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Modelling of Natural Convection Flowswith Large Temperature Differences:A Benchmark Problem for Low Mach Number Solvers. Part 1. Reference Solutions

Published online by Cambridge University Press:  15 June 2005

Patrick Le Quéré ,
Catherine Weisman ,
Henri Paillère ,
Jan Vierendeels ,
Erik Dick ,
Roland Becker ,
Malte Braack  and
James Locke
Patrick Le Quéré
Affiliation:
LIMSI, BP 133, 91403 Orsay Cedex, France. [email protected]; [email protected]
Catherine Weisman
Affiliation:
LIMSI, BP 133, 91403 Orsay Cedex, France. [email protected]; [email protected]
Henri Paillère
Affiliation:
CEA Saclay, DEN/DM2S/SFME,91191 Gif-sur-Yvette Cedex, France. [email protected]
Jan Vierendeels
Affiliation:
Ghent University, B-9000 Gent, Belgium. [email protected]; [email protected]
Erik Dick
Affiliation:
Ghent University, B-9000 Gent, Belgium. [email protected]; [email protected]
Roland Becker
Affiliation:
Heidelberg University, Germany. [email protected]
Malte Braack
Affiliation:
Heidelberg University, Germany. [email protected]
James Locke
Affiliation:
U. Warwick and British Energy Generation Ltd.
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Abstract

There are very few reference solutions in the literature onnon-Boussinesq natural convection flows. We propose here a testcase problem which extends the well-known De Vahl Davisdifferentially heated square cavity problem to the case of largetemperature differences for which the Boussinesq approximation isno longer valid. The paper is split in two parts: in this firstpart, we propose as yet unpublished reference solutions for casescharacterized by a non-dimensional temperature difference of 0.6,Ra = 106 (constant property and variable property cases) andRa = 107 (variable property case). These reference solutions wereproduced after a first international workshop organized by CEA andLIMSI in January 2000, in which the above authors volunteered toproduce accurate numerical solutions from which the presentreference solutions could be established.

Keywords

Natural convectionnon-Boussinesqlow Mach number.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 3: Special issue on Low Mach Number Flows Conference , May 2005 , pp. 609 - 616
Copyright
© EDP Sciences, SMAI, 2005

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