The simulation with StarCD

The mesh

The first thing we have to do is to create a mesh that fits our need. This mesh will be done with the mesher of starCD for the StarCD results, and with Gambit for the Fluent simulation.
In order not to have too long calculation delays, we have chosen to take 50 cells in height and 50 cells width. This will provide use poor results, but the aim is more to understand how it works and to get first results.
Here is a view of the mesh we have obtained with StarCD.

- The mesh -

As you can see, we have merely erased the cells that stand for the wall, since it is a lot easier than to define them as "wall".
So, the walls in the domain do appears like holes.
Now, we can show the boundaries we have set. This is a difficult step with StarCD and we have managed to get the correct boundaries after a large number of tries.
Here they are

- boundary conditions -

You can see that the entire upper surface is defined as an inlet (in red), whereas the outlet (green colored) is defined only on a small area.
Once again, we precise that all views are in 3D, but the study is a 2D one. The third dimension is only added by StarCD, which requires a volume.
Another thing interesting point is that we have finally set very simple boundaries, whereas we began with complicated ones. As a matter of fact, StarCD is very sensitive to the definition of the mesh, and it is then very easy to make an error. So, simplicity is the key word!

Typically, the velocity we put at the inlet is equal to 1m/s.
The phase that will transport the particles is air, and the particles properties will be defined afterwards.
We also use a k\Epsilon model for the turbulence. There would be a lot of things to say about this particular point, but this is not the question here, so we just click to enable this model and then we launch the calculations.

Velocity profiles

In this section, we will give the velocity profiles. StarCD could also provide us other profile for different other quantities, but given that the aim of the study is not to draw profiles, but rather to track particles, we will only plot the velocity profiles. We will use the vectors plotting and the contour filled profiles.
Here are the results.

The contours

- the velocity contours -

This profiles are quite satisfying. We can observe the recirculating zone where we were waiting for them. The flow is well materialized and follows the shape of our filter.
Furthermore, the option "smooth" enables to shade the drawing thus giving this nice pictures!
Concerning the values, considering the conservation of  the flow, it seems to be correct. The accelerating fluid in the smallest section is due to this conservation.

Now, we can draw the velocity vectors. We draw a general overview and we zoom in the interesting zones.

- general overview -

- what happens near the second and the third wall -

- velocity vectors at the outlet of the domain -

With those picture, we can see the recirculating phenomenon very well. This is mainly in the dark zones (the velocity is very low), that the particles will probably aggregate.
The following section is the interesting one: we will put particles in our flow and we will try to follow them.

Particle tracking

Once we have launched the calculation, StarCD permits us to make particle tracking quite easily (once you have understand all the subtleties of StarCD). The particle tracking initialization is very easy. First of all, we choose the place where we will inject the particles:

- the initial positions of the particles -

Now, we are able to choose the different characteristics of our particles, and to let them go in the flow!
We will make different tries for different diameters and different densities, as well as different injecting velocities.

D=10-6m, rho=2000kg/m3

This case is the one that seems the more appropriate to what happens in most filters.
We set the initial parameters, and then, we can give you the following pictures.

- no initial velocity and a small velocity -

Especially dedicated to P..., here is a small explanation for a very strange phenomenon.
Let us explain that StarCD does not take into account the interactions with the wall. Thus, rather than drawing an absurdity, the particles are erased when impacting the wall.

We set two different initial velocities for the particles.
On the left, the particles are injected with no initial velocity, whereas ,on the right, the velocity is taken equal to 10m/s for both the U and the V components.
As you can see,  the difference is very slight at the beginning. But when looking the first wall, you can see that the trajectories are closer from the second obstacle.
Now, let us see if a bigger particle will be more sensitive to a change in the initial velocity.

D=10-4m, rho=2000m/s

With this diameter, we will see what happens.

- the particles are a very little bit too heavy! -

Obviously, the particles are now heavy enough to be self piloted. I mean that they are no more transported by the flow, they follow their own way. Their inertia is strong enough.
If the first picture seems to be useless, on the other hand, the second one shows that, this time, the initial velocity conditions have a real effect on the particles. They behave as if the air flow merely did not exist!
The next try is to find a diameter, where the particles will be affected by the flow, even if the initial velocity as a visible effect.

D=10-5m, rho=2000m/s

Just a picture to show how the particles are injected in an incurved way, and then taken back in the flow of air.

- effect of initial velocity -

You can see that the initial tendency of the particles is to follow the original motion that we gave them, and then, given that they are not heavy enough, the air flow take the advantage, and they end up following the air motion.

D=0m, rho=0m/s

If we set all characteristics of the particles to 0, what we get is the stream lines. Given that it is interesting, here they are.

- stream lines -