Calculation of the dynamic air flow resistivity of fiber materials

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.