms of thermally driven flows for rapidly-rotating regimes shows an initial separation and eventual merger of equatorial and polar convection as the heating (i.e. the Rayleigh number) is increased. At low rotation rates, multiple-states of motion for the same external parameters were observed.

Hart, John E.↗

NASA NTRS1994

Convection in the Physical Vapor Transport Process: Thermal - 1

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra(sub tau) ranging from 1.80 x 10 to 1.92 x 10(exp 6). Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is to increase the threshold of instability. For typical ground based conditions, time dependent oscillatory convection can occur. This results in unsteady transport, and non-uniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows parametric regions exhibiting both an oscillatory approach to steady state and a chaotic transient to a periodic state. Low gravity conditions stabilize the flow field. Convective effects are effectively reduced, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗

NASA NTRS1994

Convection in the Physical Vapor Transport Process-I: Thermal

The effects of convection on diffusive-convective physical vapor transport process are examined computationally. We analyze conditions ranging from typical laboratory conditions to conditions achievable only in a low gravity environment. This corresponds to thermal Rayleigh numbers Ra, ranging from 1.80 x 10 to 1.92 x 10(exp 6). Our results indicate that the effect of the sublimation and condensation fluxes at the boundaries is to increase the threshold of instability. For typical ground based conditions, time dependent oscillatory convection can occur. This results in unsteady transport, and non- uniform temperature and concentration gradients at the crystal interface. Spectral analysis of the flow field shows parametric regions exhibiting both an oscillatory approach to steady state and a chaotic transient to a periodic state. Low gravity conditions stabilize the flow field. Convective effects are effectively reduced, thus resulting in uniform temperature and concentration gradients at the interface, a desirable condition for crystal growth.

Duval, Walter M. B.↗