NONWOVENS NEXT TOP MODEL?

1 INTRODUCTION
Material parameter inversion is a very powerful tool for the acoustic characterisation of a range of
materials. It allows for a wide collection of properties to be calculated from a single rapid acoustic
measurement with a high degree of accuracy, and can be especially useful for determining the values
of parameters that are otherwise difcult or time-consuming to measure. Above and beyond this.
acoustic characterisation also allows for some scope into the design and optimization of materials for
noise control. By allowing for the understanding of properties such as airflow resistivity. porosity. and
tortuosity. one can tailor these properties to maximize the absorption efciency without needing to
spend time or money on the synthesis and prototyping of material samples. There are a wide range
of models currently in use that deal with nonwoven media. including commonly utilized methods such
as the Bies-Hansen model1 and the Kozeny♥Carman model☜. as well as the Miki model☁. This paper
studies the application of these models to the inversion of a variety of different nonwoven samples
from acoustic impedance data. so that the key non-acoustical parameters can be related to the
material properties.
Acoustic characterisation. performed via a two-microphone sound impedance tube. is a method for
rapidly obtaining data on the acoustic absorbance and surface impedance of a material. There are
numerous models. both old and new. that can utilise this data for the calculation of other material
properties -such asporosity. tortuosity. airflow resistivity. and vice versa.
Airow resistivity is a parameter that is known to have a considerable impact of the acoustic
performance of a material. but in spite of this it can also be difcult to measure. Modelling the value
of airow resistivity can be favourable due to the time - where modelling takes seconds as opposed
to minutes. and range of equipment required to measure airflow resistivity independently.
2 MODEL INTRODUCTION
2.1 Kozeny-Carman Model
The Kozeny-Carrnan equation☜ was developed in the 19305 and was used to relate porosity
(typically of granular media). 4:. particle size. at. and ow resistivity. 0'. according to Equation 1 below:
a = -♥♥180"d(21¢_3¢)2 ☂(1)
where u is the dynamic viscosity. derived from Poiseuille☁s equation for laminar ow of a liquid, and
given a constant value of 1.81x1t2r5 for these calculations. In this experiment. d was set to the bre
diameter. d,. assuming d E d,. Porosity was calculated from the ratio of bulk material density. pm. to
the bre density, pf. in accordance with the equation ¢ = 1 ♥ 9♥". .
This model has a physical basis and is hailed as being able to accurately estimate the ow resistivity
♥ typically of polymer bres. from the bre density and diameter data