Multi-modal Acoustic Power Characterisation of Ducted Elements

Methods and guidelines for acoustic source power characterization of elements in circular ducts with flow are presented. Acoustic pressure measured by microphones is used as source data for this study conducted above plane wave propagation. Thus, a multi modal approach is considered including azimuthal and radial modes for forward and backward directions. These in-duct propagating modes are decomposed from the acoustic pressure field with the matrix of modes evaluated at the positions of the microphones for the entire frequency range considered. Mode amplitudes are then obtained by inversing this matrix and used to obtain acoustic power of propagating modes. Because of the non-intrusiveness constraint, the conditioning of the microphone-mode matrix can be bad. It is minimized by optimizing microphone positions with a Genetic Algorithm (GA). Satisfactory results are obtained for the entire frequency range considered. To validate the modal decomposition, an analytic model is developed. Straight cylindrical ducts closed with a rigid wall on an end and porous materials on the other modelized with a Johnson-Champoux-Allard (JCA) model are considered. Between both extremities, a plane acoustic source is placed on the duct and further a measurement section with the optimised positions of microphones. Amplitudes of propagating modes are calculated in the air domain and compared to the ones calculated from acoustic pressure measurement on a test-bench. A parametric study is conducted to evaluate the impact of the uncertainty induced by the measurement chain but also from the turbulent boundary layer noise with a Corcos model on the modal acoustic power. The acoustic power for each propagating mode in an infinite and rigid cylindrical duct is calculated from synthesized data with and without perturbation. The study shows that the measurement chain uncertainty has small impact on the calculated acoustic power. A denoising method based on pressure correlation is also included in the parametric study.