Injection of a water stream in a column

Heating of the base of a column

**The grid** : at the top of this column, it is very
refined in order to observe the oulet of the flow of water.

**The inlet and outlets** : the presence of the outlets
is necessary to permit the flow to go out of the column and there are setted
at the top in order to increase the recirculation and to make the analogy
with the oulet of the bubbles.

**The symmetry **: we have made the choice of a symetry
at the top of the column instead of a wall because we think that's it is
more representative of a free surface. It allows too to avoid the problem
of friction on a wall.

**The walls **: we have considered that the temperature
of the walls was constantly equal to 300K. It is logical as regard to the
choice of unsolving the energy equation.

Two different inlet speeds have been tested:

- u = 0.1m/s
- u = 1m/s

The following results are so obtained for a speed of 0.1m/s.

Speed

The two following images show the establishment of the flow in the column:

With a speed of 0.1m/s, we could expect
that the fluid should need 5 seconds to reach the top of the column. However,
it has taken 164 seconds between the first image and the third. We can
explain that phenomenon by the smallness of the two outlets.

There is a beginning of oscillation but after the first
one, the flow is attracted by the wall and we obtain a non-evolutive
solution.

It is not possible for us to know if this solution is
realistic or not. Experimental results would be necessary to confirm or
infirm this result.

Vorticity

The first image shows the recirculation
after the arrival of the flow at the top of the column. The second one
represents the big recirculation after that the flow has begun to stick
to the wall.

It seems that the flow has reached
a non-evolutive solution. The turbulence dissipates the energy of the fluid.

We still study a column of 15cm large and 50cm high. The outputs are replaced by walls which temperature is chosen constantly equal to 300K and the input is replaced by a heated wall.

Laminar
and unstable flow results:

First of all, we thought it was interesting to simulate the test for a laminar and unstable flow. Nevertheless, we have faced diffuculties in order to obtain a beginnig of oscillation. As a consequence, we have decided to initialize the flow field with the solution obtained for a stable and turbulent case. Two different heating were studied.

__20000 W/m^2__

It seems that an oscillation has appeared,
the second image and the fifth one are nearly identical. It allows us to
know the frequency of the phenomenon. The period is approximatively equal
to 380s and that means a frequency of 2.6 mHz. This is a low period which
can be explained by the slowness of the phenomenon of advection.

__50000 W/m^2__

We have obtained the following results :

It seems that the system oscillates
but it is impossible to find a period for the phenomenon. In fact, we observe
that the flow collapses at the third image at the top of the column, vorticity
is very important. An oscillation may be observed with longer times of
simulation.

**Remark:**

The study of
the turbulent and unstable case can not be justified since the terms added
in the equations can transform the results into false ones.

We found that the subject was very interesting with industrial applications, in particular for the Fluids and Processes' BEI where column with oil flows are studied.