Sound absorption prediction of linear damped acoustic resonators using a lightweight hybrid model

Abstract

A lightweight numerical method is developed to predict the sound absorption coefficient of resonators whose cross-section dimensions are significantly larger compared to the viscous and thermal boundary layer’s thicknesses. This method is based on the boundary layer theory and on the perturbations theory. According to the perturbations theory, in acoustical domains with large dimensions, the fluid viscosity and thermal conductivity only affect the boundary layers. The model proposed in this article combines the lossless Helmholtz wave equation derived from a perfect fluid hypothesis, with viscosity and thermal conductivity values of a real fluid to compute the sound dissipation of geometrical acoustical attenuators (e.g. resonators). It is therefore referred to as a “Hybrid model”. This model is computationally very efficient with regard to visco-thermal models such as the FLNS (Full Linearized Navier-Stokes) model. It remains valid and efficient in a wide range of geometries even when reduced models such as the LRF (Low Reduced Frequency) model cannot be applied. The performances of the Hybrid model was tested on several differently shaped acoustical absorbers based on quarter-wave resonators. The Hybrid model results have been compared with experimental data and FLNS simulations and proved to be accurate and very efficient.