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

¹ LIMSI, BP 133, 91403 Orsay Cedex, France. plq@limsi.fr; weisman@limsi.fr
² CEA Saclay, DEN/DM2S/SFME,91191 Gif-sur-Yvette Cedex, France. henri.paillere@cea.fr
³ Ghent University, B-9000 Gent, Belgium. Jan.Vierendeels@UGent.be; erik.dick@UGent.be
⁴ Heidelberg University, Germany. malte.braack@iwr.uni-heidelberg.de
⁵ U. Warwick and British Energy Generation Ltd.

Abstract

There are very few reference solutions in the literature on non-Boussinesq natural convection flows. We propose here a test case problem which extends the well-known De Vahl Davis differentially heated square cavity problem to the case of large temperature differences for which the Boussinesq approximation is no longer valid. The paper is split in two parts: in this first part, we propose as yet unpublished reference solutions for cases characterized by a non-dimensional temperature difference of 0.6, Ra = 10⁶ (constant property and variable property cases) and Ra = 10⁷ (variable property case). These reference solutions were produced after a first international workshop organized by CEA and LIMSI in January 2000, in which the above authors volunteered to produce accurate numerical solutions from which the present reference solutions could be established.