Numerical Simulation of the Measurement of the Diffuse Field Absorption Coefficient in Small Reverberation Rooms 2011-01-1641

The Diffuse Field Absorption Coefficient (DFAC) is a physical quantity very often used in the automotive industry to assess the performance of sound absorbing multilayers. From a theoretical standpoint, such quantity is defined under rather ideal conditions: the multilayer is assumed to be infinite in extent and the exciting acoustic field is assumed to be perfectly diffuse. From a practical standpoint, in the automotive industry the DFAC is generally measured on samples having a relatively small size (of the order of 1m2) and using relatively small cabins (in the order of 6-7 m₃). It is well known that both these factors (the finite size of the sample and the small volume of the cabin) can have an influence on the results of the measurements, generating deviations from the theoretical DFAC.

The widely used Transfer Matrix Method (TMM) allows the evaluation of the theoretical DFAC and can, in some implementations, approximately take into account the finite size of the sample by means of a suitable analytical correction. Within this method, though, the exciting acoustic field is always assumed to be ideally diffused or, in any case, given by the superposition of a set of uncorrelated plane waves impinging on the sample with incident angles within a certain predefined range.

This paper intends to present numerical investigations that allow going beyond this modeling technique.

In a first part of the paper, this is done using an analytical model consisting of a rectangular cavity having the dimensions of a small cabin. The reverberation time of this cavity is evaluated with and without an absorbing sample placed on its floor and, from these data, the corresponding DFAC is calculated using Sabine's law. Results from this model are presented and compared with results coming from testing. Using this analytical model, it is already possible not only to evaluate the effect of the finite size of the sample, but also the effect of its positioning on the cavity's floor and, more importantly, the effect of the limited volume of the measurement environment. Both these latter effects cannot be taken into account in any way by means of the TMM.

In the second part of the paper, a further degree of complexity is added: the same type of simulations are carried out by means of a finite element model of the widely used Alpha Cabin (whose volume is about 6.5 m₃), coupled to a finite element model of the absorbing sample. Also in this case, simulation results are compared to results coming from testing. The use of a finite element model allows taking into account also the effect of the diffraction around the sample's edges. Also this effect is known to have, in special cases, some influence on the results of DFAC measurements and, of course, cannot be taken into account within the analytical model based on a rectangular cavity.