Showing papers on "Natural convection published in 1991"

Stellar Turbulent Convection: A New Model and Applications

Abstract: Improvements of the mixing-length theory (MLT) of turbulent convection in stellar atmospheres are developed theoretically. It is pointed out that inaccuracies are introduced into MLT by the approximating assumptions of a single large eddy (rather than many eddies of different sizes) and of incompressibility. In the proposed new model, the full spectrum of turbulent eddies is determined using more recent turbulence models (e.g., the eddy-damped quasi-normal Markovian model of Orszag, 1977), and a new formula for the convective flux is obtained which gives values up to 10 times greater than those of the MLT at high convective efficiencies. The problem of compressibility is addressed by adding one of two new expressions (one with no free parameters) for the mixing length. Numerical results from simulations of a solar-type star and a 0.8-solar-mass globular-cluster star are presented in tables and graphs and discussed in detail; the agreement with observations is found to be better than with the MLT.

Interaction of mantle plume heads with the Earth's surface and onset of small‐scale convection

Abstract: We investigate the behavior of a spherical blob of buoyant fluid as gravity forces it toward either a rigid horizontal boundary or a free surface. The diapir fluid is assumed much less viscous than the ambient fluid. This fundamental problem is the simplest unsteady model relevant to the ascent of hot plumes of buoyant material toward Earth's surface or the base of the lithosphere and closely models the heads of starting plumes. As the diapir approaches the boundary, it collapses in the vertical and spreads horizontally while a layer of the surrounding mantle is slowly squeezed out from betweeen the diapir and the surface. Experimental results for the thinning and lateral spreading of the bouyant fluid, and for the thinning of the squeeze layer, are given for both the case of a rigid, nonslip boundary and that of a free surface. These are compared with similarity scaling laws based on a balance between the bouyancy of the diapir and viscous stresses in the diapir's surroundings. We also observe that the squeeze layer can become gravitationally unstable, leading to a bifurcation from convection on the scale of the original plume to convection on scales much smaller than the diapir. The vertical exchange on smaller horizontal scales enables the plume to more rapidly approach the boundary. At the time instability occurs the diapir has spread to roughly twice its initial diameter. Application of these results, and previous results from surface uplift, to the plumes responsible for continental flood basalts is subject to knowledge of the local value of upper mantle viscosity. If this is taken to be 3×1020 Pa s, most uplift takes place ovcer approximately 5 m.y. Eruption of voluminous basalts will not take place until at least 5–10 m.y. after the surface has reached its maximum elevation. If small-scale instabilities do develop within mantle plume heads, they may be an essential mechanism allowing the top of the plume to ascend to the shallow depths required for extensive melting. It may also explain the observation of Hooper (1990) that volcanism in the Deccan and Columbian Plateau begins before the onset of crustal extension.

A low-diffusive and oscillation-free convection scheme

Abstract: A higher-resolution and bounded discretization scheme is proposed for calculations of incompressible steady flows with finite-volume methods. The scheme combines a second-order upstream-weighted approximation with the first-order upwind differencing under the control of a convection boundedness criterion. It is easy to implement for calculations of multi-dimensional flows, and the resulting finite-difference coefficient matrix is always diagonally dominant. Applications to three test problems, two linear and one non-linear, and comparisons with two commonly used schemes, hybrid upwind/central differencing and QUICK, demonstrate the capability of the method in capturing steep gradients while maintaining the boundedness of solutions.

Natural convection in a mushy layer

Abstract: Governing equations for a mushy layer are analysed in the asymptotic regime Rm [Gt ] 1, where Rm is an appropriately defined Rayleigh number. A model is proposed in which there is downward flow everywhere in the mushy layer except in and near localized chimneys, which are characterized by having zero solid fraction. Upward, convective flow within the chimneys is driven by compositional buoyancy. The radius of each chimney is determined locally by thermal balances within a boundary layer that surrounds it. Simple solutions are derived to determine the structure of the mushy layer away from the immediate vicinity of chimneys in order to demonstrate the gross effects of convection upon the solidification within the layer.

Turbulent Compressible Convection

Abstract: Numerical simulations with high spatial resolution (up to 96-cubed gridpoints) are used to study three-dimensional, compressible convection. A sequence of four models with decreasing viscous dissipation is considered in studying the changes in the flow structure and transport properties as the convection becomes turbulent. 39 refs.

Heat Transfer with Freezing and Thawing

Abstract: 1. BASIC EQUATIONS . The Nature of the Thermodynamic System. General Energy Equation for a Continuum. Energy Balance at the Phase-Change Interface. Nonlinearity of Solidification Problems. Conservation of Mass, Momentum and Energy for Continuum. Heat, Mass, and Momentum Flow in Porous Media. Nomenclature. References. 2. PLANE PROBLEMS WITH TEMPERATURE BOUNDARY CONDITIONS. Neumann Problem and Variations. Neumann Problem With Variable Properties. Neumann Problem With Variable Temperatures. Melting Temperature Range. Subcooled Liquid - Frazil Ice. Solidification in Contact with Cold Wall. Thaw With Consolidation of Melted Medium. Freeze of a Flowing Fluid. Freeze Coating on a Moving Sheet. Continuous Casting of Slab. Convective Effects. Nomenclature. References. 3. PLANE PROBLEMS WITH CONVECTION (RADIATION) AT FREE SURFACE. Single-Phase Problems. Two-Phase Problems. Nomenclature. References. 4. PLANE PROBLEMS WITH SPECIFIED SURFACE HEAT FLUX. Exact Solution for Semi-Infinite Medium. Approximate Solutions, Single Phase, Semi-Infinite Region. Two-Phase Problems. Ablation with Complete Removal of Melt. Freezing of a Flowing Fluid. Nomenclature. References. 5. THAW BENEATH INSULATED STRUCTURES QUASI-STEADY SOLUTIONS. General Quasi-Steady Relations. Nomenclature. References. 6. CYLINDRICAL PROBLEMS . Outward Phase Change, Infinite Domain. Outward Phase Change, Finite Geometry. Inward Phase Change. Convective Effects and Relations. Nomenclature. References. 7. PROBLEMS IN SPHERICAL GEOMETRY. Outward Phase Change. Spherical Problems, Inward Growth. Nomenclature. References. 8. PHASE CHANGE IN POROUS MEDIA. Natural Convection in Porous Media Without Phase Change. Natural Convection With Phase Change. Coupled Energy and Mass Fluxes. Nomenclature. References. APPENDIX A: Quasi-Static Approximations and Perturbation Methods. APPENDIX B: The Heat Balance Integral Method. APPENDIX C: Biot's Variational Principle. APPENDIX D: Error Function and Error Integral Family. APPENDIX E: Exponential Integral and Related Functions. APPENDIX F: Porous Media and Macroscopic Equations. APPENDIX G: Laplace Transforms and Phase-Change Problems. SUBJECT INDEX. AUTHOR INDEX.

Effects of rotation on convective turbulence

Abstract: Laboratory experiments were carried out to investigate the effects of rotation on turbulent convection. The experimental facility was a bottom-heated, water-filled, cubical tank mounted on a turntable. The investigations were performed over a wide range of bottom buoyancy fluxes q0 and rotation rates Ω, including Ω = 0; q0 and Ω were held constant during each experiment. The depth of the water column H was fixed for the entire experimental programme. For the non-rotating experiments, the r.m.s. velocity fluctuations were found to scale well with the convective velocity , where the integral lengthscale is estimated as lr ≈ 0.25hc. The mean buoyancy gradient in the mixed layer was found to be much higher than in the corresponding non-rotating case, and the r.m.s. fluctuations and mean buoyancies were found to scale satisfactorily with (q0Ω)½. A spectral form for the temperature fluctuations in rotating convection is also proposed and is compared to the experimental results.

Numerical simulations of three-dimensional thermal convection in a fluid with strongly temperature-dependent viscosity

Abstract: Numerical calculations are presented for the steady three-dimensional structure of thermal convection of a fluid with strongly temperature-dependent viscosity in a bottom-heated rectangular box. Viscosity is assumed to depend on temperature T as exp ( --ET), where E is a constant ; viscosity variations across the box r (= exp (E)) as large as lo5 are considered. A stagnant layer or lid of highly viscous fluid develops in the uppermost coldest part of the top cold thermal boundary layer when r > rcl, where r = rcl = 1.18 x 103R,0~308 andR, is the Rayleigh number based on the viscosity at the top boundary. Three-dimensional convection occurs in a rectangular pattern beneath this stagnant lid. The planform consists of hot upwelling plumes at or near the centre of a rectangle, sheets of cold sinking fluid on the four sides, and cold sinking plume concentrations immersed in the sheets. A stagnant lid does not develop, i.e. convection involves all of the fluid in the box when r rc2 = 3.84 x 106R;1.36. The planform of the convection is rectangular with the coldest parts of the sinking fluid and the hottest part of the upwelling fluid occurring as plumes at the four corners and at the centre of the rectangle, respectively. Both hot uprising plumes and cold sinking plumes have sheet-like extensions, which become more well-developed as r increases. The whole-layer mode of convection occurs as two-dimensional rolls when r < min (rcl, rc2). The Nusselt number Nu depends on the viscosity at the top surface more strongly in the regime of whole-layer convection than in the regime of stagnant-lid convection. In the whole-layer convective regime, Nu depends more strongly on the viscosity at the top surface than on the viscosity at the bottom boundary.

3‐D Convection With Variable Viscosity

Abstract: Accepted 1990 September 6. Received 1990 July 16; in original form 1990 May 3 SUMMARY report numerical calculations for 3-D convection with variable viscosity. A hybrid spectral and finite difference method is used. The coupling of modes in the equation of motion, which is caused by lateral viscosity variations, is treated iteratively. Solutions for bimodal, hexagonal, square, triangular and spoke patterns are reported for bottom heated convection at infinite Prandtl number. The Rayleigh number, based on the viscosity at the mean of top and bottom temperature, is between critical and lo5, and temperature-induced viscosity contrasts up to 100 are considered (lo00 in one case). In agreement with results from laboratory experiments we find that at low Rayleigh number temperature-dependent viscosity favours flow patterns like squares or hexagons, where a columnar rising current is surrounded by sheet-like descending flow. The dichotomy in geometry between upwelling and sinking flow becomes more pronounced with increasing viscosity contrast. The temperature dependence of viscosity gives rise to a toroidal velocity component; however, it amounts only to a few per cent of the total velocity. In contrast, at the earth’s surface an approximate equipartitioning of poloidal and toroidal energy is found. We show that with non-Newtonian and depth-dependent rheology the toroidal component at the free surface can become significant, and a pattern reminiscent of plate motion can arise in a free convection model. Although these results are obtained in a parameter range which is not directly applicable to the earth, they support the conclusions that (i) upwelling flow in the mantle is unlikely to be sheet-like and will probably be in the form of columnar plumes, and that (ii) the toroidal motion found at the earth’s surface is due to the highly non-linear rheology which leads to the existence of mobile surface plates and is not caused by viscosity variations related to lateral temperature contrasts deeper in the mantle.

Mixed convection from an isolated heat source in a rectangular enclosure

Abstract: The mixed convection transport from an isolated thermal source, with a uniform surface heat flux input and located in a rectangular enclosure, is studied numerically. The enclosure simulates a practical system such as an oven or an air-cooled electronic device, where an airstream flows through the openings on the two vertical walls. The heat source represents a heater or an electronic component located in such an enclosure. The interaction of the cooling stream with the buoyancy-induced flow from the heat source is of interest in this work. Laminar, two-dimensional flow is assumed, and the problem lies in the mixed convection regime, governed by the buoyancy parameter GrIRe1 and the Reynolds number Re. Other significant variables include the locations of the heat source and the outflow opening. The inflow is kept at a fixed position. The mathematical model is developed with vorticity and stream function, along with temperature, as the dependent variables. The unsteady terms are retained in the vo...

Natural convection in the subarctic snow cover

Abstract: The purpose of this study was to determine if air convects in a natural snow cover. To detect convection, the temperature field in the subarctic snow cover in Fairbanks, Alaska, was measured hourly during three winters (1984–1987) using an array of thermistors which were suspended on threads and allowed to be buried by snowfall. The results indicate that convection occurred sporadically in 1984–1985 and almost continuously in 1985–1986 and 1986–1987. The evidence was (1) simultaneous warming and cooling at different locations in a horizontal plane in the snow, and (2) horizontal temperature gradients of up to 16°C m−1 During the winter, warm and cold zones developed in the snow and remained relatively fixed in space. We interpret these zones to be the result of a diffuse plumelike convection pattern linked to spatial variations in the temperature of the snow-soil interface. Air flow was inferred to have been primarily horizontal near the base of the snow and vertical elsewhere. Calculated flow speeds were of the order of 0.2 mm s−1, with a maximum value of 2 mm s−1 The convective circulation was time-dependent, with perturbations such as high wind or rapid changes in air temperature triggering periods when horizontal temperature gradients were strongest, suggesting that these were also periods when the air flow was fastest. The coincidence of depth hoar crystals with horizontal c axes and the horizontal flow lines at the base of the snow suggests that convection may have affected crystal growth directions.

Buoyancy-induced flow of non-Newtonian fluids over a non-isothermal body of arbitrary shape in a fluid-saturated porous medium

Abstract: The buoyancy-induced flows of non-Newtonian fluids over non-isothermal bodies of arbitrary shape within saturated porous media have been treated using the boundary layer approximations and the power-law model to characterize the non-Newtonian fluid behavior. Upon introducing a general similarity transformation which considers both the geometrical effect and the wall temperature effect on the development of the boundary layer length scale, the governing equations for a non-isothermal body of arbitrary shape have been reduced to those for a vertical flat plate. The transformed equations reveal that a plane or axisymmetric body of arbitrary shape possesses its corresponding family of the wall temperature distributions which permit similarity solutions. Numerical integrations were carried out using the Runge-Kutta-Gill method, and the results of the heat transfer function were presented once for all plane and axisymmetric bodies. As illustrations, local wall heat flux distributions were discussed for wedges, cones, spheres, circular cylinders and other geometries. Furthermore, an approximate formula based on the Karman-Pohlhausen integral relation has been presented for speedy and sufficiently accurate estimation of heat transfer rates.

Non-Darcy Mixed Convection Along a Vertical Wall in a Saturated Porous Medium

Abstract: In most of the previous studies of either natural or mixed convection, the boundary-layer formulation of Darcy's law and the energy equation were used. However, the inertial effect is expected to become very significant when the pore Reynolds number is large. This is especially true for the case of either the high Rayleigh number regime or for high-porosity media. In spite of its importance in many applications, the non-Darcy flow effect has not received much attention. In this note, non-Darcy flow effects, which include the inertial and thermal dispersion effects, are closely examined. Steady-state non-Darcy convection, in the form of natural, mixed, and forced convection, is considered for a heated vertical surface embedded in a saturated porous medium.

Convective heat and mass transfer in porous media

Abstract: Transport Processes in a Rapidly Changing World.- Modelling of Transport Phenomena in Porous Media.- Fundamentals of Mechanics of Saturated Porous Media: Basic Equations and Waves.- The Stability of Convective Flows in Porous Media.- Free Convection Heat and Mass Transfer in a Porous Medium.- Natural Convection in a Vertical Porous Annulus.- Non-Darcy Natural Convection in Saturated Porous Media.- Mixed Convection in Saturated Porous Media.- Forced Convective Flow and Heat Transfer Through a Porous Medium Exposed to a Flat Plate or a Channel.- Forced Convection Heat Transfer in a Porous Medium.- Radiation Transport in Porous or Fibrous Media.- Fundamentals of Drying of Capillary-Porous Bodies.- Heat Transfer During Unsaturated Flow in Porous Media.- Buoyancy-Induced Flow and Heat Transfer in Saturated Fissured Media.- Effect of Randomness on Heat and Mass Transfer in Porous Media.- Analytical Solutions to Transient Convective Mass Transfer Within Porous Media.- Natural Convection in Porous Media with Variable Porosity and Thermal Dispersion Effects.- Convective Flow Interaction and Heat Transfer Between Fluid and Porous Layers.- Temperature Distribution in a Porous Slab with Random Thermophysical Characteristic.- Forced Convection in Packed Tubes and Channels with Variable Porosity and Thermal Dispersion Effects.- Transient Double Diffusive Convection in a Horizontal Fluid Layer Situated on top of a Porous Substrate.- Drying of Wood Residues in a Fixed Bed.- Heat and Mass Transfer in Adsorbent Beds.- Solidification of a Binary Mixture Saturating a Bed of Glass Spheres.- Melting in the Presence of Natural Convection in a Saturated Porous Medium.- Air-Water Two-Phase Flow Pressure Drop in Large Scale Porous Media.- Boiling and Dryout in Unconsolidated Porous Media.- Heat Transfer from a Surface Covered with Hair.- Measurements of Thermal Conductivity in Porous Media.- Determination of Velocity Vectors in Porous Media with Fluorescent Particle Image Velocimetry (FPIV).- Non Invasive Measurement Techniques in Porous Media.- Flash Method of Measuring Thermal Diffusivity and Conductivity.- Mechanics, Heat and Mass Transfer in Saturated Porous Media. Application to Petroleum Technology.- Drying Complex Porous Materials-Modelling and Experiments.- Some Geophysical Problems Involving Convection in Porous Media.- Porous Surface Boiling and Its Application to Cooling Microelectronic Chips.- Heat and Mass Transfer in Spouted Beds.- Liquid Seeping into Porous Ground.- Future Research Needs in Convective Heat and Mass Transport in Porous Media.

A Numerical Study of Developing Free Convection Between Isothermal Vertical Plates

Abstract: Steady two-dimensional laminar free convection between isothermal vertical plates including entrance flow effects has been numerically investigated. The full elliptic forms of the Navier-Stokes and energy equations are solved using novel inlet flow boundary conditions. Results are presented for Prandtl number Pr = 0.7, Grashof number range 50 {le} Gr{sub b} {le} 5 {times} 10{sup 4}, and channel aspect ratios of L/b = 10, 17, 24. New phenomena, such as inlet flow separation, have been observed. The results cast doubt on the validity of previous elliptic solutions. Comparisons with the approximate boundary-layer results show that a full elliptic solution is necessary to get accurate local quantities near the channel entrance.

Electroconvection at an electrically inhomogeneous permselective interface

Abstract: This paper concerns electroconvection—a nongravitational free convection in macroscopic domains of electrolyte solution. Electroconvection results from the interaction of the electric field in the system with the respective space charge within the limits of validity of local electroneutrality approximation. It follows from the dimensional analysis that the electroconvectional Peclet number, evaluated near the equilibrium in a macroscopic ionic system, characterized by a single length scale, is universally of order unity, independently of the size of the system and of the typical electrolyte concentration. An electroconvectional flow in a two‐dimensional diffusion layer adjacent to a periodic electrically inhomogeneous permselective interface is calculated by an integral method to leading order in small electroconvectional Peclet number, occurring in the considered large aspect ratio case due to the presence of two separate macroscopic length scales. Explicit expressions for the flow characteristics are worked out through an asymptotic procedure valid in the vicinity of electrodiffusional limiting current.

Onset of convection in an anisotropic porous medium with oblique principal axes

Abstract: Summary and conclusions The present work is the first study of Rayleigh-Be'nard convection in an anisotropic porous medium with oblique principal axes. The analysis is restricted to transversely isotropic media with isotropic thermal conductivity. Qualitatively new flow patterns occur at the onset of convection. If the transverse permeability is larger than the longitudinal permeability, the planes of motion are tilted, but the cell walls are vertical as usual. On the other hand, if the longitudinal permeability is the larger one, the flow occurs in vertical planes, but the cell walls are tilted. 'The preference for these different patterns is explained as a preference for flow directions with as small a tangential permeability as possible. This preference also gives rise to a tendency of concentration of the flow along the cell boundaries when the anisotropy increases, in the case when the cell walls are tilted. The tilt is primarily of mechanical origin, because a vertical forcing due

Experimental verification of Darcy-Brinkman-Forchheimer flow model for natural convection in porous media

Abstract: Experimental results for natural convection in a horizontal porous cavity of aspect ratio A = 5 and heated from below are reported. A wide range of governing parameters are covered by careful selection of bead size, solid material, and fluid. These results fully support the effects of fluid-flow parameters (Rayleigh and Prandtl numbers), porous matrix-structure parameters (Darcy and Forchheimer numbers), and the conductivity ratio as predicted by the formulation based on the Darcy-Brinkman-Forchheimer (DBF) equations of motion. The DBF flow model, with variable porosity and variable thermal conductivity in the wall regions, predicts reasonably well in comparison with the experimental data. However, the difference between the predictions and the measurements increases as the ratio of solid-to-fluid thermal conductivity becomes very large. 32 refs.

The Ra-Pr domain of laminar natural convection in an enclosure heated from the side

Abstract: The phenomenon of natural convection in a square enclosure heated and cooled in the horizontal direction was investigated numerically in the Prandtl number range 0.01-10 and the Rayleigh number range 102-1011. The numerical method relied on the full governing equations for time-dependent flows. The study focused on the detection of inertia-sustained fluctuations in the flow field and on the highest Rayleigh number where steady-state laminar flows are possible. It was found that the highest Rayleigh number decreases dramatically as the Prandtl number decreases. This finding agrees qualitatively with experimental observations of transition to turbulent natural convection and with the “local Reynolds number” criterion of transition to turbulence recommended by the buckling theory of turbulent flow.