Airflow resistivity of models of fibrous acoustic materials

Abstract

A new way of calculating the airflow resistivity of randomly placed parallel cylinders is presented. The calculation is based on Voronoi polygons, and the resistivity is given by the mean spacing between the fibers, their diameters, and the physical properties of air. New explicit formulas for the resistivity are given, which are valid for the cylinder ͑fiber͒ concentrations found in acoustic materials. A one-dimensional model consisting of parallel plates with random spacing between the plates is first discussed. Then a two-dimensional model consisting of parallel cylinders randomly spaced is treated for flow parallel and perpendicular to the cylinders. The resistivity formulas are exact for plates and approximate for cylinders.

Calculation of the dynamic air flow resistivity of fiber materials

“…They gave results close to each other, but the Brinkman procedure is simpler to implement on a personal computer; it requires only a few lines of program in a high level mathematical program such as MATLAB. The accuracy of Brinkman's procedure is estimated to be of the order of 10% for fiber densities normally used in materials for acoustics; this was based on the calculations in this paper and Tarnow 13 and Sangani and Yao. …”

“…This is in accordance with the low-frequency value found in the present paper and the values calculated in Tarnow. 13 One can show that in the low-frequency limit, R Ќ Ј Ϸ2R ʈ Ј follows from Eqs. ͑25͒ and ͑56͒.…”

“…This argument comes from a paper by Kuwabara 16 on dc flow. The same assumption was used in Tarnow 13 for calculation of the dc flow resistivity. It was shown that it gave reasonable results.…”

“…This procedure has in the case of dc flow been compared with other methods of computing the resistivity, and it was found that it yielded reliable results. 13 In order to check the accuracy of the cell approximations, the resistivity was also computed by a self-consistent procedure, which is similar to the calculation of the dc resistivity by Brinkman's approximation. 15 …”

Measured anisotropic air flow resistivity and sound attenuation of glass wool

“…Alternatively, one could assume that the fibers all have the same diameter and are parallel but placed randomly. In this case it is shown in a paper by the author 8 that the resistivity R Ќ for flow perpendicular to fibers is…”