Development of acoustically effective foams: a new micro-macro optimization method
Résumé
Using numerical homogenization techniques at microstructure scale, one can simulate the acoustic macro-behavior of open-cell or partially closed-cell polymeric foams, typically their absorption coefficient or Transmission Loss. This link is realized through the scaling of an idealized 3D Periodic Unit Cell (PUC), which represents statistically the pores shape as regular arrays of polyhedra. Based on two non-acoustic standard measurements, namely the porosity and the static viscous permeability (airflow resistance measurement), plus a microstructure ligament length measurement, the 3D PUC is scaled including membranes interconnecting the pores in the actual foam morphology. The opening of these membranes, constituting partially closed windows or throats between pores, proves to be an essential microstructure optimization parameter for sound absorption. On this 3D PUC, Finite Element computations are carried out in order to determine the intrinsic Biot-Allard parameters of the foam (transport and elastic parameters, pure geometric ones being known), by solving asymptotically the viscous Navier-Stokes flow at low frequencies, the inertial Laplace potential flow (identical to electric conduction) at high frequencies and the thermal conduction (similar to diffusion-controlled reactions) at low frequencies. This micro-macro procedure proves to give very good correlation with complete non-acoustic and acoustic characterization measurements, like impedance tube, building a new reliable optimization scheme for foams, which will be illustrated on a PUR injected soft foam H1 (spring of insulators) and on a slab stiff PUR foam H2 (pure absorber).
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