BIFURCATIONS AND MULTIPLE SOLUTIONS IN AN AIR-FILLED DIFFERENTIALLY HEATED CUBIC CAVITY
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.