Section: New Results

Aeroacoustics

Time-harmonic acoustic scattering in a rotationnal flow

Participants : Antoine Bensalah, Patrick Joly, Jean-François Mercier.

This activity is done in the framework of the PhD of Antoine Bensalah, in partnership with EADS. We study the time-harmonic acoustic radiation in a fluid in a general flow which is not curl free, but has restricted vortical areas. The objective is to take into account the complicated coupling between acoustics and hydrodynamics. The Galbrun approach developed previously in 2D is too expensive in terms of degrees of freedom for 3D simulations. As an alternative, we propose to consider instead the Goldstein equations, which are vectorial only in the vortical areas and remain scalar elsewhere. Extending the proof done for the Galbrun equation, it is possible to prove that the Goldstein equations are well-posed in a domain $\Omega$ if the flow is $\Omega$-filling (each point of $\Omega$ is reached by a streamline coming from the inflow boundary in a finite time). Then we focused on the case of a rotating flow in an annular geometry, which is not $\Omega$-filling and we proved the well-posedness of the problem .