# Research on the Impact of a Fluid Field on an Acoustic Field in Herschel-Quincke Tube
###### Abstract
[13] considered the acoustic scattering problem of an infinite tube covered with sound-absorbing materials and assumed that the waveguide is filled with the uniform mean flow. They derived non-reflective boundary conditions on artificial boundaries based on Dirichlet-to-Neumann (DtN) mapping using a modal decomposition method and demonstrated the effectiveness of the method through numerical validation. [PERSON] and [PERSON] [14] studied noise reduction in an HQ tube and established a numerical model to calculate acoustic characteristics using GT-POWER. Both the tube without flow and with mean flow were considered, while revealing the impact of the angle and the changes of the diameters during flow. [PERSON] et al. [15] proposed a multi-dimensional computational fluid dynamics (CFD) method to calculate the transfer matrix of the muffler. The absorptive material, heat transfer and mean flow effects were considered. Due to the simplicity of the simulation model and the low noise generated by the flow, the predicted noise was very consistent with the measured results. [PERSON] et al. studied the enhancement of HQ tube for adaptive ability. Due to the narrowband frequency associated with resonance in HQ waveguides, a variable cross-section was placed inside the waveguide to generate frequency shift in resonance. They mainly considered two devices: the first variable cross-section was a fixed-diameter ball that could move axially in the waveguide to obtain frequency shift by the ball position function; the second type of variable cross-section was composed of a fixed-position diaphragm, which obtained a variable cross-section through the deformation of the diaphragm, in which case, the frequency shift depended on the diaphragm deflection function. The internal acoustics and dynamics of these two devices were analyzed and experimentally studied, and the calculated and experimental results were compared and analyzed to verify the reliability of the model [16]. Recently, [PERSON] et al. [17] investigated the sound pressure amplification mechanism of acoustic metamaterials for ultra-low frequency sound attenuation and constructed an HQtube with q flexible side panel. A new peak in sound transmission loss (STL) in the system revealed the pressure amplification mechanism generated at the interface of the embedded panel. They also demonstrated through experiments the noise reduction effect of acoustic metamaterials on ultra-low frequency noise. [PERSON] et al. [18] studied the acoustic performance in an HQ tube, including sensitivity analysis and multi-objective optimization of design variables. A model utilizing the flow characteristics of HQ tubes was established, and a multi-objective genetic algorithm for the performance of HQ tubes was proposed. The variables were mainly designed to include frequency, temperature, area ratio, and the length of the tube. The final results indicated that the length of the bypass tube was a key factor in the sensitivity index of transmission loss, and also demonstrated the enormous potential of the proposed optimization algorithm in practical applications. [PERSON] et al. [19] processed sound propagation in the tube containing fluids and reduced computational time by reducing the size of finite elements in the model. For the tube with slowly changing cross-sections, local wave numbers are found through eigenvalue problems, and the amplitude changes between two points along the propagation axis are determined through energy conservation. [PERSON] [20] established a nonlinear physical model based on three meshless sub-models to understand the physical process of vortex sound interaction. The feedback effect of sound waves was considered, and the velocity of sound was added to the potential flow of vortex shedding. Simultaneously, the interaction between the flow field, sound field and their unsteady state was obtained and the simulation results were compared and analyzed with the experimental data. [PERSON] et al. [21] constructed a virtual HQ tube system using an acoustic metamaterial.