Time harmonic acoustic scattering in presence of a shear flow and a Myers impedance condition

2011
Publication type:
International conference with proceedings
Workshop:
17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)
Publisher:
American Institute of Aeronautics and Astronautics
Abstract:
Noise reduction of aircraft engines can be achieved by a well-suited internal coating of the nacelle, which is generally modelized by the Myers impedance condition. Therefore there is a need of a numerical method for acoustics in presence of a complex °ow and treated boundaries. We consider the time harmonic acoustic radiation in a con¯ned °ow in presence of treated boundaries. The case of a potential °ow with Myers condition leads to a scalar formulation which is tractable by a standard ¯nite element method.1{3 On the other hand, Galbrun's equation4 seems to be well-suited for handling non potential °ows.5, 6 For a uniform °ow we present a scalar problem in presence of PMLs (Perfectly Matched Layers). Well-posedness is proved which ensures the convergence of the ¯nite element discretization. To extend to a shear °ow, the vectorial Galbrun's equation is used and we show that Myers condition is natural and easy to incorporate in Galbrun's framework. We explain why the proof of the well-posedness is not so easy than in the scalar case and has not been achieved, even for a uniform °ow. Finally the di±culty is solved by enriching the Myers condition.
BibTeX:
@inproceedings{Bon-Mer-Mil-2011,
    author={Anne-Sophie Bonnet-BenDhia and Jean-François Mercier and 
           Florence Millot },
    title={Time harmonic acoustic scattering in presence of a shear flow 
           and a Myers impedance condition },
    organization={17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA 
           Aeroacoustics Conference) },
    year={2011 },
    publisher={American Institute of Aeronautics and Astronautics },
}