Numerical Equivalent Acoustic Material for Air-Filled Porous Absorption Simulations in Finite Different Time Domain Methods: Design and Comparison

Abstract

Extracting the microscopic parameters of a porous material is a complex task, and attempts have been made to develop models that can simulate their characteristics, gathering the least amount of information possible. As a case in point, tests to evaluate macroscopic behaviors such as tortuosity, which depends directly on the microscopic fluid velocities, are highly susceptible to generate errors if the precision of the measurement devices is not correct, and the same goes for the other parameters. For this reason, in this paper, a sound propagation model in porous materials with a rigid frame is presented based on a local theory, which tries to simplify, even more, the way to obtain the basic characteristics of porous materials, such as their absorption coefficient at normal and random incidence, and their normal surface impedance. The proposed linearized equivalent fluid model presents four phenomenological coefficients, which characterize acoustic propagation trough the material. Their values are obtained from the material thickness and a measurement in an impedance tube following the ISO 10534 standard. Thus, what is only required is the measured absorption coefficient, either on one third or one octave bands, to fully represent the acoustic behavior in the finite different in time domain (FDTD) method. The model has been simulated with FDTD in porous and fibrous kernels, and the results show a strong agreement with the laboratory measurements and with the analytical results calculated with well-established semi-phenomenological models.