During our project, we have worked on fluid-structure interactions on two cylinders in tandem with numerical simulation. Structures in contact with fluid flow, whether natural or man-made, are subject to flow-induced forces and flow-induced vibration. Under certain conditions, the vibration may be self-excited. These instabilities cause damage in a short or the long term in nuclear power plants for example. It is why the BARESAFE project was created (it regroups EDF, AREVA and CEA) to understand these instabilities. Firms have to replace cylinders every six months due to the instabilities ; it is clearly important to understand and fix this problem. Therefore our main interest is twofold because these cylinders can be found in offshore installations or cables.

Our aim is to build a reduced model and a post-process with a big data based on an experience performed in a wind tunnel to decrease calculation times. Indeed, if calculation times are reduced, we can test more complex configurations and reach as quickly a resolution as possible.

To study the problem, we will consider two cylinders in tandem which is the simplest form. The configuration is the same as what is been studied by NASA in their experiments so we can easily compare our results with the experimental results. The first configuration was used to study noise of a aircraft because it modeled the supports of the aircrafts’ landing gear. We will use the same Reynolds 166 000 as a first step.

*Figure 1.1 – Cylinders in tandem*

Consider that we have a characteristic length D with a natural frequency fs in a flow which velocity is U. Dimensional analysis enables to show a dimensionless number u* which is the reduced velocity.

This parameter enables us to describe the fluid-structure interaction phenomena, it compares the characteristic time ofthe structure and the characteristic time of advection. By plotting amplitude of oscillation as function of the reduced velocity, we can consider three zones which correspond to different mechanisms :

*Figure 1.2 – Amplitude of oscillation as function of reduced velocity*

— Zone 1 corresponds to Turbulence Induced Vibrations (TIV). The amplitude is limited and increases steadily with the reduced velocity.

— Zone 2 is the zone of Vortex Induced Vibrations (VIV). It looks like a resonance where natural modes are excited by the wake. Amplitude increases but the system remains stable.

— Zone 3 corresponds to Movement Induced Vibrations (MIV), the system may be unstable and cause the break of the structure. 2