Influence of flow on trapped modes in ducts
Résumé
It is known that an obstacle placed in an acoustic waveguide can result in a trapped mode
around this obstacle. The presence of this trapped mode can be observed on the amplitudes
of the transmission and reflection coefficients through a Fano-like resonance. The frequency
and the quality factor of this resonance depend both on the size of the obstacle and on its
distance to the axis of the guide.
Here, a rigid cylinder is placed inside an acoustic waveguide and we study the influence of an
imposed flow around the cylinder. The flow is exponentially decaying away from the cylinder,
such that the fluid is at rest far from it. We show that the trapped mode still exists in the
presence of flow, and that it can be excited even when the cylinder is placed on the axis of the
guide. Moreover, the problem becomes asymmetric in the presence of flow. Indeed, even
though the amplitudes of the scattering coefficients remain the same regarding the direction
of the incident wave, the phase of the reflection coefficient vary whereas the incident wave
comes from the left or from the right. This phase difference appears to be happening only
around the frequency of the trapped mode. This problem is studied both in a full finite
elements model and in a simplified multi-modal one.