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On the high-Rayleigh-number structure of steady laminar natural-convection flow in a square enclosure

Published online by Cambridge University Press:  26 April 2006

M. R. Ravi ,
R. A. W. M. Henkes  and
C. J. Hoogendoorn
M. R. Ravi
Affiliation:
Faculty of Applied Physics, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands. Present address: FAST, URA-871, CNRS, Bâtiment 502, 91405 Orsay, France.
R. A. W. M. Henkes
Affiliation:
Faculty of Applied Physics, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands. Present address: Faculty of Aerospace Engineering, Delft University of Technology, PO Box 5058, 2600 GB Delft, The Netherlands.
C. J. Hoogendoorn
Affiliation:
Faculty of Applied Physics, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
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Abstract

Natural-convection flow in an enclosure with adiabatic horizontal walls and isothermal vertical walls maintained at a fixed temperature difference has been investigated. At high values of the natural-convection parameter, the Rayleigh number, a recirculating pocket appears near the corners downstream of the vertical walls, and the flow separates and reattaches at the horizontal walls in the vicinity of this recirculation. There is also a considerable thickening of the horizontal layer. In some previous studies by different authors, this corner flow was considered to be caused by an internal hydraulic jump, and the jump theory was used to predict bifurcation of the steady flow into periodic flow. The present work examines the corner phenomenon closely to decide if it is indeed caused by a hydraulic jump. The results of the analysis reveal the oversimplification of the problem made in the previous studies: there is no connection of the corner phenomenon with a hydraulic jump. The separation of flow at the ceiling is not a feature of hydraulic jumps, and the essential energy loss associated with hydraulic jumps is not observed in the corner flow. It is shown that the corner structure is caused by thermal effects. Owing to the temperature undershoots in vertical boundary layer, which are known to be caused by the stable thermal stratification of the core, relatively cold fluid reaches the upper corner. This cold fluid detaches from the ceiling like a plume at high Rayleigh numbers, and causes the separation and recirculation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 262 , 3 October 1994 , pp. 325 - 351
Copyright
© 1994 Cambridge University Press

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