Determination of end correction of Helmholtz resonator based on numerical simulation Free

Numerical simulation of acoustic processes in the single Helmholtz resonators is one of the ways to study the problems connecting with the noise suppression in aircraft engine by sound-absorbing liner. In the study the liner samples was a single Helmholtz resonator of circular shape with different porosity. An estimate of the resonance frequency of the samples was performed at sound pressure levels 110 dB, depending on the values of the end corrections. It was compared the experimental results obtained with a normal incidence impedance tube, semi-empirical models with different values of the end correction, and numerical simulation results. Numerical simulation was conducted based on the linearized Navier-Stokes equations that describe well the imaginary part of the sample impedance, regardless of the sound pressure level. These equations were solved in axisymmetric formulation by finite element method. As a result, a functional dependence of the end correction has been obtained, which makes it possible to determine the resonance frequency with a smaller error. A good coincidence of the resonance frequencies demonstrates that the obtained dependence is more accurate than known empirical and semi-empirical relationships.