## I - Theoretical validation

In order to study the influence of the profile on the eddies creation, we saved the outflow velocity profile obtained by the steady calculation in a file "velocity.prof".

Outflow velocity profile

In a second time, we created the same rectangular domain but without any cylinder. The components of the velocity inlet profile were:

Vx : profile obtained behind the circular cylinder in steady flow : "velocity.prof"
Vy : a sinusoidal oscillation whose intensity is parabolic : 0.001*(1-25y²)*sin(2*Pi*f*t)
This profile was chosen in order to demonstrate that the creation of the eddies is due to the profile shape during time and not due to the obstacle. That's why the profile is excited with the same frequency with which eddies are created.

Eddies effectively appear in the center of the flow. We can conclude that the profile shape is one of the factors of the eddies creation. Nevertheless, due to the parabolic intensity of the y-velocity, vorticity magnitude is created periodically even far from the center of the flow.

## II - Comparison with experimentation

A probe was placed in (0 ; 0.005) in order to measure the average velocity. The signal obtained was analysed in order to determine the frequency and the amplitude. The results are summarised in the square below :

 Re T (s) f (mHz) A (m) 60 12.0 83.33 0.68 10-4 70 9.8 102.04 1.24 10-4 80 8.4 119.05 1.91 10-4 90 6.8 147.06 2.77 10-4 100 6.4 156.25 7.29 10-4

### Frequency validation

Thanks to the experimental graph, we determine the Strouhal number corresponding to the Reynolds number. Thus, we calculate n with the equation below :

 Re S n (mHz) f (mHz) differential (%) 60 0.14 84 83.33 0.8 70 0.15 105 102.04 2.8 80 0.155 124 119.05 4.0 90 0.16 144 147.06 2.1 100 0.17 170 156.25 8.1

The approximations due to the lecture of the graph given by Fluent and to the lecture of the graph S = f (Re) can explain the differential which values are lower than 10%. The frequency calculated numerically can be validated by the experimentation results.

Experimental and numerical shedding frequencies

### Critical Reynolds number determination

 Re A (m) 60 0.67 10-4 70 1.24 10-4 80 1.91 10-4 90 2.77 10-4 100 7.29 10-4

Velocity amplitude measured by the probe

In order to determine the critical Reynolds number, the graph A=f(Re) was drawn. The approximation of a linear variation seems to be good and the critical Reynolds number was found near Re=50. Experimentally, the value Re=40 is commonly accepted. The difference can be explained by the meshing or the model. Furthermore, the variation is probably non-linear so, with our graph, the value Re=40 can be found.

 ESPEYRAC Lionel PASCAUD Stéphane Presentation Physics Knowledge Numerical Simulation Results Validation Conclusion