The fan of an aeronautic engine may experience aeroelastic instabilities called flutter. This phenomenon is the source of large vibrations which can lead to fatigue and even fracture. Moreover, this instability can be triggered by acoustics. By vibrating, the fan emits acoustic waves that propagate within the air intake under specific conditions. These waves are reflected at the air intake lips and they return to the fan. By modifying the instantaneous pressure acting on the fan, the waves change the aerodynamic damping which may lead to an aeroelastic instability. In the present study, this phenomenon has been studied numerically on a simplified configuration. It consists of a 6 blades fan placed in an annular duct. The link between structural modes and acoustic modes has been highlighted. Indeed, each structural mode can lead to several acoustic modes, but all acoustic waves can not propagate in the air intake. In order to propagate, their frequency must be higher than their cut-on frequency, which limits the number of harmonics. The evolution of the aerodynamic damping with the air intake length has then been investigated. It has been observed that the aerodynamic damping is depending on the phase of the returning acoustic wave. However, this phenomenon is also related to the acoustic properties of the inlet boundary condition. Therefore, a specific boundary condition capable of controlling the reflection of an acoustic wave at inlet has been developed. This boundary condition is based on the 2D method of characteristics formulated by Giles. Such a condition allows reducing the size of the fluid domain in CFD simulations by modelling the reflection instead of calculating it numerically by considering a large fluid domain surrounding the engine inlet. The implementation of the condition is detailed, and applications showing its effectiveness are presented and discussed.