Calculation of the dynamic air flow resistivity of fiber materials

Abstract

The acoustic attenuation of acoustic fiber materials is mainly determined by the dynamic resistivity to an oscillating air flow. The dynamic resistance is calculated for a model with geometry close to the geometry of real fiber material. The model consists of parallel cylinders placed randomly. Two cases are treated: flow perpendicular to the cylinder axes, and flow parallel to the axes. In each case two new approximate procedures were used. In the first procedure, one solves the equation of flow in a Voronoi cell around the fiber, and averages over the distribution of the Voronoi cells. The second procedure is an extension to oscillating air flow of the Brinkman self-consistent procedure for dc flow. The procedures are valid for volume concentration of cylinders less than 0.1. The calculations show that for the density of fibers of interest for acoustic fiber materials the simple self-consistent procedure gives the same results as the more complicated procedure based on average over Voronoi cells. Graphs of the dynamic resistivity versus frequency are given for fiber densities and diameters typical for acoustic fiber materials.

Cell model calculations of dynamic drag parameters in packings of spheres

“…5 A cell model, with additional averaging over the distribution of the Voronoi cells, has been applied to calculations of the flow resistivity of fibrous materials. 6 In highly concentrated systems the applicability of the cell model approach becomes questionable. Neighboring solid particles will be in contact and hence will penetrate the hypothetical cell around each individual particle.…”

Application of evolution strategy algorithm for optimization of a single-layer sound absorber

“…The first two models are based on the assumption of cylindrical tubes, while the latter uses the theory of sound waves propagating via a set of cylinders with air passing through them. A common example for empirical models is the formulas introduced by Delany and Bazley (1970), while Phenomenological models are used by some authors (Allard & Daigle, 1994;Attenborough, 1982Attenborough, , 1983Biot, 1956;Champoux & Stinson, 1990Lafarge, Lemarinier, Allard, & Tarnow, 1997;Stinson, 1991;Wilson, 1997;Zwikker & Kosten, 1949) and various works are presented using Microstructure models (Attenborough & Walker, 1971;Dupère, Dowling, & Lu, 2004;Kawasima, 1960;Tarnow, 1996Tarnow, , 1997.…”

Fiber movements and sound attenuation in glass wool

“…The movement of the fibers can be taken care of by changing the boundary condition on the fibers, and repeating the calculation in the paper. 10 When this is done, one finds the forces f f on the fibers in a unit volume of glass wool,…”

“…In an earlier paper 10 by the author, the forces on the fibers from the air stream are computed when the fibers do not move. The movement of the fibers can be taken care of by changing the boundary condition on the fibers, and repeating the calculation in the paper.…”

“…R Ќ Ј is the dynamic resistivity of the fibers, which will be computed by the selfconsistent method of the paper in Ref. 10 When this is set into Eq. ͑10͒, one obtains…”