#### Introduction

We are going to study fuel injection in combustion chamber with AVBP Software developped by the CERFACS. This code can solve Euler equation, Navier-Stokes equations or some differents models of turbulence (LES for example). Our study concerns the mixing of fuel and air in the injector before entry in the combustion room. The aim is to obtain a homogeneous mixing in the exit of the injector in order to obtain an optimal combustion.
The injector is composed of a main room where a flow air circulates at 10 m/s and, orthogonaly, of two fuel injectors at a different velocity. Precisely, in this study we will be test three different velocities for fuel : v=5 m/s, v=20 m/s and v=50 m/s.
We will try to solve this problem with the unsteady Euler equation. Indeed, we supposed that diffusion effects are little face to the air and fuel advection effects i.e. air and fuel injection velocity are important.

Initial condition : (see picture)

• No velocity inside injector.
• Fuel mass fraction equal to 1 inside the little fuel injector
• No fuel mass fraction inside the pricipal mixing room.
Boundary conditions :
• Air velocity inlet (on the left) : u=10 m/s
• Fuel velocity inlet (on the top and the bottom)
• Pressure outlet (on the right)  Initial condition on Fuel mass fraction
(No fuel in blue, fuel in pink)

Meshing of the injector

Three grids are proposed :

• Structured
• Unstructured
• Unstructured coarse
We used the unstructured grid because it seems to be the most appropriate. Indeed, this one is refined near the exit of fuel injectors in order to show some caracteristic phenomenons as vortex, recirculation area, etc...
For this reasons, the unstructured coarse grid and the structured grid are no appropriate i.e. cells are so coarse.
We can see the grid in the following pictures : View of the grid inside the injector Zoom of the previous picture. Grid near the down injector