Contents Introduction 
Introduction



fig. 1 This study aims at simulate the RayleighBernard instabilities. To do this, we'll use the two softwares FLUENT and PHOENICS. The case, we have chosen, is a rectangular box (1cmx2cm) composed by 2 plates (see fig. 1) maintained at two different temperatures. This box was filled of water. All of the computation will be made in the hypothesis of laminar flow.




The instabilities are determined
by the differences of temperature, T1T2, between the two walls (see fig.
1).
, steady rolls appears.
The rolls appearance mechanics is linked to the lack of balance between the Archimede force and the drag of the fluid particules. A dimensionless number caracterizing this, is the Rayleigh number (Ra). So for Ra>Rac (where Rac is the Rayleigh number for T1T2= ), we have instabilities.




We have to solve:
Moreover, we apply the Boussinesq approximation: (where is constant) in the NavierStockes equation where the expression of is replaced by . is the density at T0, and alpha is the thermal expenssion coefficient. All of this hypothesis have been computed in FLUENT and PHOENICS. Our study can start. As a first step, we chose to determined the critical Ra (Rac) and the meshing influence on this number. In a second step, we'll study the evolution of the velocity in function of the Rayleigh number. And at least, we'll make a brief study in a hypothesis of a unsteady flow. 