Due to the manufacturing process, some fibrous materials like glasswool may be transversely isotropic (TI): fibers are mostly parallel to a plane of isotropy within which material properties are identical in all directions whereas properties are different along the transverse direction. The behavior of TI fibrous material is well described by the TI Biot's model, but it requires one to measure several mechanical parameters and to solve the TI Biot's equations. This paper presents an equivalent fluid model that can be suitable for TI materials under certain assumptions. It takes the form of a classical wave equation for the pressure involving an effective density tensor combining both limp and rigid frame behaviors of the material. This scalar wave equation is easily amenable to analytical and numerical treatments with a finite element method. Numerical results, based on the proposed model, are compared with experimental results obtained for two configurations with a fibrous material. The first concerns the absorption of an incident plane wave impinging on a fibrous slab and the second corresponds to the transmission loss of a splitter-type silencer in a duct. Both configurations highlight the effect of the sample orientation and give an illustration of the unusual TI behavior for fluids.

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.

To estimate the efficiency of parallel baffle-type silencers in rectangular ducts, a two-dimensional multi-layer model is presented for predicting their transmission loss. The approach takes into account an arbitrary number of bulk reacting baffles of finite length bounded at both ends by a metallic fairing. Each layer is described by a mean pressure, which allows computing a piecewise constant modal basis for the mean pressure over the cross section. The continuity between the incoming and outgoing waves is performed by axial mode matching at the inlet and outlet cross-sections of the baffle silencer. It is shown that the model is easy to implement and suitable for optimization purposes based on design parameters such as the height of each baffle, their relative positions in the duct, and material properties. Relatively complex configurations can be simulated with relatively modest computational effort. An experimental campaign was carried out on a reduced scale test bench for standard configurations. The numerical results are in good agreement with the measurements. Noise reduction performances are analyzed in terms of reflected and dissipated sound powers. Finally, more complex geometric configurations are simulated in order to examine the influence of the relative transverse and axial positions of each baffle as well as the effect of a resistive screen between the baffles and the airways.