Contents  Combustion  AVBP simulation  Results 
Combustion chemical equation:
The NavierStokes equations can be used in the case of the combustion. Their treatment gives the following results:
and
The perfect gaze law is written : , so that we can deduce:
The equations will be of use to validate the AVBP simulation results before injecting them in a 2D geometry.
To observe the flame front, it had to be thick enough to cover around 6 to 8 cells. However the real thickness of the front is smaller than the size of only one cell. That's why, we use a parameter that is called Fthick located in the input_chem.dat file.
AVBP solves the the following transformed equation:
where according to the Arrhenius law. A_{1} and D_{1} are new parameters calculated from:
The diffusion is increased so that the front thickness can be adapted to the cell size.
We roughly know S_{L},the flame velocity. So, in order to have steady flame, we chose a fluid entrance velocity equal and opposed to S_{L}.
Pressure 
The pressure is constant as it was predicted by the theoritical equation. 

Temperature 
After calculation, we found that the values given by AVBP respect the following equations: 

Velocity 

Density 

Air mass rate 
We must notice that dplot, AVBP drawing software, does not calculate the mass rates but the product of the density by the mass rates. So to obtain the real mass rates, you have to divide the given values by the density. After calculation, we found that the values given by AVBP respect the following equations: and . 

Fuel mass rate 
Click on the pictures to enlarge them
All the results are in the perfect line of the theoritical study. So the AVBP simulation of a 1D flame give good values we can use in a 2D problem that is the flame catching on a bluff body.