Finite element analysis on the surface characteristics of acoustic resonators with thermal and viscous boundary layers

摘要

The thermal and viscous boundary layers (TVBL) around a resonator's neck play important roles in the absorption, particularly when there is no porous material near the neck. This paper presents a simple implementation of a TVBL boundary condition for the three-dimensional finite element analysis of Helmholtz equation. The implementation is verified by comparing normal incidence absorption coefficients calculated and measured for slit-type resonators. Good agreement can be observed under the appropriate calculation setting. Subsequently, a detailed investigation is conducted on surface impedances of Helmholtz resonators composed of circular holes and square baffles. Numerical values are compared with analytical values based on the classical models such as Maa, Allard-Ingard and so on. It is demonstrated that the presented method convincingly captures the surface impedance on an acoustic resonator unless the TVBL thicknesses are much larger than the perforation diameter.