Numerical Study of the Boundary Slip Effect on the Sound Absorption Performance of the Helmholtz Resonator

The Helmholtz resonator is one of the most important acoustic devices in the field of acoustic applications. It is believed that the boundary conditions in the resonator cavity are a vital factor to the sound absorption performance of the Helmholtz resonator. It should be noted that almost all the previous works on the topic assumed the no-slip boundary conditions in cavity. Recently, researchers found that the slip velocity on the surface of the fiber material results in a decrease in the attenuation coefficient and an increase in the sound velocity in predicting the acoustic properties of porous materials. However, the effect of the slip boundary condition on the sound absorption of Helmholtz resonator has not been tested up to now in the available literature. Therefore, numerical study on the sound absorption of Helmholtz resonator with slip boundary condition on its cavity is carried out via the lattice Boltzmann method. The slip length of the slip boundary condition under different inlet wave frequency and different inlet wave velocity profile effect on the sound absorption performance is studied in this work. Pout/Pin is adopted to represent the sound absorption performance. The numerical results show that the Pout/Pin decrease from 0.055 to 0.047 with the slip length increases from -1.00 to 1.00 and the change is more obvious in the range of -1.00 to -0.50 for the case of the constant inlet wave frequency and zero inlet velocity profile. The results also show the Pout/Pin increases from 0.01 to 0.16 as the inlet wave length decreases from 1.00 to 3.00 and the change is more obvious in the range from 2.00 to 3.00 when the slip length of the boundary condition is constant and the wave velocity profile is zero.

I. Introduction

The Helmholtz resonator is one of the most important acoustic devices in the field of acoustic applications. A fast-moving car with its windows open can make noise and this phenomenon is analogous to air blowing past a cavity, resulting in resonance. Such is an example of a Helmholtz resonator at work. Resonance from a Helmholtz resonator can be designed to help reduce some of the unwanted noise.