ARTICLE:

• BIFURCATIONS AND MULTIPLE SOLUTIONS IN AN AIR-FILLED DIFFERENTIALLY HEATED CUBIC CAVITY  download article

G. de Gassowski
Courcouronnes Université d'Evry, France

Olivier Daube
LMEE - Université d'Evry - CE 1455 Courcouronnes - 91020 Evry Cedex; and LIMSI-CNRS, UPR 3251, BP 133, 91403 Orsay CEDEX, FRANCE

Shihe Xin
CNRS, LIMSI, BP 133, 91403 Orsay Cedex, France; and Université Paris Sud, 91405 Orsay Cedex, France

Y. Fraigneau
LIMSI-CNRS, Orsay Cedex, FRANCE

ABSTRACT

We investigate natural convection in an air-filled differentially heated cubic cavity by doing symmetry-constrained numerical simulations. Near the onset of time-dependant flows (about Ra = 3.2·10⁷), unstable steady-state solutions are obtained and linear stability analysis using Arnoldi's method is performed (critical values were computed for the first two unstable modes which all break the reflection symmetry). At Ra = 4·10⁷, three branches of time-dependant solutions are observed. At Ra = 5·10⁷, two solution branches, one steady and another time-dependant, are discovered. At Ra = 7·10⁷, two branches of steady-state solutions are observed while at Ra = 10⁸ there are three branches of steady-state solutions. Depending on Rayleigh number, numerical solutions exhibit different symmetries.
Despite complex flow structures, no significant changes in heat transfer were observed over the range of Rayleigh number investigated.

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