V. Fuel Velocity = 50 m/s

The four cases which follow are with a fuel velocity equal to 50 m/s, but the relaxation coefficients for boundaries conditions are not the same. We will see that they are verY important parameters.

V.1. Case 1

Relaxation Coefficient :
- Superior fuel Inlet     : 1.d5
- Inferior fuel Inlet       : 1.d5
- Air Inlet                     : 1.d5

Velocity Vectors after 45000 iterations (t = 19.8m/s)

Numerical results are quite chaotics and the simulation broke down at t= 20s .
To improve results we decided to play upon relaxation coefficients of boundaries conditions

V.2. Case 2

Relaxation Coefficient :
- Superior fuel Inlet    : 3.d3
- Inferior fuel Inlet      : 3.d3
- Air Inlet                    : 1.d5

We decreased relaxation coefficients of the fuel boundaries conditions , that is to say we made the boundaries conditions become less strict.  Near the top wall, fuel mass fraction is nearly maximum and the two fluids do not really mix. On the side of the bottom wall,  we see fuel pockets  and all the green part shows that air and fuel from inferior inlet mix correctly.

We can always observe in the bottom left the numerical perturbation.

Fuel Mass Fraction after 50000 iterations (t = 22ms)

Velocity Vectors after 50000 iterations (t = 22 m/s)

V.3. Case 3

Relaxation Coefficient :
- Superior fuel Inlet    : 3.d3
- Inferior fuel Inlet      : 3.d3
- Air Inlet                    : 1.d4

Then we decided to decrease relaxation coefficient of Air inlet to obtain others results and to understand its effects on the flow and on the mixture.
It is not difficult to notice the difference with the previous case about rate mixture for superior fuel inlet. Indeed, the superior vortex is now largest and the mixture is better.

Fuel Mass Fraction after 50000 iterations (t = 22ms)

Velocity Vectors after 50000 iterations (t = 22 m/s)

V.4. Case 4

Relaxation Coefficient :
- Superior fuel Inlet    : 1.d4
- Inferior fuel Inlet      : 1.d4
- Air Inlet                    : 5.d5

To finish, we wanted to obtain results with high relaxation coefficients. The purpose was to give boundaries conditions more strict caracteristics.  The symmetry of the flow comes back and the mixture has never been as good as now.
At the right center, big fuel pockets appear where the two mixture layers join. (see movie)
These numerical results are the best as we obtained and are very different of all the previous one. This shows that these relaxation coefficients are very crucial. A second conclusion is that because of these coefficients which do not respect the real boundaries conditions, numerical perturbation is induced.

Fuel Mass Fraction after 50000 iterations (t = 22ms)

Velocity Vectors after 50000 iterations (t = 22 m/s)

The following picture is the mean fuel mass fraction at outlet.
0 location is at the bottom wall ans 1 is at the top wall. This mean field in not symmetric (first iteration taken in count).

Mean Fuel mass fraction at outlet
(mean field between t = o ms and t = 35.2 ms)

At the outlet, a perfect mean fuel mass fraction should be equal to 0.5. But it is not necessary to have such a value to obtain a correct mixture.  Moreover, inferior fuel inlet seems to be shortest than the superior one. It is certainly du to the perturbation at the bottom left which growes and which may induces a bigger momentum quantity. And this force is able to break the inferior jet sooner.
Let's go and see movie !