This study looks at numerical modeling of laminar flow around a circular cylinder.

IV.1 Oarweed  flow

In this case , viscosity model is laminar  with the steady formulation.
For Re inferior to 1, our results are easily similars to the reality, as you can see with the picture below :

Streamlines  of the flow , Re = 0.1

IV.2 Recirculation flow

In the boundary layer around the circular cylinder, the  static pressure is a maximum at the stagnation point and gradually decreases along the front half of the cylinder.
The flow stays attached in this favorable pressure region as expected.
However, the pressure starts to increase in the rear half of the cylinder and the particle now experiences an adverse pressure gradient.

Consequently, the flow separates from the surface and creating a highly turbulent region behind the cylinder called the wake.
The pressure inside the wake region remains low as the flow separates and a net pressure force (pressure drag) is produced.

Dynamic Pressure  around the cylinder, Re = 25

Recirculation flow behind the cylinder, Re = 25

IV.3 Von Karman vortex Street

Vortex shedding :

The pictures below show how vortices appear with Re number equal to 200 (i.e. u = 2.4 m/s)
Time step is 0.005 s .

                                                                                                    t = 0.5 s                                                                                                                t = 0.6 s

                                                                                                     t = 0.7 s                                                                                                              t = 0.75 s

                                                                                                        t = 0.8 s                                                                                                            t = 0.85 s

                                                                                                        t = 0.90 s                                                                                                         t = 0.95 s

As a fluid particle flows toward the leading edge of a cylinder, the pressure in the fluid particle rises from the free stream pressure to the stagnation pressure.

The high fluid static pressure near the leading edge impels flow about the cylinder as boundary layers develop about both sides.
On the other hand, the high pressure is not sufficient to force the flow about the back of the cylinder at high Reynolds numbers.
The boundary layers separate from each side of the cylinder surface and form two shear layers that trail aft in the flow and bound the wake.

Dynamic Pressure, Re  = 200

Velocity  vectors, Re = 200

Streamlines, Re = 200

Since the innermost portion of the shear layers, which is in contact with the cylinder, moves much more slowly than the outermost portion of the shear layers, which is in contact with the free flow, the shear layers roll into the near wake, where they fold on each other and coalesce into discrete swirling vortices.
Instability emerges as the shear layer vortices shed from both the top and bottom surfaces interact with one another.
They shed alternatively from the cylinder and generates a regular vortex pattern (the Karman vortex street) in the wake .

Dynamic Pressure, Re = 200

Velocity  vectors, Re = 200


Streamlines, Re = 200

vortices periodicities in time step, Re = 200

A  vortex periodicity, Re = 200

The vortex shedding occurs at a discrete frequency and is a function of the Reynolds number.
The dimensionless frequency of the vortex shedding, the shedding Strouhal number, St = f D/V, (f=frequency; D=characteristic diameter; V = characteristic velocity) is constant, approximately equal to 0.20 .
In theory , we must find a frequency : f = (0.2*2.4)/0.1 =  4.8 Hz   which corresponds to a  period : Tth = 1/4.8 = 0.21 s

In our case, time step is 0.01 s . And we can see that a period is equal to 22 time steps. So the numerical results give us a period T = 0.22 s  .

We rationally can think that ours results are similar to the reality.

IV.4 High Reynolds number flow

In this part, k-epsilon model was used .
As we did not found realistics results, we decided not to display  them .