Prediction of Airflow Resistivity of Fibrous Acoustical Media having Double Fiber Components and a Distribution of Fiber Radii

Presented here is a new airflow resistivity (AFR) prediction model that accounts for situations in which a fibrous medium comprises more than one fiber component, and when the radius of each fiber component varies within a certain range. The study started with the evaluation of existing AFR models, which were mostly developed for single-component fibrous media with uniform radius (SCUR). After comparing the SCUR predictions results with AFR measurements of different single-component fiber samples, a model of Tarnow’s was shown to yield reasonable prediction accuracy and was chosen as the starting point for further development. The Tarnow model was first modified to make it capable of predicting the AFR for double-component fibrous media with uniform radii (DCUR). It was then further modified by adding the effect of fiber radius distributions to the DCUR models and making it capable of predicting the AFR for double-component fibrous media with various radii (DCVR). After adjusting the distribution parameters of both components, the DCVR model prediction results were verified by comparison with AFR measurements on different double-component fiber samples. It was found, for example, that the DCVR model prediction results were affected by the implicit differences in their starting points: i.e., the assumption as to whether the material consisted of pores (e.g., Doutres and Horoshenkov) or fibers (e.g., Tarnow)