Computation of two-dimensional time-dependent natural convection of compressible fluid in a rectangular enclosure

Two-dimensional laminar natural convection in air contained in a long horizontal rectangular enclosure with isothermal walls at different temperatures has been investigated using numerical techniques. The time-dependent governing differential equations were solved using a method based on that of Crank and Nicholson. Steady-state solutions were obtained for height to width ratios of 1, 2.5, 10, and 20, and for values of the Grashof number, GrL′, covering the range 4 × 103 to 1.4 × 105. The bounds on the Grashof number for H/L = 20 is 8 × 103 ≤ GrL′ ≤ 4 × 104. The results were correlated with a three-dimensional power law which, yielded H/L=1Nu¯L′=0.0547(GrL′)0.3972.5≤H/L≤20Nu¯L′=0.155(GrL′)0.315(H/L)−0.265 The results compare favorably with available experimental results.

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An Experimental Study of Natural Convection in a Rectangular Enclosure Using PIV Measurement Techniques

Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B ◽

10.1115/imece2011-64276 ◽

2011 ◽

Author(s):

K. M. Akyuzlu ◽

J. Farkas

Keyword(s):

Experimental Study ◽

Natural Convection ◽

Measurement Techniques ◽

Flow Patterns ◽

Working Fluid ◽

Two Dimensional ◽

Rectangular Enclosure ◽

Aspect Ratios ◽

Circulation Patterns ◽

Piv Measurement

An experimental study is conducted to determine the circulation patterns inside a rectangular enclosure due to natural convection using a Particle Image Velocimeter (PIV). Experiments were conducted using two different fluids (air and water) and for rectangular enclosures with aspect ratios 0.5 and 1.0. Natural convection in enclosures has been experimentally studied in the past. Many of these studies cited in the literature use some kind of an optical method like interferograms, shadowgraphs, streak photographs, or multi-exposure photographs to visualize the flow patterns in the enclosure. The present study employs a commercial two-dimensional PIV to capture, instantaneously, the circulation patterns inside the test section. The test cavity in the present setup is of rectangular shape, which is 5 inches (127 mm) wide, where the height of the enclosure can be changed to obtain aspect ratios of 0.5 and 1.0. The depth of the rectangular enclosure measures 12 inches (305 mm) to minimize the effect of walls normal to the two dimensional flow patterns that are expected in this type of arrangement. The walls of the cavity are made of Aluminum plates. These plates are kept at constant but different temperatures during the experiments. In the present study, hollow glass sphere particles with 10 microns in diameter were used as seeding for water experiments and fine particles/flakes of ash generated from burned incense were used as seeding in the air experiments. For each working fluid, the experiments were repeated for different aspect ratios and for different wall temperature differences which corresponded to Rayleigh numbers in the range of 106 and 107. Velocity fields were captured at steady state for each experiment using the two-dimensional PIV system. Numerical studies were also carried out using a commercial CFD software. Comparisons of the numerical and experimental results indicate a good match in terms of circulation patterns and velocity magnitudes in the core of the buoyancy driven flow. Discrepancies in measured and predicted values of velocities are more pronounced near to the boundaries of the enclosure. Separate measurements with finer interrogation areas and different PIV setting were required to improve the accuracy of the measurements near the corners (top and bottom) of the enclosure. The results of these measurements are also presented.

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Computation of two-dimensional time-dependent natural convection in a cavity where there are internal bodies

Computers & Fluids ◽

10.1016/0045-7930(86)90006-x ◽

1986 ◽

Vol 14 (2) ◽

pp. 141-157 ◽

Cited By ~ 25

Author(s):

J.H. Adlam

Keyword(s):

Natural Convection ◽

Time Dependent ◽

Two Dimensional

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Interaction of temperature- and salinity-driven natural convection in homogeneous porous media

10.5194/egusphere-egu2020-9896 ◽

2020 ◽

Author(s):

Márk Szijártó ◽

Attila Galsa

Keyword(s):

Porous Medium ◽

Porous Media ◽

Natural Convection ◽

Rayleigh Number ◽

Numerical Simulations ◽

Theoretical Models ◽

Time Dependent ◽

Two Dimensional ◽

Thermohaline Convection ◽

Rayleigh Numbers

Onset of thermal and haline convection was studied separately by Lapwood (1948) and Wooding (1956) in theoretical models using analytical methods. They established that the buoyancy force caused by difference in temperature (&#916;T) or concentration (&#916;c) can induce natural convection depending on the model properties (e.g. geometry, permeability, etc.). In the course of further numerical simulations, the thermal (RaT) and the haline Rayleigh number (RaH) proved itself useful to characterise the type, the intensity and the form of the natural convection (e.g. Diersch and Kolditz, 2002). The main purpose of our study was to examine numerically the combined effect of temperature- and salinity-driven natural convection in a two-dimensional homogeneous porous medium.Two-dimensional finite element base model was set up in agreement with the Elder problem (Wooding, 1956) in order to verify the numerical calculation. First, it was established that (1) the critical Rayleigh numbers are mathematically equivalent in the two separated cases (RaTcr=RaHcr=4&#960;2), and (2) time-dependent thermal or haline natural convections evolve, when the Rayleigh number lies within the range of 300&#8211;600. Numerical simulations were accomplished to investigate the interaction of the temperature- and salinity-driven natural convection. Non-dimensional thermal expansion and haline concentration were increased from &#945;&#916;T=0.01 to 1 and from &#946;&#916;c=10-5 to 10-3, respectively, while the variation of the Darcy flux, the temperature, the concentration, the Nusselt and the Sherwood numbers was computed. The main points of this study were that (1) how the onset of the thermohaline convection is facilitated by the positive interaction of the thermal and haline effects (RaTHcr); (2) under what conditions time-dependent flow evolves in the theoretical models; (3) whether a new non-dimensional number can be defined instead of the two separated Rayleigh numbers in order to characterise the behaviour of the thermonaline convection. These simulations draw attention to the importance of understanding the physical background of thermohaline convection, for instance, at the margin of confined and unconfined carbonate systems (e.g. Buda Thermal Karst), or in the case of groundwater flow induced by water pumping/injection of deep geothermal power plants.The project was supported by the &#218;NKP-19-3 and &#218;NKP-19-4 New National Excellence Program of the Ministry for Innovation and Technology, the Hungarian Research Fund (K 129279) and the J&#225;nos Bolyai Scholarship of the Hungarian Academy of Science. This research is a part of a project that has received funding from the European Union&#8217;s Horizon 2020 research and innovation program under grant agreement No 810980.References:Diersch, H.-J.G., Kolditz, O. (2002), Variable-density flow and transport in porous media: approaches and challenges. Advances in Water Resources, 25, 899-944.Lapwood, E.R. (1948), Convection of a fluid in a porous medium. Mathematical Proceedings of the Cambridge Philosophical Society, 44, 508-521.Wooding, R.A. (1956), Steady state free thermal convection of liquid in a saturated permeable medium. Journal of Fluid Mechanics, 2, 273-285.

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