Inverse Poroelastic Characterization of Open-Cell Porous Materials Using an Impedance Tube

摘要

A poroelastic characterization of open-cell porous materials using an impedance tube is proposed in this paper. Commonly, porous materials are modeled using Biot’s theory. However, this theory requires several parameters which can be difficult to obtain by different methods (direct, indirect or inverse measurements). The proposed method retrieves all the Biot’s parameters with one absorption measurement in an impedance tube for isotropic poroelastic materials following the Johnson-Champoux-Allard’s model (for the fluid phase). The sample is a cylinder bonded to the rigid termination of the tube with a diameter smaller than the tube’s one. In that case, a lateral air gap is voluntary induced to prevent lateral clamping. Using this setup, the absorption curve exhibits a characteristic elastic resonance (quarter wavelength resonance) and the repeatability is ensured by controlling boundary and mounting conditions. The inversion algorithm contains a global optimization process using an axisymmetric finite element code implemented in the Foam-X characterization software. To apply the inversion, the user must provide tube diameter, together with sample diameter, thickness, density, and absorption curve. Also, when available, some other parameters can be provided, such as open porosity, airflow resistivity, tortuosity, or Poisson’s ratio. Providing these additional parameters improves the algorithm convergence. The algorithm is tested on different porous materials and compared to direct measurements. For some materials, the main experimental challenge is to make sure to excite the elastic resonance during impedance tube measurements. Once the resonance is excited, the proposed inversion algorithm finds Biot’s parameters that are generally comparable with direct measurements. The validity and main limitations of the method are finally discussed.