Prediction of airflow resistivity of fibrous acoustical media having two 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 prediction results with AFR measurements of single-component fiber samples, a model of Tarnow's was shown to yield reasonable and accurate predictions 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 two-component fibrous media with uniform radii (TCUR). It was then further modified by adding the effect of fiber radii distributions to the TCUR models and making it capable of predicting the AFR for two-component fibrous media with various radii (TCVR). The TCVR model AFR prediction accuracy was verified first by comparing predictions and measurements on different two-component fiber samples having unknown fiber size distribution. Excellent agreement was obtained by adjusting the fiber size distribution in the models. A second, more rigorous test, involved predicting the AFR of a material based on a measured fiber size distribution. Again, excellent agreement was found.