Microstructure, transport, and acoustic properties of open-cell foam samples: Experiments and three-dimensional numerical simulations

Abstract

This article explores the applicability of numerical homogenization techniques for analyzing transport properties in real foam samples mostly open-cell, to understand long-wavelength acoustics of rigid-frame air-saturated porous media, on the basis of microstructural parameters. Experimental characterization of porosity and permeability of real foam samples are used to provide the scaling of a polyhedral unit-cell. The Stokes, Laplace, and diffusioncontrolled reaction equations are numerically solved in such media by a finite element method in three-dimensions; an estimation of the materials' transport parameters is derived from these solution fields. The frequency-dependent visco-inertial and thermal response functions governing the long-wavelength acoustic wave propagation in rigid-frame porous materials are then determined from generic approximate but robust models and compared to standing wave tube measurements. With no adjustable constant, the predicted quantities were found to be in acceptable agreement with multi-scale experimental data, and further analyzed in light of scanning electron micrograph observations and critical path considerations.

Three-dimensional reconstruction of a random fibrous medium: Geometry, transport, and sound absorbing properties

“…As in our previous paper, 14 Stokes flow, potential flow, and heat conduction in the generated fiber webs were simulated using a finite element (FEM) scheme. 14 In the context of diffusion-controlled processes, u pr ð Þ is a scaled concentration field and is defined as the rate of diffusion of the diffusing species divided by the diffusion coefficient of the reactive particles.…”

“…14 In the context of diffusion-controlled processes, u pr ð Þ is a scaled concentration field and is defined as the rate of diffusion of the diffusing species divided by the diffusion coefficient of the reactive particles. For thermal diffusion, u pr ð Þ is a "temperature field", defined as the ratio of the time derivative of the acoustic pressure over the thermal conductivity of the solid frame.…”

A semi-phenomenological model to predict the acoustic behavior of fully and partially reticulated polyurethane foams

“…25. This limits the analysis to PU foam with a log-normal and sharply peaked distribution of the mean strut length 11 and thus justifies the use of the idealized isotropic cell shape shown in Fig. 1.…”

“…[7][8][9][10][11] A detailed description of these approaches has been recently given by a) the authors. 12 A combination of empirical and analytical methods was also presented in Ref.…”

“…The inverse method is based on measurements of macroscopic non-acoustic properties (e.g., porosity, airflow resistivity…) coupled to calculations from the three aforementioned micro-/macro models; i.e., empirical, analytical, or numerical models. 11 This latter method provides an effective representative unit-cell that captures the complex microstructure of the porous aggregate being isotropic or anisotropic, fully or partially reticulated. However, this representative unit-cell is not real and its characteristic properties depend on the model used for the inversion.…”