III.NUMERICAL METHOD

III.1 Meshing

The meshing of the domain was realize with GAMBIT mesher as the picture below.

Domain Extent :
x-coordinate (m) : min = -0.3 , max = 1.7
y-coordinate (m) : min = -0.5 , max = 0.5

Cylinder :
The diameter of the cylinder is 0.1 m.
center :   x-coordinate (m) = 0
y-coordinate (m) = 0

Grid Size :
Number of cells : 8706
Number of faces : 13150
Number of nodes : 4444

# The solver software with which we studied the phenomenon is Fluent 5.0
A big problem was choice of boundaries conditions. Indeed, we made attempts with superior and inferior sides as walls, then as symmetry, and to finish we had better results with outflow.
So, we fixed the following boundaries conditions  :

• superior side is an outflow
• inferior side is an outflow
• left side is an inlet flow
• right side is an outflow
• the cylinder is a wall
The next stage was to use  Fluent 5.0 .

# III.2 Methodology

To begin we etablished the inflow as a laminar flow .
About fluid, we decided to choose engine oil  because dynamic viscosity engine oil allows us to use  a biggest velocity than with water for example.
So a particle of fluid is able to cross the domain in a more convenient time, so we obtain the results after a more convenient time.

The time-dependent two-dimensional continuity and momentum equations ,( unsteady Navier-Stokes equations for an incompressible flow ) are solved on the grid.
Pressure and momentum discretizations use second-order accurate.
For time integration, a two-stage second-order accurate scheme is used.

To observe Karman vortex Street, the inflow velocity is 2.4 m/s. The  Reynolds number is 200.
Then, after several attempts with different time steps, a final time step equal to 0.01 seconds was choosen with 30 inner iterations per time step.

Finally, we can say that the magnitude of the time step, number of inner iterations per time step, boundary conditions, and grid size are variables upon which  we had to operate.

A lot of results have been obtained and only a little part are presented in the next chapter.