Theoretical and numerical investigation of optimal impedance in lined ducts with flow

Javier Rodríguez Sánchez , Estelle Piot (1) , Grégoire Casalis

1 ONERA - The French Aerospace Lab [Toulouse]

Sound attenuation in ducts with flow is an important issue in aeronautics; it might be realized by covering the inner walls with a liner characterized by its acoustic impedance. Usually, the best sound attenuation is achieved when the liner yields the highest insertion loss. In the present study, liners are considered infinite in the direction of sound propagation. Thus the interest lies within the liner with the highest sound absorption. Analytic formulas for the optimal impedance are found in the literature without flow and with a uniform flow. In this work, a linear stability analysis of the Euler equations is carried out, to find the spatial modes for a rectangular rigid duct but with the lower wall lined. Cases without flow, with uniform flow and with a sheared flow are considered. The code has been validated against analytical solutions. Without flow, for an impedance very close to the "optimal" one, a saddle point is found in the spectrum, called the double point in literature. The link between the optimal impedance and the behaviour of modes around the double point is investigated through the group velocities, in both cases without and with flow.

Mots clés: Liner; Optimal Impedance; Duct Acoustics; Stability Analysis

Domaines: Acoustique [physics.class-ph]

Javier Rodríguez Sánchez, Estelle Piot, Grégoire Casalis. Theoretical and numerical investigation of optimal impedance in lined ducts with flow. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00810734⟩