Acoustic modelling of polydisperse vegetal wools: evaluation of analytic methods based on fibre radius distribution measurement

Vegetal wools are highly porous materials made of vegetal fibres and bicomponent polymer fibres. Despite their high-level multifunctional properties, they suffer from poor low-frequency acoustic absorption for thin panels. In order to lay the foundations for optimisation, it is essential to use models with the porosity, an effective radius, and the mass ratio between fibre types as inputs.However, unlike more conventional materials, vegetal wools don’t have calibrated fibres. Not only are these fibres not cylindrical, but they also exhibit high radius polydispersity, that can be described through a probability distribution. This work aims at determining the best way to measure these radius probability distributions and to calculate the most suitable effective radii to use in these models.A measurement protocol is established to obtain these distributions for six vegetal wools, by observing them transversally through a scanning electronic microscope and approximating their profile to ellipses. Four averaging methods are investigated to determine an effective radius. Three analytical models simulate the visco-inertial and thermal effects of the wools : Tarnow-Brinkman, Umnova-JCAL and Piégay models. To calculate the sound absorption, a direct approach using one effective radius and a composite approach using two effective radius discriminating fibre types in a wool are compared. In total, 18 different methods to simulate the sound absorption and other parameters are evaluated and compared to acoustic measurements of the wools, giving us the most precise analytical estimations.This analysis concludes that, to calculate the static airflow resistivity, using Tarnow's model in direct or composite approach with an arithmetic or quadratic average as effective radius is best. The two characteristic lengths are best estimated with Umnova's model and an inverse volume weighted average radius. For sound absorption, the best approach are Umnova-JCAL in direct or composite approach, and Piégay in composite approach with an arithmetic average radius.