# Name of associated manuals : Effective working schedule. Back to index SESSION 8Dabireau (mfn03) and Massart (mfn08)Large Eddy Simulation with Fluent.

One task of this session was to install a new version of Fluent. So we have decide to explore one difference between the two versions : Large Eddy Simulation.
Our report is divided into this parts :

Problems LES creates
The choice of a case
Some of our results

Conclusion

Appendix : Kelvin-Helmoltz Instability.

# Problems LES creates

After few discussions with some of our teachers, we have learn that this task will not be so easy as we expected. :

• First LES is a mean to modelize the turbulence. Or turbulence is a 3 dimensions instationary phenomena. So we need 3D meshes. Moreover we have to stock the results at each iteration if we want to see the non stationnarity.
• Secondly the mesh must be sufficient thin to catch the eddies.
• Finnaly one of the matter with LES is to impose the boundaries conditions.
• With this example we can see that when an eddy cross the outlet, some mass get out and some masse get in at the same time. It  is very difficult to find a boundary conditions to solve this robleme.  So there is not a simple condition which can be used for simulate a simple outlet. A lot of people still research.
According to the type of the flow, the solutions are to take a periodic condition or an outlet keeped away from the singularity. The last solution require a lot of node and so a lot of memory to stock the results and a lot of time to make the software give a good solution.

## Conclusion :

LES require a lot of memory because of a large3D  grid with thin meshes. Indeed the more nodes there are, the more memory we need. Moreover the non stationnarity force to save the results very often.
LES require a lot of time because the more nodes there are, the more time the software need to give a solution.

# The choice of a case

In the aim of doing LES in spite of the diferents matters we could find on our road, we have decided to simulate of viscous fluid in a cubic box which has one moving face :

This case was firstly  done in 2 dimensions. We have obtain beatiful results but there were any difference between the case with LES and thee case without this model. So wo have choosen to not show this results without any interst for LES, a model for 3 dimensional phenomena : the turbulence.

We have had  the change to find an other study of the same case. So we had choose the same parameters in the aim of comparing our results :

• Boxe size : width of a =  10-3 m
• Reynold Number : Re = 3200
• Material : water
• time step : 10-5 s

# Some of our results

Our results will be give in the median plane y = a/2 :

## Velocity vectors :

In the previous plane, the velocity is like this :

In this figure the box's moving size in on the top. We can see that the faster velocity is under the moving wall. Then it seem that there is a global rotation. In fact there are two litlle recirculation on the two bottom angles. The next graph show this :

While doing different cases, we could observe that the more the Reynold number is high, the more the recirculation are large.

## Results comparison :

Let's normalize the velocity by the moving face velocity, and the position by the box size. We can now compare our results with those of  Isabelle Calmet :

 Our results Isabelle results

There are some differences between her and us results. One reason may be that in fact the paramaters which are draw are not the same. In fact Isabelle show the time average of all her results. And we show only the velocity in a given time.

## Model comparison :

Then we would know if LES worthed the trouble to spend so much time. So we have decided to compare the LES results with two others which came from a case with a k-e model and an other without any model :

--- no model
---  k-e
°°° LES

It seems that we do not lst our time with doing LES because the results are quite different according to th model. Nevertheless we do not have experimental measures to proove which model is the best.

## Path lines :

To show the path lines we have introduce 10  particules in the left and right bottom corners of the box. These particules are  in the median plane we have seen before, and they are place like this :

And we have obtain this :

This picture in less beautiful than those we had in the 2D case, but here we can see the 3D nature of turbulence...

# Conclusion

As aconclusion we can say that we have some results because our case was not so difficult compare to those nature can provide. In spite of this, Fluent offers LES but any tools to interpret the results. Particulary there is no tools to take the average of the results neither to calculate 2 order moments or more .

Moreover we have tried to simulated the Kelvin Helmoltz instability, a more complicated case, but we do not have any succes ...

# Kelvin-Helmoltz Instability

The Kelvin-Helmoltz instability:

Two fluids separated by an plane interface flow with different velocities, the interface is unstable and waves are created.

For example : clouds, jet...

The stabilisant mecanism can be interpreted like a "Bernoulli effect". The fluid accelerates on the ridges, so there is a pressure diminution. The phenomenon is amplified...

Gravity (for the long wavelength) and interfacial tension (for the short wavelength) are stabilisant forces because they are opposed to the amplification of instability.

The case chosen : air-water flow in a rectangular tube.

The mesh of the geometry:

This is a structured mesh, raffined on the center.

Results of the simulation:

Here is the initial configuration of the flow. The air on the top, the water in blue.

We used the Patch initialisation with Multiphase flow of Fluent (NB. The previous simulations were made with a k-epsilon model).

We didn't succeed in this simulation. We took several velocities, boundary conditions, initialisations...

The results, when the calculation is converged, is a stable flow!

To conclude on this appendix:

We didn't have enough time to improve the conditions of the simulation.

Initialisation has to be adapted to the study of instability...

Maybe the size of the geometry creates problems : influence of the walls for example...

The boundary conditions like periodic conditions are difficult to use because of the geometry adopted. It needs to be improved...