Presentation of Rayleigh-Benard instabilities

The rolls of onvection, described by Rayleigh and Benard, are a common natural phenomena and can easily be observed in the every day life. It can be found in systems such as geophysic fluids, the weather with the atmospheric circulation  (creation of some clouds) , the oceans with the oceanic streams...

This study aims at simulating the Rayleigh-Bénard instabilities with the software FLUENT. The problem concerns a fluid contained between two parallel horizontal plates at different temperatures. When the fluid is "heated  from below" and the temperature gradient exceeds a critical value (the critical number of Rayleigh Rac), we see the appearance of stationary controrotatifs rolls. This can be explained with the non-equilibrium between stabilisation forces - the drag force - and the destabilisation forces - Archimede force. Indeed, the bottom fluid, hot and light, moves to the top and the fluid on the top, cold and heavy, moves to the bottom. The following graph describes this mecanism :


Where :


We try to evaluate the conditions and the nature of the convective motions of the fluid in a box whose dimensions are 2 cm * 1 cm.
The mesh was done with PRE-BFC and is composed of 40*20 nodes. The boundary conditions are SYMETRICAL on the sides and WALL  on the two plates.