A time-harmonic/time-domain hybrid approach based on displacement-based formulations to compute the absorbing coefficient in alpha cabins

The absorption coefficient of a porous sample is usually measured in an alpha cabin, where the operational frequency range is limited, and the absorbent sample size is typically small. Those characteristics are well adapted to the requirements of automotive acoustics but far from the standard reverberant chambers used in building acoustics, ensuring the conditions to perform measurements under a diffusive field. Since there are no standard norms to measure the absorption coefficient under non-diffusive fields, this work proposes a time-harmonic/time-domain hybrid approach to compute the absorption coefficient in alpha cabins. For this purpose, pointwise numerical predictions of the sound pressure level decay rate are used to calculate the absorption coefficient associated with a porous sample. To generate the pressure field acting inside the alpha cabin and, subsequently, approximate its decay rate, time-harmonic numerical simulations at a fixed frequency and a full time-dependent discretization of the wave problem have been considered. The proposed methodology is validated in a manufactured scenario where the exact solution is known in closed form. Finally, a realistic three-dimensional alpha cabin is deemed to predict the diffuse field absorption coefficient from the computed reverberation times using the proposed hybrid approach and the heuristic Sabine and Millington formulas.