Identification of the full anisotropic flow resistivity tensor for multiple glass wool and melamine foam samples

The main purpose of this article is to present, within a unified framework, a technique based on numerical homogenization, to model the acoustical properties of real fibrous media from their geometrical characteristics and to compare numerical results with experimental data. The authors introduce a reconstruction procedure for a random fibrous medium and use it as a basis for the computation of its geometrical, transport, and sound absorbing properties. The previously ad hoc “fiber anisotropies” and “volume weighted average radii,” used to describe the experimental data on microstructure, are here measured using scanning electron microscopy. The authors show that these parameters, in conjunction with the bulk porosity, contribute to a precise description of the acoustical characteristics of fibrous absorbents. They also lead to an accurate prediction of transport parameters which can be used to predict acoustical properties. The computed values of the permeability and frequency-dependent sound absorption coefficient are successfully compared with permeability and impedance-tube measurements. The authors' results indicate the important effect of fiber orientation on flow properties associated with the different physical properties of fibrous materials. A direct link is provided between three-dimensional microstructure and the sound absorbing properties of non-woven fibrous materials, without the need for any empirical formulae or fitting parameters.

Section: Resultsmentioning

confidence: 99%

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

Luu

Perrot

Monchiet

et al. 2017

“…1). In a more general case, note that suitable methods can be found in 9,11,12 . Even if elastic parameters are not required by the TI equivalent model, these will be useful later (in Sec.…”

Section: A Materials Characterizationmentioning

confidence: 99%

“…The viscous dissipation effects depend of the air flow resistivity σ and of the viscous characteristic length Λ. It has been measured and shown theoretically [12][13][14]46,47 that the flow resistivity is larger in the stacking direction than in the in-plane direction. It is classical to express the air flow resistivity as a second-order tensor which is diagonal in the orthogonal basis of principal directions:…”

Section: Appendix A: Johnson-champoux-allard Modelmentioning

confidence: 99%

See 1 more Smart Citation

A transverse isotropic equivalent fluid model combining both limp and rigid frame behaviors for fibrous materials

Nennig

Binois

Dauchez

et al. 2018

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.

“…G€ oransson et al 26 proposed a methodology for the inverse estimation of the anisotropic flow resistivity through porous materials. This methodology was then refined by Van der Kelen and G€ oransson, 27 who applied it to identify the full anisotropic flow resistivity tensor of multiple glass wool and melamine foam samples.…”

Section: Introductionmentioning

confidence: 99%

Normalized inverse characterization of sound absorbing rigid porous media

Zieliński

2015

This paper presents a methodology for the inverse characterization of sound absorbing rigid porous media, based on standard measurements of the surface acoustic impedance of a porous sample. The model parameters need to be normalized to have a robust identification procedure which fits the model-predicted impedance curves with the measured ones. Such a normalization provides a substitute set of dimensionless (normalized) parameters unambiguously related to the original model parameters. Moreover, two scaling frequencies are introduced, however, they are not additional parameters and for different, yet reasonable, assumptions of their values, the identification procedure should eventually lead to the same solution. The proposed identification technique uses measured and computed impedance curves for a porous sample not only in the standard configuration, that is, set to the rigid termination piston in an impedance tube, but also with air gaps of known thicknesses between the sample and the piston. Therefore, all necessary analytical formulas for sound propagation in double-layered media are provided. The methodology is illustrated by one numerical test and by two examples based on the experimental measurements of the acoustic impedance and absorption of porous ceramic samples of different thicknesses and a sample of polyurethane foam.