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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Geoid and topography for infinite Prandtl number convection in a spherical shell

Geoid anomalies and surface and lower-boundary topographies are calculated for numerically generated thermal convection for an infinite Prandtl number, Boussinesq, axisymmetric spherical fluid shell with constant gravity and viscosity, for heating both entirely from below and entirely from within. Convection solutions are obtained for Rayleigh numbers Ra up to 20 times the critical Ra in heating from below and 27 times critical for heating from within. Geoid parallels surface undulations, and boundary deformation generally increases with increasing cell wavelength. Dimensionless geoid and topography in heating from below are about 5 times greater than in heating from within. Values for heating from within correlate more closely with geophysical data than values from heating from below, suggesting a predominance of internal heating in the mantle. The study emphasizes that dynamically induced topography and geoid are sensitive to the mode of heating in the earth's mantle.

Bercovici, D.↗
NASA NTRS1987

Analysis of the fluid dynamics and heat transfer during micro-gravity Bridgman-Stockbarger growth of semiconductors in steady periodic gravitational fields

The effect of periodic variations in the magnitude and direction of gravitational acceleration on buoyancy-driven convection in the melt during microgravity growth of low Prandtl number semiconductor materials in Brigdman-Stockbarger configuration is investigated through the numerical solution of the transient Navier-Stokes and energy equations. Results are presented over a wide range of Rayleigh numbers and frequency spectrum of periodic g-level variations corresponding to conditions present on earth and on board spacecrafts. The frequency response of convection in the melt during growth is found to be similar to that of a first order dynamic system with a cutoff frequency determined by the diffusion of momentum in the system. Results indicate that during growth of small diameter Germanium crystals, convection in the melt is insensitive to the measured g-gitter on board the shuttle.

Griffin, Patrick R.↗
NASA NTRS1979

Stellar convection 2: A multi-mode numerical solution for convection in spheres

The convective flow of a self gravitating sphere of Boussinesq fluid for small Reynolds and Peclet numbers is numerically determined. The decomposition of the equations of motion into modes is reviewed and a relaxation method is developed and presented to compute the solutions to these equations. The stable equilibrium flow for a Rayleigh number of 10 to the 4th power and a Prandtl number of 10 is determined. The 2 and 3 dimensional spectra of the kinetic and thermal energies and the convective flux as a function of wavelengths are calculated in terms of modes. The anisotropy of the flow as a function of wavelength is defined.

Marcus, P. S.↗
NASA NTRS1980

Infinite Prandtl number thermal convection in a spherical shell

A Galerkin technique is used to calculate the steady-state axisymmetric nonlinear convective motions in an infinite-Prandtl-number Boussinesq fluid in a relatively thick spherical shell heated from below. A reasonably complete study of the properties of the even and general axisymmetric steady states is carried out for a range of moderately supercritical Rayleigh numbers. In addition, stability analyses are conducted to determine which form of axisymmetric steady convection is the preferred one and whether the axisymmetric steady flows are unstable to azimuthal perturbations.

Zebib, A.↗
NASA NTRS1984

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗
NASA NTRS1992

Physical vapor transport of mercurous chloride under a nonlinear thermal profile

Our study investigates numerically the flow field characteristics during the growth of mercurous chloride (Hg2Cl2) crystals in a rectangular ampoule under terrestrial and microgravity conditions for a nonlinear thermal gradient. With a residual gas lighter than the nutrient, the solutal Grashof number is dominant. We observe that in tilted configurations, when solutal convection is dominant, the maximum transport rate occurs at approximately 40 percent. For the vertical configurations, we were able to obtain solutions only for the cases either below the critical Rayleigh numbers or the stabilized configurations. The total mass flux decreases exponentially with an increase of pressure of residual gas, but it increases following a power law with the temperature difference driving the transport. The nonlinear thermal gradient appears to destabilize the flow field when thermal convection is dominant for both vertical top-heated and bottom-heated configurations. However, when the solutal Grashof number is dominant, the density gradient resulting from the solutal gradient appears to stabilize the flow for the bottom-heated configuration. The flow field for the top-heated configuration is destabilized for high Grashof numbers. The microgravity environment provides a means for lowering convection. For gravity levels of 10(exp -3) g(0) or less, the Stefan wind drives the flow, and no recirculating cell is predicted.

Mennetrier, Christophe↗
NASA NTRS1979

Free convection about a rectangular prismatic crystal growing from a solution

Sodium chlorate crystals growing from unstirred aqueous solutions were observed by Schlieren techniques. Growth rate data were best correlated by a Sherwood number with finite interface kinetics and a characteristic length equal to the crystal height plus the inverse reciprocal sum of the horizontal dimensions. The growth rate was slightly higher when the plume was laminar than when it was irregular. The horizontal growth rate was greater than the vertical growth rate, with the ratio tending to decrease with increasing plume instability. The threshold Grashof number for plume instability was greatly decreased with decreasing height for crystals with the same horizontal dimensions. The velocity of the eddies approached a constant value with increasing distance above the crystal surface, the terminal value being roughly proportional to the ratio of the square root of the Rayleigh number to the crystal characteristic length.

Chen, P.-S.↗
NASA NTRS2001

Fluid Physics Under a Stochastic Acceleration Field

The research summarized in this report has involved a combined theoretical and computational study of fluid flow that results from the random acceleration environment present onboard space orbiters, also known as g-jitter. We have focused on a statistical description of the observed g-jitter, on the flows that such an acceleration field can induce in a number of experimental configurations of interest, and on extending previously developed methodology to boundary layer flows. Narrow band noise has been shown to describe many of the features of acceleration data collected during space missions. The scale of baroclinically induced flows when the driving acceleration is random is not given by the Rayleigh number. Spatially uniform g-jitter induces additional hydrodynamic forces among suspended particles in incompressible fluids. Stochastic modulation of the control parameter shifts the location of the onset of an oscillatory instability. Random vibration of solid boundaries leads to separation of boundary layers. Steady streaming ahead of a modulated solid-melt interface enhances solute transport, and modifies the stability boundaries of a planar front.

Vinals, Jorge↗
NASA NTRS1993

Hard turbulent thermal convection and thermal evolution of the mantle

Hard turbulent convection is investigated using laboratory experiments and numerical simulations. In Newtonian mantle convection, the appearance of disconnected plumes marks the transition from soft to hard turbulence. For non-Newtonian rheology, the transition to hard turbulence takes place at much lower Nusselt numbers than it does for Newtonian rheology. This has important ramifications for the mantle. Large curvatures are developed in the trajectories of non-Newtonian plumes in the hard turbulent regime, in contrast to the trajectories of Newtonian plumes. When phase transitions are considered, mantle convection tends to become more layered with increasing Rayleigh numbers. The manner of mantle convection might have changed with time from a layered to a more whole mantle type of flow. Superplume events could have been caused by catastrophic overturns associated with strong gravitational instabilities in the transition zone.

Yuen, D. A.↗
NASA NTRS1988

On the aspect ratio of Rayleigh-Benard convection cells

Numerical model calculations of isoviscous bottom-heated convection in a two-dimensional box with aspect ratio twelve are reported. The aim was to determine the preferred aspect ratio of convection cells. Time-dependent runs were started from two widely different initial conditions. At Rayleigh numbers in the range 10 to the 5th to 10 to the 6th about eight cells with a mean aspect ratio of 1.5 formed eventually in each case. Thus neither the preference for approximately square cells nor the stability of very elongated cells could be confirmed. The existence of large-scale convective structures in the earth's mantle must be due to deviations from the simple Rayleigh-Benard model of convection.

Christensen, Ulrich↗
NASA NTRS1984

Thermosolutal convection during directional solidification

During solidification of a binary alloy at constant velocity vertically upward, thermosolutal convection can occur if the solute rejected at the crystal-melt interface decreases the density of the melt. We assume that the crystal-melt interface remains planar and that the flow field is periodic in the horizontal direction. The time-dependent nonlinear differential equations for fluid flow, concentration, and temperature are solved numerically in two spatial dimensions for small Prandtl numbers and moderately large Schmidt numbers. For slow solidification velocities, the thermal field has an important stabilizing influence: near the onset of instability the flow is confined to the vicinity of the crystal-melt interface. Further, for slow velocities, as the concentration increases, the horizontal wavelength of the flow decreases rapidly - a phenomenon also indicated by linear stability analysis. The lateral inhomogeneity in solute concentration due to convection is obtained from the calculations. For a narrow range of solutal Rayleigh numbers and wavelengths, the flow is periodic in time.

Mcfadden, G. B.↗
NASA NTRS1982

Large Prandtl number finite-amplitude thermal convection with Maxwell viscoelasticity

It has long been known that the earth behaves viscoelastically. Viscoelasticity may be of importance in two aspects of mantle convection, including time-dependent behavior and local storage of recoverable work. The present investigation makes use of thermal convection in a box as a prototype of mantle flow. It is demonstrated that recoverable work can be important to the local mechanical energy balance in the descending lithosphere. It is shown that, even when assuming large viscoelastic parameters, an inherent time-dependence of viscoelastic convection appears only in local exchanges of mechanical energy. There is no strong exchange between buoyant potential energy and recoverable strain energy in the Rayleigh number range investigated. The investigation is mainly concerned with viscoelastic effects occurring on a buoyant time scale. It is found that viscoelastic effects have a negligible influence on the long term thermal energetics of mantle convection.

Ivins, E. R.↗
NASA NTRS1983

Multiple buoyancy driven flows in a vertical cylinder heated from below

The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite element solution of the Boussinesq equations coupled with computed-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with Prandtl number of one and for cylinders with aspect ratio (Lambda) (defined as the height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curve for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous evolution of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and lambda are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Lambda or = Lambda * approximately 0.80 or by a limit point for Lambda Lambda *. The transition between these two modes may be described by the theory of multiple limit point bifurcation.

Yamaguchi, Y.↗
NASA NTRS1994

Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

Balachandar, S.↗
NASA NTRS1983

Character and stability of axisymmetric thermal convection in spheres and spherical shells

The influence of shell size and mode of heating on the behavior and stability of axisymmetric, infinite Prandtl number convection in a spherical geometry is studied. Heating from within and below features convection onset governed by a self-adjoint system of equations and boundary conditions. For heating only from within or from below, linearized equations and boundary conditions are non-self-adjoint. Identification of the parameter which initiates the departure from self-adjointness, together with the properties of the self-adjoint solution, provide a basis for calculating the heat transfer characteristics of the non-self-adjoint situations. The investigations are an effort to develop a model for heat transfer in planetary interiors. Further development of the technique by modifying the Galerkin method by the introduction of diagonal mode truncation is suggested to permit the consideration of higher values of the Rayleigh numbers, i.e., those more commensurate with terrestrial planet mantles.

Zebib, A.↗
DOE OSTI2024

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3 × 10 5 ≤ Ra ≤ 5 × 10 9 and Ekman numbers 10 − 6 ≤ Ek ≤ 10 − 4 for Prandtl number Pr = 0.8 and aspect ratios 1 / 5 ≤ Γ ≤ 5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity u z and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of u z is δ u z ∼ Ek 1 / 3 r / H whereas δ T ∼ e − k r ( k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek = 10 − 6 means that the heat transport is dominated by the radial structure of u z since T varies slowly over the radial scale δ u z . We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport ( Nu ) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

58 GEOSCIENCES↗
NASA NTRS1967

Theoretical Study of Natural Convection Flows in Closed-End Cylindrical Vessels Final Report

This study is concerned with the analytical solutions of natural convection flows in closed-end cylindrical vessels to obtain exact solutions of temperature and velocity distribution in the laminar flow region under steady state condition. The temperature and velocity distributions, in general power series of displacements, are substituted into the three basic equations of continuity, momentum and energy. The relationships between coefficients of all powers are obtained through initial and boundary conditions and recurrence formulae. For constant wall temperature conditions the general solution of temperature and velocity may be expressed as a function of displacement, geometry ratio and Rayleigh number. Prandtl number does not enter as an independent parameter.

Convective flow↗