# Objectives of the study:

We would like to study particular phenomenon which appear in chemical columns. We consider a chemical column where bubbles are injected at the center of the base, experiments show that harmonic oscillations of the flow of bubbles appear. We would like to observe similar phenomenon with Fluent in two different cases :

Injection of a water stream in a column
Heating of the base of a column

# Injection of a water stream in a column:

### Presentation of the case:

We study a column of 15cm large and 50cm high. It is composed of an inlet of 3cm large in the middle of the base of the column and of two outlets (1cm large) at the top of the vertical walls. The grid-builder software preBFC allows to create a regular grid of 60x100 boxes:

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.

### Laminar and unstable case:

#### Parameters

In this case, the equation of energy is not solved and the density is considered as a constant. ( Boussinesq approximation )
Two different inlet speeds have been tested:
1. u = 0.1m/s
2. u = 1m/s
We remarked that for the slowest speed, it took 150s for the oscillations to appear, so we thought it was better to increase the inlet speed of the water. As expected, with a higher speed, the oscillations develop faster. However, we could doubt on the truth of the results in so far as the speed is probably too high for a laminar regime.
The following results are so obtained for a speed of 0.1m/s.

#### Results

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.

### Turbulent and stable case:

#### Parameters :

To study the turbulent and stable case, we have used the results of the laminar case at the time 120s which is shown above.Turbulence is modelised with k-epsilon. The speed is always equal to 0.1m/s.

#### Results :

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

# Heating of the base of a column:

Presentation of the case:

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.

# Conclusion :

To conclude we would like to underline the fact that all the tests we have been made have not been used. It was very difficult to know how to choose all the criterions in Fluent. (viscosity conditions, speed, temperature and stability). The hypethesis were sometimes criticable. We have managed to get oscillations with a flow of heated fluid in a lamimar case but the speed needed to see the establishment of the phenomenon was too high (10 m/s) to consider the results given by Fluent as correct results. Starting with a turbulent hypethesis wasn't possible since the viscosity was to high to let the flow get in the column. The lack of experimental results was another difficulty, we couldn't compare our results to reality.
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.