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

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.