title: A homogenization method used to predict the performance of silencers containing parallel splitters.
abstract: An analytical model based on a homogenization process is used to predict and understand the behavior of finite length splitter/baffle-type silencers inserted axially into a rigid rectangular duct. Such silencers consist of a succession of parallel baffles made of porous material and airways inserted axially into a rigid duct. The pore network of the porous material in the baffle and the larger pores due to the airway can be considered as a double porosity (DP) medium with well-separated pore sizes. This scale separation leads by homogenization to the DP model, widely used in the porous material community. This alternative approach based on a homogenization process sheds physical insight into the attenuation mechanisms taking place in the silencer. Numerical comparisons with a reference method are used to show that the theory provides good results as long as the pressure wave in the silencer airways propagates as a plane wave parallel to the duct axis. The explicit expression of the axial wavenumber in the DP medium is used to derive an explicit expression for the optimal resistivity value of the porous material, ensuring the best dissipation for a given silencer geometry.
authors.affiliation: Laboratoire d'Ingénierie des Systemes Mécaniques et des Matériaux (LISMMA-QUARTZ EA2336), SUPMECA, 3 Rue Fernand Hainaut, 93407 Saint-Ouen Cedex, France.
authors.forename: Benoit
authors.initials: B
authors.lastname: Nennig
authors.affiliation: Laboratoire d'Ingénierie des Systemes Mécaniques et des Matériaux (LISMMA-QUARTZ EA2336), SUPMECA, 3 Rue Fernand Hainaut, 93407 Saint-Ouen Cedex, France.
authors.forename: Remy
authors.initials: R
authors.lastname: Binois
authors.affiliation: Sorbonne Universités, Université de Technologie de Compiégne, Laboratoire Roberval, UMR CNRS 7337, CS 60319, 60203 Compiégne Cedex, France.
authors.forename: Emmanuel
authors.initials: E
authors.lastname: Perrey-Debain
authors.affiliation: Sorbonne Universités, Université de Technologie de Compiégne, Laboratoire Roberval, UMR CNRS 7337, CS 60319, 60203 Compiégne Cedex, France.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Dauchez