Convection in an Enclosure-Source and Sink Located Along a Single Horizontal Boundary

Dust devils are convective vortices with a vertical axis of rotation mainly characterized by a local minimum in pressure and a local maximum in vertical vorticity within the vortex core. They are made visible by entrained dust particles. That's why they occur primarily in dry and hot areas. Currently, there is great uncertainty about the extent to which dust devils contribute to the atmospheric aerosol and heat transport and thereby influence earth's radiation budget as well as boundary layer properties. Past efforts to quantify the aerosol or heat transport and to study dust devils' formation, maintenance, and statistics using large-eddy simulation (LES) as well as direct numerical simulation (DNS) have been of limited success. Therefore, this study aims to provide better statistical information about dust devil-like structures and to extend, prove or disprove existing theories about the development and maintenance of dust devils. Especially, the vortex strength measured through the pressure drop in the vortex core is regarded, which is, in past LES simulations, almost one order of magnitude smaller compared to the observed range of several hundreds Pascals. So far, we are able to reproduce observed core pressures with LES of the convective boundary layer by using a high spatial resolution of 2m while considering a domain of 4km x 4km x 2km, a model setup with moderate background wind and a spatially heterogeneous surface heat flux. It is found that vortices mainly appear at the vertices and branches of the cellular pattern and at lines of horizontal flow convergence above the centers of the strongly heated patches. The latter result is in contrast to some older observations in which vortices seemed to be created along the patch edges. Also further statistical properties, like lifetimes, diameters or frequency of occurrence, fit quite well in the observed range. Nevertheless, statistics of dust devils from LES face the general problem that they are highly influenced by the used grid spacing and thereby by the structures that can be explicitly resolved. For example, the near surface layer, which plays a major role for the vortex development, is poorly resolved and turbulent processes in this layer are highly parameterized. DNS would overcome this problem. Therefore, dust devil-like structures are also investigated with DNS by simulating laboratory-like Rayleigh-B&#233;nard convection with Rayleigh numbers up to 1012. Such high Rayleigh numbers have never been used in DNS studies of dust devils. The focus is on the vortex formation dependence on the used Rayleigh number and aspect ratio. First results of the laboratory-like Rayleigh-B&#233;nard convection simulated with DNS confirm the existence of dust devil-like structures also on small scales with much lower Rayleigh numbers than in the atmosphere. In a next step, detailed statistics of dust devil-like structures in Rayleigh-B&#233;nard convection will be derived focusing on Rayleigh number and aspect ratio dependencies. Afterwards, results will be compared to LES simulations of dust devils and experimental data.

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Transient Natural Convection in Enclosures at High Rayleigh Number

Journal of Heat Transfer ◽

10.1115/1.2910612 ◽

1991 ◽

Vol 113 (3) ◽

pp. 635-642 ◽

Cited By ~ 11

Author(s):

D. A. Olson ◽

L. R. Glicksman

Keyword(s):

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Transient Behavior ◽

Full Scale ◽

Scale Model ◽

Mixed Gas ◽

Transient Natural Convection ◽

Physical Scale ◽

Rayleigh Numbers

Transient natural convection at Rayleigh numbers of 1010 was studied experimentally in two enclosures of aspect ratio 1/3, one a 1:5.5 physical scale model containing the dense refrigerant gas R114, and the second a full-scale room containing air. In one type of transient the vertical endwall temperature was suddenly changed, while in a second type of transient the isothermal, well-mixed gas was suddenly exposed to hot and cold vertical endwalls. The experiments indicated that the dominant time constant was a convective one. Comparisons between the scale model and full scale show that R114 gas can simulate the transient behavior of air-filled enclosures.

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Parametric Analysis for Thermal and Fluid Dynamic Management of Natural Convection in a Channel-Chimney System

Volume 4: Fatigue and Fracture, Heat Transfer, Internal Combustion Engines, Manufacturing, and Technology and Society ◽

10.1115/esda2006-95585 ◽

2006 ◽

Author(s):

Assunta Andreozzi ◽

Bernardo Buonomo ◽

Oronzio Manca

Keyword(s):

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Wall Temperature ◽

Parametric Analysis ◽

Fluid Dynamic ◽

Numerical Procedure ◽

Uniform Heat Flux ◽

Extension Ratio ◽

Channel Aspect Ratio

In this paper a parametric analysis of natural convection in air in a channel-chimney system symmetrically heated at uniform heat flux, obtained by means of a numerical simulation, is carried out. The analysed regime is two-dimensional, laminar and steady-state. The numerical procedure employs the full Navier-Stokes and energy equations in terms of the stream function-vorticity approach. Results are presented in terms of wall temperature profiles in order to show the more thermally convenient configurations which correspond to the channel-chimney system with the lowest maximum wall temperature. The analysis is obtained for a Rayleigh number in the range between 102 and 105, for a channel aspect ratio equal to 5, 10 and 20 and the extension and expansion ratios between 1.0 and 4.0. Correlations for dimensionless mass flow rate, maximum wall temperature and average Nusselt number in terms of Rayleigh number, aspect ratio, extension and expansion ratios are presented. Geometric optimal configurations, for assigned Rayleigh number and aspect ratio, are estimated as a function of the extension ratio. For considered Rayleigh number the difference between the highest and the lowest maximum wall temperatures increases increasing the channel aspect ratio. This behaviour is as greater as the extension ratio is. These differences decrease significantly for the highest Rayleigh number value. The optimal expansion ratio values depend strongly on Rayleigh number and extension ratio values and slightly on the aspect ratio.

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NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

Revista de Engenharia Térmica ◽

10.5380/reterm.v3i2.3530 ◽

2004 ◽

Vol 3 (2) ◽

pp. 100

Author(s):

T. Dias Jr. ◽

L. F. Milanez

Keyword(s):

Heat Flux ◽

Nusselt Number ◽

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Prandtl Number ◽

High Aspect Ratio ◽

Three Dimensional ◽

Uniform Heat Flux ◽

Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

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Numerical analysis of laminar natural convection in isosceles triangular enclosures

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1122 ◽

2009 ◽

Vol 223 (5) ◽

pp. 1157-1169 ◽

Cited By ~ 14

Author(s):

E F Kent

Keyword(s):

Heat Transfer ◽

Natural Convection ◽

Numerical Analysis ◽

Rayleigh Number ◽

Flow Field ◽

Water Heaters ◽

Thermal Boundary Conditions ◽

Laminar Natural Convection ◽

Solar Water Heaters ◽

Rayleigh Numbers

In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 103 to 105. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.

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Numerical Study of Laminar Natural Convection From a Plate to its Cylindrical Enclosure

Journal of Solar Energy Engineering ◽

10.1115/1.2930492 ◽

1991 ◽

Vol 113 (3) ◽

pp. 194-199 ◽

Cited By ~ 1

Author(s):

M. M. Elshamy ◽

M. N. Ozisik

Keyword(s):

Nusselt Number ◽

Steady State ◽

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Average Nusselt Number ◽

Numerical Study ◽

Hot Plate ◽

Cell Pattern ◽

Laminar Natural Convection

The steady-state laminar natural convection for air bounded by a hot plate and a cold cylindrical enclosure has been studied numerically for the case of cold isothermal cylinder and hot isothermal plate. A correlation is presented for the average Nusselt number over the range of Rayleigh number from 105 to 106 for different values of the width-aspect ratio Sw and thickness aspect-ratio St of the plate. It is found that the average Nusselt number increases with increasing Sw and Rayleigh number. A two-cell pattern is observed for Sw=1.5 and less. The effect of Sw on the average Nusselt number is found to be stronger than that of St.

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NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

Revista de Engenharia Térmica ◽

10.5380/ret.v3i2.3530 ◽

2004 ◽

Vol 3 (2) ◽

Author(s):

T. Dias Jr. ◽

L. F. Milanez

Keyword(s):

Heat Flux ◽

Nusselt Number ◽

Natural Convection ◽

Rayleigh Number ◽

Aspect Ratio ◽

Prandtl Number ◽

High Aspect Ratio ◽

Three Dimensional ◽

Uniform Heat Flux ◽

Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

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Convective Heat Transfer in a Rectangular Porous Cavity—Effect of Aspect Ratio on Flow Structure and Heat Transfer

Journal of Heat Transfer ◽

10.1115/1.3246629 ◽

1984 ◽

Vol 106 (1) ◽

pp. 158-165 ◽

Cited By ~ 105

Author(s):

V. Prasad ◽

F. A. Kulacki

Keyword(s):

Heat Transfer ◽

Rayleigh Number ◽

Aspect Ratio ◽

Aspect Ratios ◽

Family Of Curves ◽

Different Temperatures ◽

Vertical Walls ◽

Rayleigh Numbers ◽

Cavity Effect ◽

Cavity Width

Two-dimensional steady natural convection in a porous rectangular cavity bounded by isothermal vertical walls at different temperatures and adiabatic horizontal walls has been studied numerically for aspect ratios less than unity and Rayleigh numbers up to 104. Results indicate the presence of multicellular flow. Also, the average Nusselt number based on cavity width is observed to be a maximum in a restricted range of aspect ratio, depending on the Rayleigh number. Effects of aspect ratio are summarized by a family of curves for constant Rayleigh number, based on cavity height, for aspect ratios from 0.05 to 100. For a cavity with fixed height, the heat transfer rate always increases as the aspect ratio is increased, except when the flow exhibits boundary layers on the vertical walls. Criteria in terms of aspect ratio and Rayleigh number have been established for the existence of different flow regimes.

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Convection in a rotating cylinder. Part 1 Linear theory for moderate Prandtl numbers

Journal of Fluid Mechanics ◽

10.1017/s0022112093000928 ◽

1993 ◽

Vol 248 ◽

pp. 583-604 ◽

Cited By ~ 77

Author(s):

H. F. Goldstein ◽

E. Knobloch ◽

I. Mercader ◽

M. Net

Keyword(s):

Rayleigh Number ◽

Aspect Ratio ◽

Prandtl Number ◽

Boundary Conditions ◽

Rotation Rate ◽

Critical Rayleigh Number ◽

Onset Of Convection ◽

Aspect Ratios ◽

Prandtl Numbers ◽

Rayleigh Numbers

The onset of convection in a uniformly rotating vertical cylinder of height h and radius d heated from below is studied. For non-zero azimuthal wavenumber the instability is a Hopf bifurcation regardless of the Prandtl number of the fluid, and leads to precessing spiral patterns. The patterns typically precess counter to the rotation direction. Two types of modes are distinguished: the fast modes with relatively high precession velocity whose amplitude peaks near the sidewall, and the slow modes whose amplitude peaks near the centre. For aspect ratios τ ≡ d/h of order one or less the fast modes always set in first as the Rayleigh number increases; for larger aspect ratios the slow modes are preferred provided that the rotation rate is sufficiently slow. The precession velocity of the slow modes vanishes as τ → ∞. Thus it is these modes which provide the connection between the results for a finite-aspect-ratio System and the unbounded layer in which the instability is a steady-state one, except in low Prandtl number fluids.The linear stability problem is solved for several different sets of boundary conditions, and the results compared with recent experiments. Results are presented for Prandtl numbers σ in the range 6.7 ≤ σ ≤ 7.0 as a function of both the rotation rate and the aspect ratio. The results for rigid walls, thermally conducting top and bottom and an insulating sidewall agree well with the measured critical Rayleigh numbers and precession frequencies for water in a τ = 1 cylinder. A conducting sidewall raises the critical Rayleigh number, while free-slip boundary conditions lower it. The difference between the critical Rayleigh numbers with no-slip and free-slip boundaries becomes small for dimensionless rotation rates Ωh2/v ≥ 200, where v is the kinematic viscosity.

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Dimensionless Correlating-Equations for Predicting the Optimal Tilting Angle of Water-Filled Square and Shallow Enclosures Differentially Heated at Sides

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.394.163 ◽

2013 ◽

Vol 394 ◽

pp. 163-172

Author(s):

Marta Cianfrini ◽

Roberto de Lieto Vollaro ◽

Alessandro Quintino ◽

Massimo Corcione

Keyword(s):

Heat Transfer ◽

Rayleigh Number ◽

Aspect Ratio ◽

Convection Heat Transfer ◽

Heated Wall ◽

Tilting Angle ◽

Shallow Cavities ◽

Correlating Equations ◽

Laminar Natural Convection ◽

Dimensionless Correlations

Laminar natural convection heat transfer inside water-filled, tilted square and shallow cavities heated at one side and cooled at the opposite side, is studied numerically. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. Simulations are performed using the Rayleigh number based on the length of the heated and cooled sides, the height-to-width aspect ratio of the enclosure, and the positive tilting angle with respect to the gravity vector (which corresponds to configurations with the heated wall facing upwards), as independent variables. It is found that the heat transfer performance has a peak at an optimal tilting angle which increases as the Rayleigh number is decreased and the aspect ratio is increased. On the basis of the results obtained, a set of dimensionless correlations is developed.

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