Introduction

This configuration of flow and combustion is very difficult to observe. Indeed, the flame must catch on the bluff body. This phenomenon is due to the recirculation that happened when an object is in a flow. This recirculation is well know as the « Von Karmann Street ».

This flow configuration is hard to obtain even without combustion, so it is useless to try to obtain it with combustion. Moreover, the combustion uses the hot produced gases to catch on the bluff body.

This remarks give us the way we have to follow. Firstly, we tried to simulate the flow without the chemical reaction, in order to obtain the recirculation which are the huge point of the phenomenon. Then, we used the results to initialise the combution in the flow.

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Calculation without chemical reaction

There is in AVBP the possibility to make the simulation without combustion. This possibility exist in the file : input_chem.dat. The user can choose a pure mixing or a Arrhenius reaction rate. For this first part, we have use a pure mixing. So the simulation will correspond to the flow of the mixture at the ambiant temperature.

We have initialise the flow with a constant velocity in all the domain. With a scheme of Lax-Wendorf, we obtain after 20 000 iterations, the hooped result. That is to say that the flow is unsteady and that we can see whirlwind behind the bluff body.

Click on the picture to enlarge

This image represente the absolute velocity of the flow. The velocity is the only interesting value of the flow because there is no chemical reaction.

This image shows that there is a recirculation zone just behind the bluff body. The mass rate in Fuel is naturally constant.

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Initialisation of the combustion

In the real case, the flame is catching on the bluff body. The combustion products hot gases which stay behind the Bluff because of the recirculation. So the fresh gases are getting warmer and the combustion can continue.

The problem is that this phenomenon is self maintained. So the initialisation is very difficult. To solve this problem the idee is to use the simulation without reaction and the results on the laminar one dimensionnal flame.

We have seen that the caracteristic values of the flow respected relations before and after the flame front. We will use these relations in order to superpose to the pure mixing flow a combustion. We must bear in mind that, we couldn't find the solution, we just have to create an initial condition as close as possible of a physical solution.

We have use a fortran script for the treatment of the data. This script reads the caracteristic values of the flow :

then it calculates the new values, and finally it writes a new file with the new values for the initialisation of the combustion.

The initialisation will be a flame front at the X axis : x=0,2 . Now we just have to determine how fix the new values. For that, we will use the values that no depend on the kinetic properties of the flow. These values are the temperature and the mass rate. They only depend on the chemical reaction and on the thermodynamic.

1. Determination of the temperature

Before the flame front the temperature is the same as the fresh gases. Far away of the flame front the temperature of the burned gases is determined by the the heat of the reaction. As we have made the hypothesis that Cp is constant, the temperature will be :

In order that the temperature stays a continuous function, we have used a joining up with a hyperbolic tangent.

1. Determination of the density, the velocity and the total energy

With the one dimensionnal flame, we have remarked that the there were some values which are the same before and after the flame. We have used the theoretical study to fixed these value.

For example the pressure is constant. It allows us to fix the density. Indeed, we have the pressure and the temperature, the gas follow the law of the perfect gases so the density is :

The tangent velocity is constant, so :

And finally, the value is constant. We are able to obtain the value after the flame.

To conclude we can have all the kinetic value before and after the flame. So the energy can be calculated before and after the front fame.

2. Determination of the mass rates

The mass rate are fixed by the reaction and by and composition of the mix. We can fixed them in the same way as the temperature.

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Calculation with chemical reaction

With the initialisation we have made, we hope that the front flame will spread and will be catch on the bluff body. As in the case of the one dimensionnal flame, we have adjusted the coefficient Fthick to the mesh.

After a thousand of iterations, we get the following result for the temperature.

Click on the picture to enlarge

As expected, the fame front spread. But after 40 000 iterations, we have not had a flame catched on the bluff. The recirculation was too considerable. The « Von Karman street » prevent the fame to catch on the bluff.

To conclude this part, we can say that the initialisation was not the good one to obtain the hoped result. The next part will show the good result in a bluff body.

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Classical result in a bluff body

In this case the solution has been initialised by the solution of a one dimensionnal flame. With this initialisation the fame catch on the bluff body and we can show the classical result of the bluff body.

Click on the picture to see the animation

On this animation we can see that the flame is catch on the Bluff Body. At the beginning of the simulation the flow and the combustion are symetric. In fact the recirculation behind the bluff body is favoured. That may be why in our first simulation the flame was not catch on the bluff body. Indeed the « Von Karman street » is too violent to allow the flame.

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