## I -

Theoretical validation

II -Comparison with experimentation

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:

VThis 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._{x}: profile obtained behind the circular cylinder in steady flow : "velocity.prof"

V_{y}: a sinusoidal oscillation whose intensity is parabolic : 0.001*(1-25y²)*sin(2*Pi*f*t)

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.

Click here to see the animation (.gif - 1.2Mo).

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} |

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*

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 |