The objective
of this project is to study a combustion problem and to get familiar with
reacting flows. AVBP, a code of CERFACS is used and run on CICT workstations.
Combustion introduces delicate numerical complexities, and the following
steps will be followed:

1 : Introduction to the AVBP flow solver, execution
of a simple test case.

2 : One-dimensional premixed flame calculation.

3 : Simulation of a flame developing behind a bluff body.

**1)
INTRODUCTION TO AVBP: FLOW AROUND A BUMP**

AVBP is a parallel CFD code that solves the laminar and turbulent compressible Navier-Stokes equations in two and three space dimensions on unstructured, structured and hybrid grids. An Arrhenius law simple chemistry model allows to study reacting flows in the field of combustion.

Execution
of a simple test case is first performed in order to get familiar with
AVBP solver. This test case consists of the flow around a bump.

The incident
Mach number is set to M=0.85.

**MESH**

An unstructured
mesh is used. This mesh is refined near the bump to catch the shock.

**CONVERGENCE**

10000 iterations
were computed. The following graph shows the residual evolution.

**RESULTS**

We observe
a shock created by the bump: the subsonic flow (Mach number=0.85) becomes
supersonic (M>1).

**2)
ONE-DIMENSIONAL PREMIXED FLAME**

A basic 1D study of a one-dimensional premixed flame proves to be an interesting problem to deal with to get used with reacting flows. Premixed combustion corresponds to the propagation of a flame front in a mixture of fresh gases. The front moves at a speed Sl of the order of 20 to 100 cm/s and a a thickness of lf of the order of 1 mm.

Consider the case of a one step-reaction:

In this particular
case we have this following combustion chemical equation:

CH4 + 2 O2 -> CO2 + 2 H2O

A flame propagates
from left to right burning fresh gases and producing burnt gases. To have
a steady flame and then to save space a good idea is to blow it. As we
know the flame speed we can choose the appropriate velocity inlet.

Conservations equations can be written this way in this1D case:

The perfect gas law is used:

We have programmed
an initialization with these equations in the routine flam.f :

*exctracted from flam.f, the initialization routine*

As the thickness of the flame front is smaller than cells
size, it is necessary to thick it artificially. In AVBP the parameter Fthick
(input_chem.dat file) enable to adapt the thickness.

**RESULTS**

5 0 000 iterations were computed. We can check the results
by comparing theorical values and computed values.

We check that the pressure is constant and that rho*u
is almost constant.

---> Shaded contours of temperature,
total
velocity, density and pressure

**3)
SIMULATION OF A FLAME DEVELOPPING BEHIND A BLUFF BODY**

In this part, we simulate a flame developing behind a
bluff body. The aim is to catch the flame using the recirculation
created by the bluff body. Indeed hot produced gases
enable the combustion to go on.

The mass fraction Yi of each species follows a conservation equation given by:

We can deduce from the Navier-Stokes equations the
following relations :

We have programmed the initialization using the previous
equations. A front flame is set at x=0.15. We used a linear variation for
the temperature instead of tangent hyperbolic.

*exctracted from flam.f, the initialization routine*

As the thickness of the flame front is smaller than cells
size, it is necessary to thick it artificially. In AVBP the parameter Fthick
(input_chem.dat file) enable to adapt the thickness.

**MESH**

The following mesh is used. It is refined behind the bluff body to catch the recirculation area.

**RESULTS**

The flame
front moves to the left but the flame fails to catch on the bluff body.
We tried to change parameters such as the flame speed,

the flame
thickness and the pre-exponential term of the production rate without success.
The problem seems to come from the initialization.

-> click
here to see an animation

**INITIALIZATION**

**AFTER 38000 ITERATIONS**

This work
was a good introduction to CFD problems of reacting flows and showed
the difficulty to handle them.

A first difficulty
was to get used with AVBP solvers and all the different files. A good experience
of the code is required

to use it
efficiently.

Bibliography :

The
AVBP User's Manual, T. Schönfeld, CERFACS, 1999.

Link about
AVBP solver: www.cerfacs.fr/cfd/research/avbp/avbp_code.html