Position of the problem

The fluid choosen is water-liquid, it is defined by

we use the Boussinesq-approximation
set in the pannel : Define-materials

For the pressure, the model
used is PRESTO! . If we use the default one, we find that the vertical
component of the velocity at the walls is not nul.

with PRESTO!, this problem is resolved

Back to the top of the page

We used Prebfc to generate the mesch.

The grid dimensions are 1cm * 0.5cm
. We put 50 cells horizontaly and 25 cells vertically. We used a structured
mesch as it is described next.

The boundary conditions are symetry
for the vertical sides and walls at different temperatures for the horizontal
sides.

Back to the top of the page

We have put the lower
side at the temperature T2=283k and the upper at T1=280k. The distance
between the two planes is 0.5 cm .we find a Raylleigh number Ra=3582.5.

Theoritically, with this rayleigh,
we can have different nombre of rolls depending of the initial conditions.

Our objectif
is to try to find the appropriate initialisation in order to have 1,2,3
and 4 rolls. in each case, we initialise first the temperature. If we don't
obtain the

result, we initialise also the
velocity. We try in each case to force the motion to go in the wanted direction.

With temperature,
we made different zones that create convection which push the fluid to
move like the wanted result.

With velocity,
we initialise with the result searched . We impose directly the number
of rolls using this formula :

Vx=-Vxo.sin(pi.Nb.x /Lx ) cos(pi. y /Ly)

Vy=Vyo.sin(pi. y /Ly ) cos(pi. Nb. x /Lx)

with

Vxo , Vyo : amplitudes

Nb : number
of rolls expected

Lx , Ly : Dimensions
of the box in the two dircections

Here is an example of velocity initialisation
with four rolls

Back to the top of the page